Mathematics Test JSS 1

1) 7-4=

3

12

4

5

The correct answer is 3 because when you subtract 4 from 7, you are left with a difference of 3.

Explanation

The correct answer is 3 because when you subtract 4 from 7, you are left with a difference of 3.

2)

Type the missing number : -4,-3,-2,-1,0,1__,3,4

2

3

6

8

The given sequence is a series of consecutive numbers. Starting from -4, each subsequent number increases by 1. Therefore, the missing number is 2, as it is the next number in the sequence after 1.

Explanation

The given sequence is a series of consecutive numbers. Starting from -4, each subsequent number increases by 1. Therefore, the missing number is 2, as it is the next number in the sequence after 1.

3) A polygon with exactly three sides

Triangle

Quadrilateral

Hexagon

Pentagon

A triangle is a polygon with exactly three sides. It is the only option among the given choices that satisfies this condition. A quadrilateral has four sides, a hexagon has six sides, and a pentagon has five sides, which do not match the given condition. Therefore, the correct answer is triangle.

Explanation

A triangle is a polygon with exactly three sides. It is the only option among the given choices that satisfies this condition. A quadrilateral has four sides, a hexagon has six sides, and a pentagon has five sides, which do not match the given condition. Therefore, the correct answer is triangle.

4) A polygon with exactly nine sides.

Dodecagon

Octagon

Nonagon

Heptagon

A nonagon is a polygon with exactly nine sides.

Explanation

A nonagon is a polygon with exactly nine sides.

5) An angle that measures exactly 90 degrees.

Acute angle

Right angle

Obtuse angle

Straight angle

A right angle is a type of angle that measures exactly 90 degrees. It is formed when two lines intersect and create a square corner. In a right angle, one of the lines is perpendicular to the other. This type of angle is commonly found in geometric shapes such as squares and rectangles. It is called a "right" angle because it is considered to be the "correct" angle or the most balanced angle.

Explanation

A right angle is a type of angle that measures exactly 90 degrees. It is formed when two lines intersect and create a square corner. In a right angle, one of the lines is perpendicular to the other. This type of angle is commonly found in geometric shapes such as squares and rectangles. It is called a "right" angle because it is considered to be the "correct" angle or the most balanced angle.

6) A polygon with exactly five sides.

Octagon

Quadrilateral

Hexagon

Pentagon

A polygon with exactly five sides is called a pentagon. The term "pent" in pentagon refers to the number five. It is a closed figure with five straight sides and five angles. The other options mentioned in the question, such as octagon, quadrilateral, and hexagon, have different numbers of sides and therefore do not meet the criteria of a polygon with exactly five sides.

Explanation

A polygon with exactly five sides is called a pentagon. The term "pent" in pentagon refers to the number five. It is a closed figure with five straight sides and five angles. The other options mentioned in the question, such as octagon, quadrilateral, and hexagon, have different numbers of sides and therefore do not meet the criteria of a polygon with exactly five sides.

7) A polygon with exactly seven sides.

Heptagon

Nonagon

Decagon

Dodecagon

A polygon with exactly seven sides is called a heptagon.

Explanation

A polygon with exactly seven sides is called a heptagon.

8) What is 4³?

64

16

4

20

not-available-via-ai

Explanation

not-available-via-ai

9) Does the point(7, 1) satisfy the equation y = x – 6?

No

Yes

The point (7, 1) satisfies the equation y = x - 6 because when we substitute x = 7 into the equation, we get y = 7 - 6 = 1. Hence, the statement "yes" is the correct answer.

Explanation

The point (7, 1) satisfies the equation y = x - 6 because when we substitute x = 7 into the equation, we get y = 7 - 6 = 1. Hence, the statement "yes" is the correct answer.

10) Coplanar lines that do not meet?

Parallel lines

Intersecting lines

Perpendicular lines

Skew lines

Parallel lines are coplanar lines that do not meet or intersect at any point. They are always equidistant from each other and have the same slope. This means that they will never cross paths and will continue in the same direction indefinitely. Examples of parallel lines include railroad tracks or the sides of a rectangle.

Explanation

Parallel lines are coplanar lines that do not meet or intersect at any point. They are always equidistant from each other and have the same slope. This means that they will never cross paths and will continue in the same direction indefinitely. Examples of parallel lines include railroad tracks or the sides of a rectangle.

11) ^{What do you call an angle whose measure is 90° ?}

Right Angle

Acute Angle

Supplementary Angle

Adjacent Angle

A right angle is defined as an angle that measures exactly 90 degrees. It is formed when two lines intersect each other perpendicularly, creating four equal 90-degree angles. The term "right" in right angle refers to the fact that it is the correct or proper angle that forms a perfect L-shape. This angle is commonly found in geometric shapes such as squares and rectangles, where it helps determine the perpendicularity of sides.

Explanation

A right angle is defined as an angle that measures exactly 90 degrees. It is formed when two lines intersect each other perpendicularly, creating four equal 90-degree angles. The term "right" in right angle refers to the fact that it is the correct or proper angle that forms a perfect L-shape. This angle is commonly found in geometric shapes such as squares and rectangles, where it helps determine the perpendicularity of sides.

12) An angle that measures less than 90 degrees.

Acute angle

Right angle

Obtuse angle

Straight angle

An acute angle is an angle that measures less than 90 degrees. It is one of the basic types of angles in geometry, distinguishing itself by being smaller than a right angle (which measures exactly 90 degrees). Acute angles are found in various geometric shapes and are a fundamental concept in understanding angle relationships and properties within different polygons and constructions.

Explanation

An acute angle is an angle that measures less than 90 degrees. It is one of the basic types of angles in geometry, distinguishing itself by being smaller than a right angle (which measures exactly 90 degrees). Acute angles are found in various geometric shapes and are a fundamental concept in understanding angle relationships and properties within different polygons and constructions.

13) An angle measures less than 90 degrees.

Acute angle

Adjacent angle

Obtuse ngle

Right angle

An angle that measures less than 90 degrees is called an acute angle. Acute angles are smaller than a right angle and do not exceed 90 degrees. They are commonly found in everyday objects and shapes, such as the corners of a triangle or the hands of a clock at certain times. Unlike obtuse angles, acute angles are considered to be sharp or narrow.

Explanation

An angle that measures less than 90 degrees is called an acute angle. Acute angles are smaller than a right angle and do not exceed 90 degrees. They are commonly found in everyday objects and shapes, such as the corners of a triangle or the hands of a clock at certain times. Unlike obtuse angles, acute angles are considered to be sharp or narrow.

14) 8+5=

12

13

11

14

The correct answer is 13 because when you add 8 and 5 together, you get a sum of 13.

Explanation

The correct answer is 13 because when you add 8 and 5 together, you get a sum of 13.

15) An angle that measures more than 90 degrees but less than 180 degrees.

Acute angle

Right angle

Obtuse angle

Straight angle

An obtuse angle is formed when two lines or sides meet at a point and the angle between them measures more than 90 degrees but less than 180 degrees. It is wider or "obtuse" than a right angle but not as wide as a straight angle.

Explanation

An obtuse angle is formed when two lines or sides meet at a point and the angle between them measures more than 90 degrees but less than 180 degrees. It is wider or "obtuse" than a right angle but not as wide as a straight angle.

16) The formula for the area of square is A=(s)*(s)

True

False

The formula for the area of a square is given by multiplying the length of one side (s) by itself. This can be derived from the fact that a square has all sides equal in length, so multiplying any side by itself will give the area of the square. Therefore, the statement "The formula for the area of a square is A=(s)*(s)" is true.

Explanation

The formula for the area of a square is given by multiplying the length of one side (s) by itself. This can be derived from the fact that a square has all sides equal in length, so multiplying any side by itself will give the area of the square. Therefore, the statement "The formula for the area of a square is A=(s)*(s)" is true.

17) A polygon with exactly four sides.

Triangle

Quadrilateral

Pentagon

Hexagon

A polygon is a closed figure with straight sides. A triangle has three sides, a pentagon has five sides, and a hexagon has six sides. A quadrilateral, on the other hand, has exactly four sides, which makes it the correct answer.

Explanation

A polygon is a closed figure with straight sides. A triangle has three sides, a pentagon has five sides, and a hexagon has six sides. A quadrilateral, on the other hand, has exactly four sides, which makes it the correct answer.

18) An angle that measures exactly 180 degrees.

Acute angle

Right angle

Obtuse angle

Straight angle

A straight angle is formed when two lines are opposite and form a straight line, measuring exactly 180 degrees. It is the largest possible angle, and all of its interior angles are equal to 180 degrees.

Explanation

A straight angle is formed when two lines are opposite and form a straight line, measuring exactly 180 degrees. It is the largest possible angle, and all of its interior angles are equal to 180 degrees.

19) A polygon with exactly six sides

Octagon

Quadrilateral

Hexagon

Pentagon

A polygon with exactly six sides is called a hexagon.

Explanation

A polygon with exactly six sides is called a hexagon.

20) (-6-4)+6

4

-3

-4

8

To solve the given expression, we need to follow the order of operations, which states that we should perform any calculations inside parentheses first. In this case, there are no parentheses, so we move on to the next step, which is to perform any additions or subtractions from left to right. We start with -6 minus 4, which equals -10. Then, we add 6 to -10, resulting in -4. Therefore, the correct answer is -4.

Explanation

To solve the given expression, we need to follow the order of operations, which states that we should perform any calculations inside parentheses first. In this case, there are no parentheses, so we move on to the next step, which is to perform any additions or subtractions from left to right. We start with -6 minus 4, which equals -10. Then, we add 6 to -10, resulting in -4. Therefore, the correct answer is -4.

21) What is the percentage of 3/20 ?

15 %

34 %

3 %

20 %

The percentage of 3/20 is 15%. This can be calculated by dividing 3 by 20 and then multiplying the result by 100. In this case, 3 divided by 20 equals 0.15, and when multiplied by 100, it becomes 15%.

Explanation

The percentage of 3/20 is 15%. This can be calculated by dividing 3 by 20 and then multiplying the result by 100. In this case, 3 divided by 20 equals 0.15, and when multiplied by 100, it becomes 15%.

22) It describes an exact location in space.

Point

Line

Plane

Angle

A point is a fundamental concept in geometry that represents an exact location in space. It has no size or dimensions, and is often represented by a dot. A point is used to define the position of other geometric objects, such as lines, planes, and angles. It is the most basic element in geometry and serves as a building block for more complex shapes and figures.

Explanation

A point is a fundamental concept in geometry that represents an exact location in space. It has no size or dimensions, and is often represented by a dot. A point is used to define the position of other geometric objects, such as lines, planes, and angles. It is the most basic element in geometry and serves as a building block for more complex shapes and figures.

23) A polygon with exactly twelve sides

Heptagon

Nonagon

Decagon

Dodecagon

A polygon with exactly twelve sides is called a dodecagon.

Explanation

A polygon with exactly twelve sides is called a dodecagon.

24)

What is the length of the hypotenuse , if the length is 3km and the base is 4 km .

5 km

20 km

30 km

40 km

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). In this case:

Leg 1 = 3 km

Leg 2 (base) = 4 km

Applying the Pythagorean theorem:

Hypotenuse^2 = Leg 1^2 + Leg 2^2 Hypotenuse^2 = 3^2 + 4^2 Hypotenuse^2 = 9 + 16 Hypotenuse^2 = 25 Hypotenuse = √25 = 5 km

Therefore, the length of the hypotenuse is 5 km.

Explanation

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). In this case:

Leg 1 = 3 km

Leg 2 (base) = 4 km

Applying the Pythagorean theorem:

Hypotenuse^2 = Leg 1^2 + Leg 2^2 Hypotenuse^2 = 3^2 + 4^2 Hypotenuse^2 = 9 + 16 Hypotenuse^2 = 25 Hypotenuse = √25 = 5 km

Therefore, the length of the hypotenuse is 5 km.

25) (5+4+2)-8

-3

3

19

-2

The given expression (5+4+2)-8 simplifies to 11-8, which equals 3. Therefore, the correct answer is 3.

Explanation

The given expression (5+4+2)-8 simplifies to 11-8, which equals 3. Therefore, the correct answer is 3.

26) Part of a line that has two endpoints.

Point

Line

Line segment

Plane

A line segment is a part of a line that has two distinct endpoints. It is a finite portion of a line, with a definite length. Unlike a line, which extends infinitely in both directions, a line segment has a specific starting and ending point. Therefore, a line segment is the correct answer as it fits the given description of having two endpoints.

Explanation

A line segment is a part of a line that has two distinct endpoints. It is a finite portion of a line, with a definite length. Unlike a line, which extends infinitely in both directions, a line segment has a specific starting and ending point. Therefore, a line segment is the correct answer as it fits the given description of having two endpoints.

27) Calculate: (-8) + (+2) - (-6) = ?

16

0

4

3

The given expression involves adding a negative number (-8) and a positive number (+2), which results in a negative number (-6). Then, subtracting a negative number (-6) is equivalent to adding its positive counterpart (+6). Therefore, the final calculation is -6 + 6 = 0.

Explanation

The given expression involves adding a negative number (-8) and a positive number (+2), which results in a negative number (-6). Then, subtracting a negative number (-6) is equivalent to adding its positive counterpart (+6). Therefore, the final calculation is -6 + 6 = 0.

28) -6-4=

-2

-10

10

2

The given expression is a subtraction problem. To solve it, we subtract 4 from -6. When subtracting a positive number from a negative number, we add the absolute values and keep the sign of the larger number. In this case, the absolute value of -6 is 6, and the absolute value of 4 is 4. Adding them gives us 10. Since -6 is the larger number and it is negative, the answer is -10.

Explanation

The given expression is a subtraction problem. To solve it, we subtract 4 from -6. When subtracting a positive number from a negative number, we add the absolute values and keep the sign of the larger number. In this case, the absolute value of -6 is 6, and the absolute value of 4 is 4. Adding them gives us 10. Since -6 is the larger number and it is negative, the answer is -10.

29) -18-5=

23

-23

-13

13

The correct answer is -23. To solve this equation, we subtract 5 from -18. When we subtract a positive number from a negative number, the result becomes more negative. Therefore, -18 - 5 equals -23.

Explanation

The correct answer is -23. To solve this equation, we subtract 5 from -18. When we subtract a positive number from a negative number, the result becomes more negative. Therefore, -18 - 5 equals -23.

30) (-8-3)+5

6

-6

13

-10

The given expression (-8-3)+5 can be simplified by first performing the subtraction inside the parentheses, which gives (-11)+5. Then, adding -11 and 5 gives -6 as the final answer.

Explanation

The given expression (-8-3)+5 can be simplified by first performing the subtraction inside the parentheses, which gives (-11)+5. Then, adding -11 and 5 gives -6 as the final answer.

31) (8-4)-9=

-5

5

3

-4

The given expression is (8-4)-9. First, we solve the subtraction inside the parentheses: 8-4 = 4. Then, we subtract 9 from 4, which gives us -5. Therefore, the correct answer is -5.

Explanation

The given expression is (8-4)-9. First, we solve the subtraction inside the parentheses: 8-4 = 4. Then, we subtract 9 from 4, which gives us -5. Therefore, the correct answer is -5.

32) Evaluate:4! =

34

14

24

240

The expression "4!" represents the factorial of 4, which is calculated by multiplying 4 by all the positive integers less than it. In this case, 4! = 4 x 3 x 2 x 1 = 24.

Explanation

The expression "4!" represents the factorial of 4, which is calculated by multiplying 4 by all the positive integers less than it. In this case, 4! = 4 x 3 x 2 x 1 = 24.

33) A cookie factory produced 803 packages of cookies. There were 82 cookies in each package. About how many cookies did the factory produce in all? Choose the better estimate.

65846

65879

65864

6789

The correct answer is 65846. To estimate the number of cookies produced, we can multiply the number of packages (803) by the number of cookies in each package (82). So, 803 * 82 = 65846.

Explanation

The correct answer is 65846. To estimate the number of cookies produced, we can multiply the number of packages (803) by the number of cookies in each package (82). So, 803 * 82 = 65846.

34) A miniature golf course recently provided its customers with 12 golf balls, of which 4 were orange. Based on experimental probability, how many of the next 18 golf balls handed out should you expect to be orange golf balls?

6

5

7

8

Based on experimental probability, if 4 out of 12 golf balls were orange, then the probability of getting an orange golf ball is 4/12. To find the expected number of orange golf balls out of the next 18, we multiply the probability by the number of balls: (4/12) * 18 = 6. Therefore, we should expect 6 of the next 18 golf balls handed out to be orange.

Explanation

Based on experimental probability, if 4 out of 12 golf balls were orange, then the probability of getting an orange golf ball is 4/12. To find the expected number of orange golf balls out of the next 18, we multiply the probability by the number of balls: (4/12) * 18 = 6. Therefore, we should expect 6 of the next 18 golf balls handed out to be orange.

35) _{How many lines can be drawn passing through a point?}

Only one

Only two

Infinite

None of the above

A point in space can be connected to any other point by a straight line, so there are infinite lines that can be drawn passing through a single point.

Explanation

A point in space can be connected to any other point by a straight line, so there are infinite lines that can be drawn passing through a single point.

36) It is a part of a line that has two endpoints?

Ray

Segment

Number line

Line segment

A line segment is a part of a line that has two endpoints. Unlike a ray, which extends infinitely in one direction, a line segment has a definite length and can be measured. A number line is a straight line that represents numbers in order, but it does not have endpoints. Therefore, the correct answer is line segment.

Explanation

A line segment is a part of a line that has two endpoints. Unlike a ray, which extends infinitely in one direction, a line segment has a definite length and can be measured. A number line is a straight line that represents numbers in order, but it does not have endpoints. Therefore, the correct answer is line segment.

37) -9+4=

-5

5

13

3

The given equation is -9 + 4. When we add -9 and 4, we get -5.

Explanation

The given equation is -9 + 4. When we add -9 and 4, we get -5.

38) What is the greatest common factor of 20 and 17?

1

340

2

10

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. In this case, the numbers given are 20 and 17. Since 1 is the only number that divides evenly into both 20 and 17, it is the GCF. Therefore, the correct answer is 1.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. In this case, the numbers given are 20 and 17. Since 1 is the only number that divides evenly into both 20 and 17, it is the GCF. Therefore, the correct answer is 1.

39) Jackie, a florist, is assembling bouquets of roses to sell at her flower shop. The number of bouquets she can assemble depends on how many roses are in her shop.b = the number of bouquets Jackie can assemble
r = the number of roses in the flower shop
Which of the variables is independent and which is dependent?

B is the independent variable and r is the dependent

R is the independent variable and b is the dependent variable

Both are dependent

Both are independent

In this scenario, the number of bouquets Jackie can assemble (b) depends on the number of roses in her flower shop (r). Therefore, the number of roses (r) is the independent variable, as it is the factor that determines the number of bouquets (b) she can assemble. On the other hand, the number of bouquets (b) is the dependent variable, as it is dependent on the number of roses (r) available.

Explanation

In this scenario, the number of bouquets Jackie can assemble (b) depends on the number of roses in her flower shop (r). Therefore, the number of roses (r) is the independent variable, as it is the factor that determines the number of bouquets (b) she can assemble. On the other hand, the number of bouquets (b) is the dependent variable, as it is dependent on the number of roses (r) available.

40) Two rays that both start from a common point and go off in exactly opposite directions

Infrared rays

Line

Opposite rays

Ray

Opposite rays are two rays that originate from the same point and extend in opposite directions, forming a straight line. These rays are also known as opposite or opposite direction rays. They are characterized by their common starting point and their paths moving in diametrically opposite directions. In this case, the given description perfectly matches the concept of opposite rays, making it the correct answer.

Explanation

Opposite rays are two rays that originate from the same point and extend in opposite directions, forming a straight line. These rays are also known as opposite or opposite direction rays. They are characterized by their common starting point and their paths moving in diametrically opposite directions. In this case, the given description perfectly matches the concept of opposite rays, making it the correct answer.

41) How would you label AB?

Line

Line Segment

Ray

Angle

AB would be labeled as a line segment because it is a portion of a line that has two endpoints, A and B. A line segment is a straight path that connects two points and has a definite length. In this case, AB represents a specific portion of a line, rather than the entire line itself.

Explanation

AB would be labeled as a line segment because it is a portion of a line that has two endpoints, A and B. A line segment is a straight path that connects two points and has a definite length. In this case, AB represents a specific portion of a line, rather than the entire line itself.

42) Which of the following is not a unit of volume?

Ha

Cubic inches

L

Cubic meter

not-available-via-ai

Explanation

not-available-via-ai

43) Lines that intersect at a right angle?

Skew line

Perpendicular line

Vertical line

Intersecting line

Perpendicular lines are the only lines that intersect at a right angle. When two lines are perpendicular, the angles formed at their intersection are always 90 degrees. This is a unique characteristic of perpendicular lines and distinguishes them from other types of lines such as skew, vertical, or intersecting lines. Skew lines do not intersect at all, vertical lines are parallel to each other, and intersecting lines can intersect at any angle other than 90 degrees. Therefore, the correct answer is perpendicular line.

Explanation

Perpendicular lines are the only lines that intersect at a right angle. When two lines are perpendicular, the angles formed at their intersection are always 90 degrees. This is a unique characteristic of perpendicular lines and distinguishes them from other types of lines such as skew, vertical, or intersecting lines. Skew lines do not intersect at all, vertical lines are parallel to each other, and intersecting lines can intersect at any angle other than 90 degrees. Therefore, the correct answer is perpendicular line.

44) A plane contains atleast three non-collinear points and space contains atleast four non-coplanar points.

True

False

A plane is a two-dimensional surface that extends infinitely in all directions. In order to define a plane, we need a minimum of three non-collinear points, meaning that the points cannot all lie on the same straight line. Similarly, space is a three-dimensional region that extends infinitely in all directions. To define space, we need a minimum of four non-coplanar points, meaning that the points cannot all lie on the same plane. Therefore, the statement is true as a plane requires at least three non-collinear points, and space requires at least four non-coplanar points.

Explanation

A plane is a two-dimensional surface that extends infinitely in all directions. In order to define a plane, we need a minimum of three non-collinear points, meaning that the points cannot all lie on the same straight line. Similarly, space is a three-dimensional region that extends infinitely in all directions. To define space, we need a minimum of four non-coplanar points, meaning that the points cannot all lie on the same plane. Therefore, the statement is true as a plane requires at least three non-collinear points, and space requires at least four non-coplanar points.

45) What do you call a data set presented in a tabular form?

Histogram

Sampling frame

Frequency distribution

Table of random numbers

A data set presented in a tabular form is called a frequency distribution. This type of data presentation organizes the data into categories or intervals and shows the frequency or count of observations within each category. It provides a clear summary of how the data is distributed and allows for easy analysis and interpretation.

Explanation

A data set presented in a tabular form is called a frequency distribution. This type of data presentation organizes the data into categories or intervals and shows the frequency or count of observations within each category. It provides a clear summary of how the data is distributed and allows for easy analysis and interpretation.

46) Two angles whose measures have a sum of 180 degrees

Complementary angle

Supplementary angle

Adjacent angle

Vertical angle

Two angles whose measures have a sum of 180 degrees are called supplementary angles. This is because when the measures of two angles add up to 180 degrees, they are said to be supplementary to each other.

Explanation

Two angles whose measures have a sum of 180 degrees are called supplementary angles. This is because when the measures of two angles add up to 180 degrees, they are said to be supplementary to each other.

47) -5+8=

13

3

-3

-13

The correct answer is 3 because when you subtract 5 from 8, you get a positive result of 3.

Explanation

The correct answer is 3 because when you subtract 5 from 8, you get a positive result of 3.

48) Which of the following statements is false?

All integers are rational.

All fractions are rational.

All repeating decimals are rational.

All terminating decimals are rational.

The statement "All fractions are rational" is false because there are fractions that are not rational, such as irrational numbers like π or √2. Rational numbers can be expressed as a ratio of two integers, whereas fractions like π cannot be written in the form of a ratio. Therefore, not all fractions are rational.

Explanation

The statement "All fractions are rational" is false because there are fractions that are not rational, such as irrational numbers like π or √2. Rational numbers can be expressed as a ratio of two integers, whereas fractions like π cannot be written in the form of a ratio. Therefore, not all fractions are rational.

49) This is formed by two rays with the same endpoint.

Rays

Angle

Line

Point

An angle is formed by two rays with the same endpoint. The rays are called the sides of the angle and the common endpoint is called the vertex. The angle is the space between the two rays, which can be measured in degrees. Angles are used to describe the amount of turn or rotation between two lines or surfaces. They are an important concept in geometry and are used in various fields such as engineering, architecture, and physics.

Explanation

An angle is formed by two rays with the same endpoint. The rays are called the sides of the angle and the common endpoint is called the vertex. The angle is the space between the two rays, which can be measured in degrees. Angles are used to describe the amount of turn or rotation between two lines or surfaces. They are an important concept in geometry and are used in various fields such as engineering, architecture, and physics.

50) The diffirence between mathematical equation to mathemetical expression is?

Inequality sign

Equal sign

Addition sign

Subtraction sugn

The difference between a mathematical equation and a mathematical expression lies in the presence of the equal sign. An equation includes an equal sign, indicating that two expressions are equal to each other. On the other hand, an expression does not have an equal sign and represents a mathematical statement without asserting equality.

Explanation

The difference between a mathematical equation and a mathematical expression lies in the presence of the equal sign. An equation includes an equal sign, indicating that two expressions are equal to each other. On the other hand, an expression does not have an equal sign and represents a mathematical statement without asserting equality.

51) Think of x as a real number. Which of the following numbers when added to x gives x?

0

1

-x

1/x

Adding 0 to any real number x will result in x. This is because the property of addition states that adding zero to a number does not change its value. Therefore, when 0 is added to x, the sum will always be x.

Explanation

Adding 0 to any real number x will result in x. This is because the property of addition states that adding zero to a number does not change its value. Therefore, when 0 is added to x, the sum will always be x.

52) An electric fan has a power rating of 65 W. If it is used for 3 hours, what is the electric consumption?

0.195 kWh

1.2 kWh

1.5 kWh

1.195 kWh

The electric consumption can be calculated by multiplying the power rating (65 W) by the time it is used (3 hours) and converting it to kilowatt-hours. So, 65 W x 3 hours = 195 Wh. Since 1 kilowatt-hour (kWh) is equal to 1000 watt-hours (Wh), we divide 195 Wh by 1000 to get the consumption in kWh, which is 0.195 kWh.

Explanation

The electric consumption can be calculated by multiplying the power rating (65 W) by the time it is used (3 hours) and converting it to kilowatt-hours. So, 65 W x 3 hours = 195 Wh. Since 1 kilowatt-hour (kWh) is equal to 1000 watt-hours (Wh), we divide 195 Wh by 1000 to get the consumption in kWh, which is 0.195 kWh.

53) Two angles whose measures have a sum of 90 degrees.

Complementary angle

Supplementary angle

Adjacent angle

Vertical angle

Complementary angles are two angles whose measures add up to 90 degrees. In this case, the two angles mentioned have a sum of 90 degrees, indicating that they are complementary angles.

Explanation

Complementary angles are two angles whose measures add up to 90 degrees. In this case, the two angles mentioned have a sum of 90 degrees, indicating that they are complementary angles.

54) Which equation is true?

5/8 = -5/8

5/8 = -(-5/-8)

-5/8=4/8

-3/-4= -3/4

The equation 5/8 = -(-5/-8) is true because when we simplify the right side of the equation, we get -(-5/-8) = -(5/8) = -5/8. Therefore, the left side of the equation is equal to the right side, making the equation true.

Explanation

The equation 5/8 = -(-5/-8) is true because when we simplify the right side of the equation, we get -(-5/-8) = -(5/8) = -5/8. Therefore, the left side of the equation is equal to the right side, making the equation true.

55) Write the prime factorization of 6. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).

2*3

2^2^2

3*2

2^4

The prime factorization of 6 is 2 * 3. This means that 6 can be expressed as the product of the prime numbers 2 and 3.

Explanation

The prime factorization of 6 is 2 * 3. This means that 6 can be expressed as the product of the prime numbers 2 and 3.

56) Look at this set of 8 numbers:

28

52

44

28

11

57

15

61

How would the mean change if the number 41 replaced the number 57 in the set?

Decrease

Increase

No change

Both have increased and decreased

If the number 41 replaced the number 57 in the set, the mean would decrease. This is because the number 57 is larger than the mean of the set, so replacing it with a smaller number like 41 would bring down the overall average.

Explanation

If the number 41 replaced the number 57 in the set, the mean would decrease. This is because the number 57 is larger than the mean of the set, so replacing it with a smaller number like 41 would bring down the overall average.

57) These are points on the same line?

Noncollinear Points

Line

Ray

Collinear

The given answer "Collinear" is correct because collinear points are points that lie on the same line. In this case, the question asks if the points are on the same line, and "Collinear" is the term that specifically refers to points on the same line. Therefore, the points mentioned in the question are collinear.

Explanation

The given answer "Collinear" is correct because collinear points are points that lie on the same line. In this case, the question asks if the points are on the same line, and "Collinear" is the term that specifically refers to points on the same line. Therefore, the points mentioned in the question are collinear.

58) It has no dimension?

Angle

Point

Plane

Line

A point is a basic geometric entity that has no dimension. It is represented by a dot and does not have any length, width, or height. It is considered to be a location in space and is used to define other geometric objects such as lines, planes, and angles. Unlike lines, planes, and angles, which have measurable dimensions, a point is considered to be dimensionless. Therefore, the statement "It has no dimension" is a characteristic that specifically applies to a point.

Explanation

A point is a basic geometric entity that has no dimension. It is represented by a dot and does not have any length, width, or height. It is considered to be a location in space and is used to define other geometric objects such as lines, planes, and angles. Unlike lines, planes, and angles, which have measurable dimensions, a point is considered to be dimensionless. Therefore, the statement "It has no dimension" is a characteristic that specifically applies to a point.

59) What is the factors of 8x² - 13x + 5 ?

(8x - 5) and (x - 1)

(2x - 5) and (4x - 1)

(8x + 1) and (x - 5)

(2x - 1) and (4x - 5)

( 4x-1) and (2x-5)

The given expression is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the equation. By using the product-sum method or trial and error, we can determine that the factors of 8x^2 - 13x + 5 are (8x - 5) and (x - 1).

Explanation

The given expression is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the equation. By using the product-sum method or trial and error, we can determine that the factors of 8x^2 - 13x + 5 are (8x - 5) and (x - 1).

60) How many lines in a plane are said to be concurrent if all of therm intersect at the same point?

Only two

Three or More

Only three

None of the above

In a plane, lines are said to be concurrent if they intersect at the same point. The correct answer is "Three or More" because when three or more lines intersect at a single point, they are considered to be concurrent.

Explanation

In a plane, lines are said to be concurrent if they intersect at the same point. The correct answer is "Three or More" because when three or more lines intersect at a single point, they are considered to be concurrent.

61) A flat surface that extends in all directions.

Point

Line

Line segment

Plane

A plane is a flat surface that extends infinitely in all directions. It has no thickness or boundaries. It can be thought of as a two-dimensional surface that goes on forever. Unlike a line or line segment, which are one-dimensional, a plane has length and width. Therefore, the correct answer is plane.

Explanation

A plane is a flat surface that extends infinitely in all directions. It has no thickness or boundaries. It can be thought of as a two-dimensional surface that goes on forever. Unlike a line or line segment, which are one-dimensional, a plane has length and width. Therefore, the correct answer is plane.

62) Which property of multiplication is shown? 9 m (1 m 4) = (9 m 1) m 4

Commutative

Distributive

Identity

Associative

The given equation, 9 × (1 × 4) = (9 × 1) × 4, demonstrates the property of associativity in multiplication. This property states that the grouping of numbers being multiplied does not affect the final product. In this case, regardless of whether we multiply 1 and 4 first or 9 and 1 first, the end result will be the same.

Explanation

The given equation, 9 × (1 × 4) = (9 × 1) × 4, demonstrates the property of associativity in multiplication. This property states that the grouping of numbers being multiplied does not affect the final product. In this case, regardless of whether we multiply 1 and 4 first or 9 and 1 first, the end result will be the same.

63) Last year Jan had 25 model airplanes in her collection. This year she has 32% more model airplanes. Jan then gave her brother 6 model airplanes to start a collection. How many model airplanes does Jan have after she gave 6 to her brother?

8

27

33

51

Jan started with 25 model airplanes. This year, she has 32% more, which is 0.32 * 25 = 8 model airplanes. So, she has a total of 25 + 8 = 33 model airplanes. After giving 6 to her brother, she has 33 - 6 = 27 model airplanes remaining.

Explanation

Jan started with 25 model airplanes. This year, she has 32% more, which is 0.32 * 25 = 8 model airplanes. So, she has a total of 25 + 8 = 33 model airplanes. After giving 6 to her brother, she has 33 - 6 = 27 model airplanes remaining.

64) These two lines do not lie on a plane?

Skew line

Coplanar

Parallel line

Collinear

Skew lines are lines that do not lie on the same plane and do not intersect. Therefore, it is correct to say that these two lines do not lie on a plane.

Explanation

Skew lines are lines that do not lie on the same plane and do not intersect. Therefore, it is correct to say that these two lines do not lie on a plane.

65) These are points that are on the same plane?

Coplanar Points

Line Points

Collinear Points

Nonecollinear Points

Coplanar points are points that lie on the same plane. In other words, they can be connected by a single flat surface without any bending or folding. Therefore, coplanar points are the correct answer as they fulfill the condition of being on the same plane.

Explanation

Coplanar points are points that lie on the same plane. In other words, they can be connected by a single flat surface without any bending or folding. Therefore, coplanar points are the correct answer as they fulfill the condition of being on the same plane.

66) Which of the following is not a subset of set A = {1, 4, 9, 16, 25}?

{ }

{1, 4, 16}

{1, 2, 3, 4, 5}

{1, 4, 9, 16, 25}

The set {1, 2, 3, 4, 5} is not a subset of set A = {1, 4, 9, 16, 25} because it contains elements that are not present in set A. Set A only contains the squares of the numbers 1 to 5, so any set that includes numbers other than 1, 4, 9, 16, or 25 cannot be a subset of set A.

Explanation

The set {1, 2, 3, 4, 5} is not a subset of set A = {1, 4, 9, 16, 25} because it contains elements that are not present in set A. Set A only contains the squares of the numbers 1 to 5, so any set that includes numbers other than 1, 4, 9, 16, or 25 cannot be a subset of set A.

67) Two angles that share a vertex and side but do not overlap.

Complementary angle

Supplementary angle

Adjacent angle

Vertical angle

Adjacent angles are two angles that share a common vertex and a common side, but do not overlap. In other words, they are side by side and do not intersect.

Explanation

Adjacent angles are two angles that share a common vertex and a common side, but do not overlap. In other words, they are side by side and do not intersect.

68) Angles formed when two lines intersect making the angles opposite each other congruent.

Complementary angles

Supplementary angles

Complementary angles

Vertical angles

When two lines intersect, the angles that are opposite each other are called vertical angles. Vertical angles are congruent, meaning they have the same measure. Therefore, the correct answer is vertical angles.

Explanation

When two lines intersect, the angles that are opposite each other are called vertical angles. Vertical angles are congruent, meaning they have the same measure. Therefore, the correct answer is vertical angles.

69) Find the next three terms in the sequence: 1, 1, 2, 4, 7, 13, 24

3, 40, 67

44, 81, 149

13, 7, 4

37, 61, 98

The sequence is formed by adding the previous three terms. Starting with 1, 1, 2, the next term is obtained by adding 1 + 2 + 4 = 7. Similarly, the next term is obtained by adding 2 + 4 + 7 = 13, and so on. Therefore, the next three terms in the sequence are obtained by adding 4 + 7 + 13 = 24, 7 + 13 + 24 = 44, and 13 + 24 + 44 = 81. Hence, the correct answer is 44, 81, 149.

Explanation

The sequence is formed by adding the previous three terms. Starting with 1, 1, 2, the next term is obtained by adding 1 + 2 + 4 = 7. Similarly, the next term is obtained by adding 2 + 4 + 7 = 13, and so on. Therefore, the next three terms in the sequence are obtained by adding 4 + 7 + 13 = 24, 7 + 13 + 24 = 44, and 13 + 24 + 44 = 81. Hence, the correct answer is 44, 81, 149.

70) It is a collection of points along a straight path that goes on and on in opposite directions.

Point

Plane

Line

Line segment

A line is a collection of points that extends infinitely in opposite directions. It does not have any endpoints and continues indefinitely. A line can be thought of as a straight path that goes on forever in both directions.

Explanation

A line is a collection of points that extends infinitely in opposite directions. It does not have any endpoints and continues indefinitely. A line can be thought of as a straight path that goes on forever in both directions.

71) What angle was shown below?

Complementary angle

Adjacent angle

Right angle

Vertical angle

The given question is asking for the angle shown below. The correct answer is "Adjacent angle." An adjacent angle is an angle that shares a common side with another angle and has a common vertex. In this case, the angle shown below is adjacent to another angle, as they share a common side and vertex.

Explanation

The given question is asking for the angle shown below. The correct answer is "Adjacent angle." An adjacent angle is an angle that shares a common side with another angle and has a common vertex. In this case, the angle shown below is adjacent to another angle, as they share a common side and vertex.

72) An angle formed by an intersecting lines that are on the diagonals and have the same measure?

Corresponding

Supplementary Angle

Vertical Angle

Adjacent Angle

Vertical angles are formed by intersecting lines that are on the diagonals and have the same measure. Vertical angles are opposite angles formed by the intersection of two lines. They are congruent, meaning they have the same measure. In other words, if one angle measures x degrees, then the other angle will also measure x degrees. Therefore, vertical angle is the correct answer.

Explanation

Vertical angles are formed by intersecting lines that are on the diagonals and have the same measure. Vertical angles are opposite angles formed by the intersection of two lines. They are congruent, meaning they have the same measure. In other words, if one angle measures x degrees, then the other angle will also measure x degrees. Therefore, vertical angle is the correct answer.

73) Which of the following is an infinite set?

Empty set

Universal set

The set of natural numbers

Both b and c

The set of natural numbers is an infinite set because it includes all positive whole numbers starting from 1 and continuing indefinitely. It does not have an endpoint or a largest number, so it goes on forever. In contrast, the empty set has no elements and is finite, while the universal set contains all possible elements but can still be finite if it has a specific limit or endpoint.

Explanation

The set of natural numbers is an infinite set because it includes all positive whole numbers starting from 1 and continuing indefinitely. It does not have an endpoint or a largest number, so it goes on forever. In contrast, the empty set has no elements and is finite, while the universal set contains all possible elements but can still be finite if it has a specific limit or endpoint.

74) What property is illustrated by the equation (5)(3+4)=(5)(3)+(5)(4)?

Associative property

Distributive property

Property of opposites

Commutative property

The equation (5)(3+4)=(5)(3)+(5)(4) demonstrates the distributive property. This property states that when multiplying a number by a sum of two or more numbers, you can distribute the multiplication to each term inside the parentheses. In this equation, the number 5 is being multiplied by the sum (3+4), and according to the distributive property, we can multiply 5 by each term inside the parentheses separately. This results in (5)(3) + (5)(4), which shows the distributive property in action.

Explanation

The equation (5)(3+4)=(5)(3)+(5)(4) demonstrates the distributive property. This property states that when multiplying a number by a sum of two or more numbers, you can distribute the multiplication to each term inside the parentheses. In this equation, the number 5 is being multiplied by the sum (3+4), and according to the distributive property, we can multiply 5 by each term inside the parentheses separately. This results in (5)(3) + (5)(4), which shows the distributive property in action.

75) A glass vase factory recently produced 2 vases that were chipped and 8 vases that were not. Considering this data, how many of the next 20 vases would you expect to be chipped?

4

8

16

32

Based on the given data, out of the recent 10 vases produced, 2 were chipped and 8 were not. This means that 20% of the vases produced were chipped. Therefore, if we apply the same percentage to the next 20 vases, we would expect 4 of them to be chipped.

Explanation

Based on the given data, out of the recent 10 vases produced, 2 were chipped and 8 were not. This means that 20% of the vases produced were chipped. Therefore, if we apply the same percentage to the next 20 vases, we would expect 4 of them to be chipped.

76) What is |-9|?

-9

9

90

.09

The absolute value of a number is its distance from zero on the number line. In this case, |-9| is asking for the distance of -9 from zero. Since -9 is 9 units away from zero in the negative direction, the absolute value of -9 is 9.

Explanation

The absolute value of a number is its distance from zero on the number line. In this case, |-9| is asking for the distance of -9 from zero. Since -9 is 9 units away from zero in the negative direction, the absolute value of -9 is 9.

77) Which of the following is not a term in the expansion of (x + y + 3)²?

2xy

6xy

6x

6y

In the expansion of (x + y + 3)2, all the terms will be obtained by multiplying the terms in the binomial (x + y + 3) twice. The term 6xy is not present in the expansion because it cannot be obtained by multiplying any combination of the terms in the binomial. The terms in the expansion will be x^2, xy, 3x, y^2, 3y, and 9.

Explanation

In the expansion of (x + y + 3)2, all the terms will be obtained by multiplying the terms in the binomial (x + y + 3) twice. The term 6xy is not present in the expansion because it cannot be obtained by multiplying any combination of the terms in the binomial. The terms in the expansion will be x^2, xy, 3x, y^2, 3y, and 9.

78) Which of the following equations is not equivalent to 3 + 2x = 1?

2x - 1 = -3

1 - 2x = 3

1 = 3 - 2x

1 = 2x + 3

The equation 1 = 3 - 2x is not equivalent to 3 + 2x = 1 because the terms are arranged in a different order. In the original equation, the constant term (1) is on the right side, while in the given equation, it is on the left side. Additionally, the coefficients of x have opposite signs in the two equations.

Explanation

The equation 1 = 3 - 2x is not equivalent to 3 + 2x = 1 because the terms are arranged in a different order. In the original equation, the constant term (1) is on the right side, while in the given equation, it is on the left side. Additionally, the coefficients of x have opposite signs in the two equations.

79) If the sum of the measures of two angles is 90 degrees, what do you cal the two angles?

Right angles

Adjacent angles

Supplementary angles

Complementary angles

When the sum of the measures of two angles is 90 degrees, they are called complementary angles. Complementary angles are two angles that add up to form a right angle. In this case, since the sum of the measures of the two angles is 90 degrees, they are complementary angles.

Explanation

When the sum of the measures of two angles is 90 degrees, they are called complementary angles. Complementary angles are two angles that add up to form a right angle. In this case, since the sum of the measures of the two angles is 90 degrees, they are complementary angles.

80) An angle formed by an intersecting lines that are supplementary and are next to each other?

Vertical angles

Adjacent Angle

Complementary Angle

Supplementary Angle

Adjacent angles are formed by intersecting lines that are supplementary and are next to each other. Adjacent angles share a common vertex and a common side. In this case, since the intersecting lines are supplementary (add up to 180 degrees) and are next to each other, the correct answer is adjacent angle.

Explanation

Adjacent angles are formed by intersecting lines that are supplementary and are next to each other. Adjacent angles share a common vertex and a common side. In this case, since the intersecting lines are supplementary (add up to 180 degrees) and are next to each other, the correct answer is adjacent angle.

81) Which of the following describe an adjacent angle?

Three or more lines in a plane

An angle have a common side and a common vertex

Each of the pairs of opposite angles made by two intersecting lines.

All of the above

An adjacent angle is defined as an angle that shares a common side and a common vertex with another angle. This means that the two angles are right next to each other and share a common point and a common line segment. Adjacent angles are commonly found in geometric figures and can be used to determine relationships between angles in a shape.

Explanation

An adjacent angle is defined as an angle that shares a common side and a common vertex with another angle. This means that the two angles are right next to each other and share a common point and a common line segment. Adjacent angles are commonly found in geometric figures and can be used to determine relationships between angles in a shape.

82) What system of measurement is internationally recognized and widely used by nearly all countries in the world?

Metric system

English system

US Customary system

International System of Units or SI

The International System of Units or SI is internationally recognized and widely used by nearly all countries in the world. It is a decimal-based system of measurement that provides a standardized way to measure various physical quantities such as length, mass, time, and temperature. The SI system is used in fields such as science, engineering, and industry, ensuring consistency and uniformity in measurements across different countries and disciplines.

Explanation

The International System of Units or SI is internationally recognized and widely used by nearly all countries in the world. It is a decimal-based system of measurement that provides a standardized way to measure various physical quantities such as length, mass, time, and temperature. The SI system is used in fields such as science, engineering, and industry, ensuring consistency and uniformity in measurements across different countries and disciplines.

83) If angles form a linear pair, which of the following statements is true?

They are adjacent and complementary.

They are adjacent and supplementary.

They are supplementary but not necessarily adjacent.

They are complementary but not necessarily adjacent.

When angles form a linear pair, it means they are adjacent (share a common vertex and side) and their non-common sides form a straight line. In this case, the angles are supplementary, meaning their measures add up to 180 degrees. Therefore, the correct statement is that they are adjacent and supplementary.

Explanation

When angles form a linear pair, it means they are adjacent (share a common vertex and side) and their non-common sides form a straight line. In this case, the angles are supplementary, meaning their measures add up to 180 degrees. Therefore, the correct statement is that they are adjacent and supplementary.

84) Progression series: what is the next digit - 1,2,6,42,1806,_____.?

The given series does not follow a typical mathematical pattern. However, upon closer observation, we can see that each number in the series is obtained by multiplying the previous number by the sum of its digits and then adding 1. For example, 1 * (1+0) + 1 = 2, 2 * (2+0) + 1 = 6, and so on. Applying the same pattern to the last number in the series, 1806 * (1+8+0+6) + 1 = 3263442. Therefore, the next number in the series is 3263442.

Explanation

The given series does not follow a typical mathematical pattern. However, upon closer observation, we can see that each number in the series is obtained by multiplying the previous number by the sum of its digits and then adding 1. For example, 1 * (1+0) + 1 = 2, 2 * (2+0) + 1 = 6, and so on. Applying the same pattern to the last number in the series, 1806 * (1+8+0+6) + 1 = 3263442. Therefore, the next number in the series is 3263442.

Submit

85) What represents (-4)

(+)(+)(-)

(-)(-)(+)(+)

(+)(-)(+)(-)(-)(-)(-)(-)

(-)(+)(-)(-)(-)

The given representation (-4) corresponds to the pattern (+)(-)(+)(-)(-)(-)(-)(-). This pattern indicates that there are 4 negative signs (-) alternating with 4 positive signs (+).

Explanation

The given representation (-4) corresponds to the pattern (+)(-)(+)(-)(-)(-)(-)(-). This pattern indicates that there are 4 negative signs (-) alternating with 4 positive signs (+).

86) An aquarium is a closed box with a length of 50 cm, a width of 40 cm, and a height of 30 cm. Find the surface area of this aquarium.

18 800 cm2

60 000 cm2

4700 cm2

9400 cm2

8400 cm2

The surface area of a rectangular box can be found by adding up the areas of all its sides. In this case, the aquarium has six sides: a bottom, a top, a front, a back, a left side, and a right side. The area of each side can be found by multiplying the length by the width. The bottom and top have the same dimensions, so their areas are the same. The front and back also have the same dimensions, as do the left and right sides. Thus, the surface area of the aquarium is equal to twice the sum of the areas of the bottom, front, and left side. By plugging in the given dimensions, we find that the surface area is 9400 cm2.

Explanation

The surface area of a rectangular box can be found by adding up the areas of all its sides. In this case, the aquarium has six sides: a bottom, a top, a front, a back, a left side, and a right side. The area of each side can be found by multiplying the length by the width. The bottom and top have the same dimensions, so their areas are the same. The front and back also have the same dimensions, as do the left and right sides. Thus, the surface area of the aquarium is equal to twice the sum of the areas of the bottom, front, and left side. By plugging in the given dimensions, we find that the surface area is 9400 cm2.

87) Which of the following represents the algebraic expression 5(x - y)?

Five times y diminished by x

Five times x diminished by y

The difference between 5x and y

Five times the difference of x and y

The expression 5(x - y) represents "five times the difference of x and y." This can be understood by breaking down the expression: 5 multiplied by (x - y). Since (x - y) represents the difference between x and y, multiplying it by 5 gives us "five times the difference of x and y."

Explanation

The expression 5(x - y) represents "five times the difference of x and y." This can be understood by breaking down the expression: 5 multiplied by (x - y). Since (x - y) represents the difference between x and y, multiplying it by 5 gives us "five times the difference of x and y."

88) Match column A to column B.

2(5)+2

3(2-5)

6(4+1)

-(2-3)

3+2(1+1)

Submit

89) What is the cardinality of the empty set?

0

1

2

Infinite

The cardinality of a set refers to the number of elements in the set. The empty set, also known as the null set, is a set that contains no elements. Therefore, the cardinality of the empty set is 0, as there are no elements to count.

Explanation

The cardinality of a set refers to the number of elements in the set. The empty set, also known as the null set, is a set that contains no elements. Therefore, the cardinality of the empty set is 0, as there are no elements to count.

90) The figure below is a_____.

Coplanar

Letter line

Collinear line

Line segment

A collinear line refers to a set of points that lie on the same straight line. In the given figure, the points are arranged in a straight line, indicating that they are collinear. Therefore, the correct answer is "Collinear line".

Explanation

A collinear line refers to a set of points that lie on the same straight line. In the given figure, the points are arranged in a straight line, indicating that they are collinear. Therefore, the correct answer is "Collinear line".

91) If lnl = 8, which integer/s can replace it n?

-8

0

8

Both a and c

If lnl = 8, it means that the absolute value of n is 8. Therefore, n can be either -8 or 8, as both of these values have an absolute value of 8. So, both option a (-8) and option c (8) can replace n.

Explanation

If lnl = 8, it means that the absolute value of n is 8. Therefore, n can be either -8 or 8, as both of these values have an absolute value of 8. So, both option a (-8) and option c (8) can replace n.

92) If a line can be drawn through a set of points, then the points are called ______ points.

Coplanar

Collinear

Vertical

Noncollinear

Collinear points are points that lie on the same line. If a line can be drawn through a set of points, it means that those points are collinear. Coplanar points, on the other hand, lie in the same plane, but not necessarily on the same line. Vertical points refer to points that lie on the same vertical line. Noncollinear points are points that do not lie on the same line. Therefore, the correct answer is Collinear.

Explanation

Collinear points are points that lie on the same line. If a line can be drawn through a set of points, it means that those points are collinear. Coplanar points, on the other hand, lie in the same plane, but not necessarily on the same line. Vertical points refer to points that lie on the same vertical line. Noncollinear points are points that do not lie on the same line. Therefore, the correct answer is Collinear.

93) Which of the following best describes vertical angles?

They don't have to be next to each other, just so long as the total is 180 degrees.

They don't have to point in the same direction.

The same vertex and one side

Opposite angles formed by intersecting lines

Vertical angles are formed when two lines intersect. They are opposite angles that share the same vertex but do not have to be next to each other. The sum of the measures of vertical angles is always equal to 180 degrees. Therefore, the correct answer is "Opposite angles formed by intersecting lines."

Explanation

Vertical angles are formed when two lines intersect. They are opposite angles that share the same vertex but do not have to be next to each other. The sum of the measures of vertical angles is always equal to 180 degrees. Therefore, the correct answer is "Opposite angles formed by intersecting lines."

94) The ____________ of the triangle is greater than each of its remote interior angles.

In a triangle, an exterior angle (formed by one side of the triangle and the extension of an adjacent side) is always greater than each of the two non-adjacent (remote) interior angles. This principle is a well-known geometric property that follows from the fact that an exterior angle is equal to the sum of the two opposite interior angles, making it necessarily larger than each of them individually.

Explanation

In a triangle, an exterior angle (formed by one side of the triangle and the extension of an adjacent side) is always greater than each of the two non-adjacent (remote) interior angles. This principle is a well-known geometric property that follows from the fact that an exterior angle is equal to the sum of the two opposite interior angles, making it necessarily larger than each of them individually.

Submit

95) Which of the following measures divides a given data set such that half of the data is greater than it and the other half is less than it?

Mean

Mode

Range

Median

The mean is not the correct answer because it is the average of all the data points and does not necessarily divide the data set into two equal halves. The mode is not the correct answer either because it represents the value that appears most frequently in the data set and does not divide the data set into two halves. The range is not the correct answer because it is the difference between the maximum and minimum values in the data set and does not divide the data set into two halves. The correct answer is the median because it is the middle value in the data set when arranged in ascending or descending order, dividing the data set into two equal halves.

Explanation

The mean is not the correct answer because it is the average of all the data points and does not necessarily divide the data set into two equal halves. The mode is not the correct answer either because it represents the value that appears most frequently in the data set and does not divide the data set into two halves. The range is not the correct answer because it is the difference between the maximum and minimum values in the data set and does not divide the data set into two halves. The correct answer is the median because it is the middle value in the data set when arranged in ascending or descending order, dividing the data set into two equal halves.

96) What is the degree of the polynomial x³ - 9x²y + 7xy² + y⁵?

3

2

5

14

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "y" is 5, therefore the degree of the polynomial x^3 - 9x^2y + 7xy^2 + y^5 is 5.

Explanation

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "y" is 5, therefore the degree of the polynomial x^3 - 9x^2y + 7xy^2 + y^5 is 5.

97) Which of the following is a/are solution/s to the equation x³ - x = 0?

-1

0

1

All of the above

The equation x^3 - x = 0 can be factored as x(x^2 - 1) = 0. This implies that either x = 0 or x^2 - 1 = 0. Solving the second equation, we get x = 1 or x = -1. Therefore, all of the given options (-1, 0, 1) are solutions to the equation x^3 - x = 0.

Explanation

The equation x^3 - x = 0 can be factored as x(x^2 - 1) = 0. This implies that either x = 0 or x^2 - 1 = 0. Solving the second equation, we get x = 1 or x = -1. Therefore, all of the given options (-1, 0, 1) are solutions to the equation x^3 - x = 0.

98) The parts of a polygons are/is.

Apex

Vertex

Side

Reterior angles

Angles

Diaghonals

The given answer lists the different parts of a polygon, which include vertices, sides, angles, and diagonals. A vertex is a point where two or more sides of a polygon meet. Sides are the line segments that form the boundaries of a polygon. Angles are formed at each vertex when two sides meet. Diagonals are line segments that connect non-adjacent vertices of a polygon. Therefore, the answer correctly identifies the various components of a polygon.

Explanation

The given answer lists the different parts of a polygon, which include vertices, sides, angles, and diagonals. A vertex is a point where two or more sides of a polygon meet. Sides are the line segments that form the boundaries of a polygon. Angles are formed at each vertex when two sides meet. Diagonals are line segments that connect non-adjacent vertices of a polygon. Therefore, the answer correctly identifies the various components of a polygon.

Submit

99) How many diagonals can be drawn in a dodecagon?

12

35

45

54

A dodecagon is a polygon with 12 sides. To find the number of diagonals that can be drawn in a dodecagon, we can use the formula n(n-3)/2, where n is the number of sides. Plugging in 12 for n, we get 12(12-3)/2 = 12(9)/2 = 108/2 = 54. Therefore, the correct answer is 54.

Explanation

A dodecagon is a polygon with 12 sides. To find the number of diagonals that can be drawn in a dodecagon, we can use the formula n(n-3)/2, where n is the number of sides. Plugging in 12 for n, we get 12(12-3)/2 = 12(9)/2 = 108/2 = 54. Therefore, the correct answer is 54.