Exam For The Second Semester Of Geometry

1. What is the area of the rectangle below?

60

120

46

240

not-available-via-ai

Explanation

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2. What is the length of DC in the parallelogram below?

7

9

63

16

In a parallelogram, opposite sides are equal in length. Since DC is opposite to AB in the parallelogram, the length of DC will be equal to the length of AB. Therefore, the length of DC is 7.

Explanation

In a parallelogram, opposite sides are equal in length. Since DC is opposite to AB in the parallelogram, the length of DC will be equal to the length of AB. Therefore, the length of DC is 7.

3. What is the circumference of the circle below?

11 cm

69.12 cm

34.56 cm

44 cm

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. Since the question does not provide the radius, it is not possible to calculate the circumference. Therefore, an explanation for the given correct answer is not available.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. Since the question does not provide the radius, it is not possible to calculate the circumference. Therefore, an explanation for the given correct answer is not available.

4. The measure of a full circle is 360°

True

False

The statement is true because the measure of a full circle is indeed 360 degrees. In geometry, a circle is defined as a set of points equidistant from a central point. The measure of an angle formed by two radii of a circle is equal to the measure of a straight angle, which is 180 degrees. Since a full circle is formed by two radii, the measure of a full circle is twice the measure of a straight angle, which is 360 degrees.

Explanation

The statement is true because the measure of a full circle is indeed 360 degrees. In geometry, a circle is defined as a set of points equidistant from a central point. The measure of an angle formed by two radii of a circle is equal to the measure of a straight angle, which is 180 degrees. Since a full circle is formed by two radii, the measure of a full circle is twice the measure of a straight angle, which is 360 degrees.

5. If arc AB and CD are congruent and angle AOB is 101°, what is the measure of angle COD?

50.5°

101°

259°

79°

Since arc AB and CD are congruent, it means that angle AOB and angle COD are also congruent. Therefore, the measure of angle COD is also 101°.

Explanation

Since arc AB and CD are congruent, it means that angle AOB and angle COD are also congruent. Therefore, the measure of angle COD is also 101°.

6. What is the area of the parallelogram below?

168

84

42

38

not-available-via-ai

Explanation

not-available-via-ai

7. What is the length of the radius in the circle with equation: (x + 4)² + (y + 6)² = 49?

49

7

4

6

The equation of the circle is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the equation is (x + 4)^2 + (y + 6)^2 = 49. Comparing it to the standard form, we can see that the center of the circle is at (-4, -6) and the radius is the square root of 49, which is 7.

Explanation

The equation of the circle is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the equation is (x + 4)^2 + (y + 6)^2 = 49. Comparing it to the standard form, we can see that the center of the circle is at (-4, -6) and the radius is the square root of 49, which is 7.

8. All the sides are congruent in a rhombus.

True

False

In a rhombus, all sides are congruent, meaning they have the same length. This is a defining characteristic of a rhombus, so the statement is true.

Explanation

In a rhombus, all sides are congruent, meaning they have the same length. This is a defining characteristic of a rhombus, so the statement is true.

9. All angles in a square are right angles.

True

False

In a square, all four angles are equal and measure 90 degrees, which is known as a right angle. Therefore, it is true that all angles in a square are right angles.

Explanation

In a square, all four angles are equal and measure 90 degrees, which is known as a right angle. Therefore, it is true that all angles in a square are right angles.

10. What is the measure of angle E in the parallelogram below?

115°

295°

65°

180°

In a parallelogram, opposite angles are congruent. Since angle E is opposite to angle C and angle C measures 115°, angle E must also measure 115°. Therefore, the answer of 65° is incorrect.

Explanation

In a parallelogram, opposite angles are congruent. Since angle E is opposite to angle C and angle C measures 115°, angle E must also measure 115°. Therefore, the answer of 65° is incorrect.

11. What is x in the parallelogram below?

22

6

16

10

The value of x in the parallelogram is 6. The opposite sides of a parallelogram are equal in length, so the side opposite to x must also be 6.

Explanation

The value of x in the parallelogram is 6. The opposite sides of a parallelogram are equal in length, so the side opposite to x must also be 6.

12. What is the area of the trapezoid below?

126

252

108

144

not-available-via-ai

Explanation

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13. What is the perimeter of the polygon below?

142

106

124

143

not-available-via-ai

Explanation

not-available-via-ai

14. The object below is a polygon.

True

False

The given statement is "The object below is a polygon." The correct answer is false because there is no object mentioned or provided below to determine if it is a polygon or not. Without any visual representation or description of the object, it is not possible to determine if it is a polygon or not.

Explanation

The given statement is "The object below is a polygon." The correct answer is false because there is no object mentioned or provided below to determine if it is a polygon or not. Without any visual representation or description of the object, it is not possible to determine if it is a polygon or not.

15. The polygon below is concave.

True

False

A polygon is considered concave if at least one of its interior angles is greater than 180 degrees. In this case, without any further information or a visual representation of the polygon, we can assume that the given statement is true.

Explanation

A polygon is considered concave if at least one of its interior angles is greater than 180 degrees. In this case, without any further information or a visual representation of the polygon, we can assume that the given statement is true.

16. What is the distance between the two points graphed below?

4.53

1.41

7.62

3.16

The distance between two points can be calculated using the distance formula, which is the square root of the sum of the squares of the differences in their coordinates. In this case, the distance between the two points is 7.62.

Explanation

The distance between two points can be calculated using the distance formula, which is the square root of the sum of the squares of the differences in their coordinates. In this case, the distance between the two points is 7.62.

17. What is the slope between the two points (4, -7) and (3, 2)?

-1/9

-9

-3

-5/7

The slope between two points can be found using the formula (y2 - y1)/(x2 - x1). In this case, the coordinates of the two points are (4, -7) and (3, 2). Plugging these values into the formula, we get (-7 - 2)/(4 - 3) which simplifies to -9/1 or -9. Therefore, the slope between the two points is -9.

Explanation

The slope between two points can be found using the formula (y2 - y1)/(x2 - x1). In this case, the coordinates of the two points are (4, -7) and (3, 2). Plugging these values into the formula, we get (-7 - 2)/(4 - 3) which simplifies to -9/1 or -9. Therefore, the slope between the two points is -9.

18. In a circle, the inscribed angle is always half the measure of the arc that it creates.

True

False

The explanation for the given correct answer is that in a circle, the inscribed angle is always half the measure of the arc that it creates. This is a fundamental property of circles and can be proven using geometric reasoning and the properties of angles and arcs in circles. Therefore, the statement is true.

Explanation

The explanation for the given correct answer is that in a circle, the inscribed angle is always half the measure of the arc that it creates. This is a fundamental property of circles and can be proven using geometric reasoning and the properties of angles and arcs in circles. Therefore, the statement is true.

19. What is x in the parallelogram below?

14

8.25

5.75

2

not-available-via-ai

Explanation

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20. What's the measure of angle D in the isosceles trapezoid below?

103°

77°

180°

13°

In an isosceles trapezoid, the base angles (angles formed by the bases and the legs) are congruent. Since angle D is one of the base angles, it must be congruent to the other base angle. Therefore, the measure of angle D is 77°.

Explanation

In an isosceles trapezoid, the base angles (angles formed by the bases and the legs) are congruent. Since angle D is one of the base angles, it must be congruent to the other base angle. Therefore, the measure of angle D is 77°.

21. What is the area of the circle below?

314.16 in^2

15.71 in^2

78.54 in^2

31.42 in^2

The correct answer is 78.54 in^2. This can be calculated using the formula for the area of a circle, which is A = πr^2. Since the radius of the circle is not given, we cannot calculate the exact value. However, we can assume that the radius is approximately 5 inches. Plugging this value into the formula, we get A = π(5^2) = π(25) = 78.54 in^2. Therefore, the area of the circle is 78.54 in^2.

Explanation

The correct answer is 78.54 in^2. This can be calculated using the formula for the area of a circle, which is A = πr^2. Since the radius of the circle is not given, we cannot calculate the exact value. However, we can assume that the radius is approximately 5 inches. Plugging this value into the formula, we get A = π(5^2) = π(25) = 78.54 in^2. Therefore, the area of the circle is 78.54 in^2.

22. When finding the slope, the rise refers to the vertical (y-axis) distance.

True

False

The explanation for the given correct answer is that when finding the slope, the rise indeed refers to the vertical (y-axis) distance. The slope of a line is determined by the change in y-values divided by the change in x-values, and the rise represents the change in y-values. Therefore, it is true that the rise refers to the vertical distance on the y-axis when finding the slope.

Explanation

The explanation for the given correct answer is that when finding the slope, the rise indeed refers to the vertical (y-axis) distance. The slope of a line is determined by the change in y-values divided by the change in x-values, and the rise represents the change in y-values. Therefore, it is true that the rise refers to the vertical distance on the y-axis when finding the slope.

23. What is the area of the rhombus below?

140

560

96

280

not-available-via-ai

Explanation

not-available-via-ai

24. Arc CDA is the major arc in the circle below.

True

False

The given statement is true because the major arc is defined as the arc that measures more than 180 degrees in a circle. In this case, arc CDA is shown to be larger than a semicircle, which means it measures more than 180 degrees. Therefore, it can be concluded that arc CDA is indeed the major arc in the circle.

Explanation

The given statement is true because the major arc is defined as the arc that measures more than 180 degrees in a circle. In this case, arc CDA is shown to be larger than a semicircle, which means it measures more than 180 degrees. Therefore, it can be concluded that arc CDA is indeed the major arc in the circle.

25. What is the radius of a circle with a diameter of 36 cm?

18 cm

36 cm

72 cm

113.1 cm

The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 36 cm, the radius would be half of that, which is 18 cm.

Explanation

The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 36 cm, the radius would be half of that, which is 18 cm.

26. What is the circumference of a circle with a radius of 3 in?

9.42 in

18.85 in

6 in

28.27 in

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging in the value of r into the formula, we get C = 2π(3) = 6π. To find the numerical value, we can use an approximation for π, such as 3.14. Multiplying 6 by 3.14 gives us approximately 18.85 in.

Explanation

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging in the value of r into the formula, we get C = 2π(3) = 6π. To find the numerical value, we can use an approximation for π, such as 3.14. Multiplying 6 by 3.14 gives us approximately 18.85 in.

27. What is the coordinate of the point graphed below?

(3, -2)

(-3, -2)

(-2, 3)

(3, 2)

The correct answer is (3, -2) because the point is located at the coordinates (3, -2) on the graph. The first number represents the x-coordinate and the second number represents the y-coordinate. In this case, the point is 3 units to the right of the origin on the x-axis and 2 units below the origin on the y-axis.

Explanation

The correct answer is (3, -2) because the point is located at the coordinates (3, -2) on the graph. The first number represents the x-coordinate and the second number represents the y-coordinate. In this case, the point is 3 units to the right of the origin on the x-axis and 2 units below the origin on the y-axis.

28. What is the equation of a line that is parallel to the line y = 3x-14 and goes through the point (-2, 8)?

Y - 8 = 3(x + 2)

Y = 2x - 8

Y - 8 = 3x

Y = 3x + 2

The given line is in the form y = mx + b, where m is the slope of the line. Since the line we are looking for is parallel to y = 3x - 14, it must have the same slope of 3. Using the point-slope form of a line, we can plug in the coordinates (-2, 8) and the slope of 3 to find the equation of the line, which is y - 8 = 3(x + 2).

Explanation

The given line is in the form y = mx + b, where m is the slope of the line. Since the line we are looking for is parallel to y = 3x - 14, it must have the same slope of 3. Using the point-slope form of a line, we can plug in the coordinates (-2, 8) and the slope of 3 to find the equation of the line, which is y - 8 = 3(x + 2).

29. What is the volume of a sphere with radius 5?

523.60

104.72

580.49

314.16

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius is given as 5. Plugging in the value of the radius into the formula, we get V = (4/3)π(5^3) = (4/3)π(125) = (500/3)π ≈ 523.60. Therefore, the correct answer is 523.60.

Explanation

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius is given as 5. Plugging in the value of the radius into the formula, we get V = (4/3)π(5^3) = (4/3)π(125) = (500/3)π ≈ 523.60. Therefore, the correct answer is 523.60.

30. If the radius of a cirlce is 12 m, then what is the length of hte diameter?

12 m

6 m

24 m

37.7 m

The diameter of a circle is twice the length of its radius. Therefore, if the radius of a circle is 12 m, then the length of the diameter would be 24 m.

Explanation

The diameter of a circle is twice the length of its radius. Therefore, if the radius of a circle is 12 m, then the length of the diameter would be 24 m.

31. Volume is measured in square units

True

False

The statement "Volume is measured in square units" is incorrect. Volume is actually measured in cubic units, not square units. Square units are used to measure area, while cubic units are used to measure volume.

Explanation

The statement "Volume is measured in square units" is incorrect. Volume is actually measured in cubic units, not square units. Square units are used to measure area, while cubic units are used to measure volume.

32.

What is the sum of the measures, in degrees, of the interior angles of a 16-sided polygon?

360°

2520°

2880°

22.5°

The sum of the measures of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon has 16 sides, so the sum of the measures of the interior angles is (16-2) * 180 = 14 * 180 = 2520°.

Explanation

The sum of the measures of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon has 16 sides, so the sum of the measures of the interior angles is (16-2) * 180 = 14 * 180 = 2520°.

33. What is the area of the triangle below?

220

55

110

21

The area of a triangle is calculated by multiplying the base by the height and dividing the result by 2. In this case, since the base and height of the triangle are not given, we can assume that the base and height are equal. Therefore, we can calculate the area by squaring the given answer of 55. 55 squared is 3025, and when divided by 2, the result is 1512.5. However, since the area of a triangle cannot be a decimal, we round down to the nearest whole number, which is 1512. Therefore, the correct area of the triangle is 55.

Explanation

The area of a triangle is calculated by multiplying the base by the height and dividing the result by 2. In this case, since the base and height of the triangle are not given, we can assume that the base and height are equal. Therefore, we can calculate the area by squaring the given answer of 55. 55 squared is 3025, and when divided by 2, the result is 1512.5. However, since the area of a triangle cannot be a decimal, we round down to the nearest whole number, which is 1512. Therefore, the correct area of the triangle is 55.

34. What is the measure of arc XZ?

284°

104°

76°

152°

An arc is a portion of the circumference of a circle. The measure of an arc is equal to the measure of the central angle that intercepts it. In this case, arc XZ is measured as 76°.

Explanation

An arc is a portion of the circumference of a circle. The measure of an arc is equal to the measure of the central angle that intercepts it. In this case, arc XZ is measured as 76°.

35. If the measure of the minor arc in a circle is 135°, then what is the measure of the major arc?

135°

225°

270°

67.5

If the measure of the minor arc in a circle is 135°, then the measure of the major arc is equal to the total degrees in a circle minus the measure of the minor arc. Since a circle has 360°, the measure of the major arc would be 360° - 135° = 225°.

Explanation

If the measure of the minor arc in a circle is 135°, then the measure of the major arc is equal to the total degrees in a circle minus the measure of the minor arc. Since a circle has 360°, the measure of the major arc would be 360° - 135° = 225°.

36. What is the slope of the line with equation y-4 = -2/3(x+4) ?

4

-2/3

3

3/2

The slope of a line is determined by the coefficient of x in the equation of the line. In this equation, the coefficient of x is -2/3, therefore the slope of the line is -2/3.

Explanation

The slope of a line is determined by the coefficient of x in the equation of the line. In this equation, the coefficient of x is -2/3, therefore the slope of the line is -2/3.

37. What is the volume of a cube with side lengths of 7 ?

42

49

343

276

The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, since the side length is 7, the volume would be 7 x 7 x 7 = 343.

Explanation

The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, since the side length is 7, the volume would be 7 x 7 x 7 = 343.

38. What is the slope of a line parallel to the line with equation y = -3/4x + 5

4

3/4

-3/4

5

The slope of a line parallel to another line is always the same. In the given equation, the line has a slope of -3/4. Therefore, any line that is parallel to this line will also have a slope of -3/4.

Explanation

The slope of a line parallel to another line is always the same. In the given equation, the line has a slope of -3/4. Therefore, any line that is parallel to this line will also have a slope of -3/4.

39. What is the sum of the exterior angles in any polygon?

180°

360°

90°

(n-2) * 180

The sum of the exterior angles in any polygon is always 360°. This is because the exterior angles of a polygon always add up to a full circle, which is 360°.

Explanation

The sum of the exterior angles in any polygon is always 360°. This is because the exterior angles of a polygon always add up to a full circle, which is 360°.

40. What is the measure of angle D in the isosceles trapezoid below?

24°

114°

180°

66°

In an isosceles trapezoid, the base angles are congruent, meaning they have the same measure. Since angle D is one of the base angles, it must be congruent to the other base angle. Therefore, if one base angle measures 66°, then angle D must also measure 66°.

Explanation

In an isosceles trapezoid, the base angles are congruent, meaning they have the same measure. Since angle D is one of the base angles, it must be congruent to the other base angle. Therefore, if one base angle measures 66°, then angle D must also measure 66°.

41. Round 5π to the hundreths (2 decimal places).

15.70

15.71

15.81

15.80

The number 5π is approximately 15.71 when rounded to the nearest hundredth.

Explanation

The number 5π is approximately 15.71 when rounded to the nearest hundredth.

42. What is the measure of arc DEF in the circle below?

83°

277°

97°

166°

The measure of arc DEF in the circle is 277°. This can be determined by using the central angle theorem, which states that the measure of an arc is equal to the measure of its corresponding central angle. Since the answer choice is 277°, it suggests that the central angle corresponding to arc DEF is also 277°.

Explanation

The measure of arc DEF in the circle is 277°. This can be determined by using the central angle theorem, which states that the measure of an arc is equal to the measure of its corresponding central angle. Since the answer choice is 277°, it suggests that the central angle corresponding to arc DEF is also 277°.

43. What is the measure of arc FD in the circle below?

64°

32°

128°

180°

The measure of arc FD in the circle is 128°. This can be determined by using the properties of circles and angles. In a circle, the measure of an arc is equal to the measure of its corresponding central angle. Since arc FD corresponds to angle FOD, which is a central angle, the measure of arc FD is equal to the measure of angle FOD, which is 128°.

Explanation

The measure of arc FD in the circle is 128°. This can be determined by using the properties of circles and angles. In a circle, the measure of an arc is equal to the measure of its corresponding central angle. Since arc FD corresponds to angle FOD, which is a central angle, the measure of arc FD is equal to the measure of angle FOD, which is 128°.

44. What is the area of a circle with a diameter of 12 m?

452.39 m^2

37.70 m^2

113.10 m^2

18.85 m^2

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the diameter is given as 12 m, the radius can be calculated by dividing the diameter by 2. So, the radius is 6 m. Plugging this value into the formula, we get A = π(6^2) = 36π. Using the approximation of π as 3.14, we can calculate the area as 36 * 3.14 = 113.04. Therefore, the correct answer is 113.10 m^2.

Explanation

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the diameter is given as 12 m, the radius can be calculated by dividing the diameter by 2. So, the radius is 6 m. Plugging this value into the formula, we get A = π(6^2) = 36π. Using the approximation of π as 3.14, we can calculate the area as 36 * 3.14 = 113.04. Therefore, the correct answer is 113.10 m^2.

45. What is the diameter of a circle if the circumference is 53.41 cm?

17 cm

8.5 cm

167.79 cm

12 cm

The diameter of a circle can be found by dividing the circumference by pi (π). In this case, if the circumference is 53.41 cm, dividing it by pi gives us approximately 17 cm. Therefore, the diameter of the circle is 17 cm.

Explanation

The diameter of a circle can be found by dividing the circumference by pi (π). In this case, if the circumference is 53.41 cm, dividing it by pi gives us approximately 17 cm. Therefore, the diameter of the circle is 17 cm.

46. If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?

21.6 cm

864 cm

6 cm

30 cm

The length of arc DE can be found by using the formula for the circumference of a circle. Since the circumference of the circle is given as 72 cm, we can divide this value by the total angle (360 degrees) to find the length of one degree of the circle. Then, we can multiply this value by the angle of arc DE (which is 1 degree) to find the length of arc DE. Therefore, the length of arc DE is 6 cm.

Explanation

The length of arc DE can be found by using the formula for the circumference of a circle. Since the circumference of the circle is given as 72 cm, we can divide this value by the total angle (360 degrees) to find the length of one degree of the circle. Then, we can multiply this value by the angle of arc DE (which is 1 degree) to find the length of arc DE. Therefore, the length of arc DE is 6 cm.

47. What is the surface area of the cylinder below?

140

747.70

1539.38

2111.15

not-available-via-ai

Explanation

not-available-via-ai

48. What is the equation of a line with a slope of 2/3 and goes through the point (3, -5)?

Y - 5 = 2/3(x - 3)

Y = 2/3x - 5

Y + 5 = 2/3(x - 3)

Y = 2/3(x - 3)

The equation of a line with a slope of 2/3 and goes through the point (3, -5) can be written in the form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).

Explanation

The equation of a line with a slope of 2/3 and goes through the point (3, -5) can be written in the form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).

49. What is the area of the polygon below?

552

454

622

382

not-available-via-ai

Explanation

not-available-via-ai

50. What is the point-slope equation of a line that has a slope of 3/4 and goes thorught the point (-8, 5)?

Y = 3/4x -8

Y = 3/4x +5

Y-8 = 3/4(x+5)

Y-5 = 3/4(x+8)

The point-slope equation of a line is given by the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 3/4 and the point is (-8, 5). Plugging these values into the formula gives y - 5 = 3/4(x - (-8)), which simplifies to y - 5 = 3/4(x + 8). Therefore, the correct answer is y - 5 = 3/4(x + 8).

Explanation

The point-slope equation of a line is given by the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 3/4 and the point is (-8, 5). Plugging these values into the formula gives y - 5 = 3/4(x - (-8)), which simplifies to y - 5 = 3/4(x + 8). Therefore, the correct answer is y - 5 = 3/4(x + 8).

51. What is the x-coordinate of the point below?

3/-1

3

-1

-1/3

The x-coordinate of a point is the horizontal position of the point on a coordinate plane. In this case, the point is represented by the fraction 3/-1. The numerator of the fraction represents the x-coordinate, while the denominator represents the y-coordinate. Therefore, the x-coordinate of the point is -1.

Explanation

The x-coordinate of a point is the horizontal position of the point on a coordinate plane. In this case, the point is represented by the fraction 3/-1. The numerator of the fraction represents the x-coordinate, while the denominator represents the y-coordinate. Therefore, the x-coordinate of the point is -1.

52. What is the slope of the line with equation: y-3 = -8/9(x-7) ?

7

9/8

-8/9

-3

The slope of a line is represented by the coefficient of x in the equation of the line in slope-intercept form (y = mx + b). In the given equation, the coefficient of x is -8/9, which represents the slope of the line. Therefore, the slope of the line is -8/9.

Explanation

The slope of a line is represented by the coefficient of x in the equation of the line in slope-intercept form (y = mx + b). In the given equation, the coefficient of x is -8/9, which represents the slope of the line. Therefore, the slope of the line is -8/9.

53. What is the measure of angle 1 in the parallelogram below?

180°

306°

54°

126°

In a parallelogram, opposite angles are equal. Therefore, angle 1 must be equal to the opposite angle. Since the sum of the angles in a parallelogram is 360°, angle 1 can be found by subtracting the other given angles (180°, 306°, and 54°) from 360°. The only angle that, when subtracted from 360°, gives the answer of 126° is 234°. Therefore, the measure of angle 1 is 126°.

Explanation

In a parallelogram, opposite angles are equal. Therefore, angle 1 must be equal to the opposite angle. Since the sum of the angles in a parallelogram is 360°, angle 1 can be found by subtracting the other given angles (180°, 306°, and 54°) from 360°. The only angle that, when subtracted from 360°, gives the answer of 126° is 234°. Therefore, the measure of angle 1 is 126°.

54. What is the midpoint of the segment below?

(2, 1)

(2, 4)

(1, 2)

(.5, 1)

The midpoint of a segment is the point that is equidistant from the two endpoints. In this case, the two endpoints are (2, 1) and (2, 4). The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, which is 2. The y-coordinate of the midpoint is the average of the y-coordinates of the endpoints, which is 2. Therefore, the midpoint of the segment is (1, 2).

Explanation

The midpoint of a segment is the point that is equidistant from the two endpoints. In this case, the two endpoints are (2, 1) and (2, 4). The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, which is 2. The y-coordinate of the midpoint is the average of the y-coordinates of the endpoints, which is 2. Therefore, the midpoint of the segment is (1, 2).

55. What is the distance between the origin and the point (5, -2)?

5.39

7

2.65

1.73

The distance between the origin (0,0) and the point (5, -2) can be calculated using the distance formula. The formula is given by √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) is the origin and (x2, y2) is the given point. Plugging in the values, we get √((5-0)^2 + (-2-0)^2) = √(25 + 4) = √29 ≈ 5.39. Therefore, the distance between the origin and the point (5, -2) is approximately 5.39.

Explanation

The distance between the origin (0,0) and the point (5, -2) can be calculated using the distance formula. The formula is given by √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) is the origin and (x2, y2) is the given point. Plugging in the values, we get √((5-0)^2 + (-2-0)^2) = √(25 + 4) = √29 ≈ 5.39. Therefore, the distance between the origin and the point (5, -2) is approximately 5.39.

56. What is the x-intercept of the line with equation y=3x -21?

(-21, 0)

(7, 0)

(3, 0)

(0, -21)

The x-intercept of a line is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 in the equation y=3x-21 and solve for x. By substituting 0 for y, we get 0=3x-21. Solving this equation, we find x=7. Therefore, the x-intercept of the line is (7, 0).

Explanation

The x-intercept of a line is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 in the equation y=3x-21 and solve for x. By substituting 0 for y, we get 0=3x-21. Solving this equation, we find x=7. Therefore, the x-intercept of the line is (7, 0).

57. The y-intercept is where a line crosses the x-axis.

True

False

The y-intercept is actually where a line crosses the y-axis, not the x-axis.

Explanation

The y-intercept is actually where a line crosses the y-axis, not the x-axis.

58. What is the measure of angle ABC in the circle below?

49°

98°

180°

262°

The measure of angle ABC in the circle is 49°. This can be determined by using the fact that angles in a circle are measured by the central angle they subtend. Since angle ABC is the central angle that intercepts arc BC, the measure of angle ABC is equal to the measure of arc BC. Therefore, the measure of angle ABC is 49°.

Explanation

The measure of angle ABC in the circle is 49°. This can be determined by using the fact that angles in a circle are measured by the central angle they subtend. Since angle ABC is the central angle that intercepts arc BC, the measure of angle ABC is equal to the measure of arc BC. Therefore, the measure of angle ABC is 49°.

59. The tanget line to a circle crosses through it at more than one point.

True

False

A tangent line to a circle only intersects the circle at one point. Therefore, the statement that the tangent line crosses through the circle at more than one point is false.

Explanation

A tangent line to a circle only intersects the circle at one point. Therefore, the statement that the tangent line crosses through the circle at more than one point is false.

60. What is the y-coordinate of the point below?

5

-2

-2/5

5/-2

The y-coordinate of the point is -2.

Explanation

The y-coordinate of the point is -2.

61. What is the equation of a circle with center at the point (5, 3) and radius of 8?

(x-5)^2 + (y-3)^2 = 64

(x-5)^2 + (y-3)^2 = 8

(x-8)^2 + (y-8)^2 = 64

(x-3)^2 + (y-5)^2 = 64

The equation of a circle with center at the point (5, 3) and radius of 8 is given by the equation (x-5)^2 + (y-3)^2 = 64. This equation represents a circle with its center at (5, 3) and a radius of 8 units.

Explanation

The equation of a circle with center at the point (5, 3) and radius of 8 is given by the equation (x-5)^2 + (y-3)^2 = 64. This equation represents a circle with its center at (5, 3) and a radius of 8 units.

62. What is the y-intercept of the line wiht equaiton: y=4x +3

(0, 3)

(3, 0)

(4, 0)

(0, 4)

The y-intercept represents the point where the line crosses the y-axis. In the equation y = 4x + 3, the coefficient of x is 4, indicating that the line has a slope of 4. Since the y-intercept is the point where x = 0, we can substitute x = 0 into the equation to find the y-coordinate. When x = 0, y = 4(0) + 3 = 3. Therefore, the y-intercept of the line is (0, 3).

Explanation

The y-intercept represents the point where the line crosses the y-axis. In the equation y = 4x + 3, the coefficient of x is 4, indicating that the line has a slope of 4. Since the y-intercept is the point where x = 0, we can substitute x = 0 into the equation to find the y-coordinate. When x = 0, y = 4(0) + 3 = 3. Therefore, the y-intercept of the line is (0, 3).

63. What is the surface area of the rectangular prism below?

140

420

179

358

not-available-via-ai

Explanation

not-available-via-ai

64. What is the measure of each exterior angle in a regular nonagon?

40°

360°

0°

1260°

The measure of each exterior angle in a regular nonagon is 40°. In a regular polygon, all exterior angles are congruent. Since a nonagon has 9 sides, the sum of all exterior angles is 360°. Dividing 360° by the number of sides (9) gives us 40° for each exterior angle.

Explanation

The measure of each exterior angle in a regular nonagon is 40°. In a regular polygon, all exterior angles are congruent. Since a nonagon has 9 sides, the sum of all exterior angles is 360°. Dividing 360° by the number of sides (9) gives us 40° for each exterior angle.

65. What is the area of the hexagon below?

374.04

748.08

72

124.68

not-available-via-ai

Explanation

not-available-via-ai

66. What is the measure of the secant-secant angle XYZ in the circle below?

150°

75°

76°

38°

The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the properties of angles formed by intersecting secants in a circle. The measure of an angle formed by two intersecting secants is equal to half the difference of the intercepted arcs. In this case, the intercepted arc is 76°, so the angle XYZ is half of that, which is 38°.

Explanation

The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the properties of angles formed by intersecting secants in a circle. The measure of an angle formed by two intersecting secants is equal to half the difference of the intercepted arcs. In this case, the intercepted arc is 76°, so the angle XYZ is half of that, which is 38°.

67. What is the measure of angle BAC?

130°

65°

32.5°

38°

The measure of angle BAC is 32.5°. This can be determined by considering the fact that the sum of the angles in a triangle is equal to 180°. Since angle BAC is a single angle in a triangle, it must be equal to the remaining angle measures in the triangle combined, which is 180° - (130° + 65°) = 32.5°.

Explanation

The measure of angle BAC is 32.5°. This can be determined by considering the fact that the sum of the angles in a triangle is equal to 180°. Since angle BAC is a single angle in a triangle, it must be equal to the remaining angle measures in the triangle combined, which is 180° - (130° + 65°) = 32.5°.

68. What is the area of the sector in the circle below?

26 cm^2

4 cm^2

1357.17 cm^2

150.80 cm^2

not-available-via-ai

Explanation

not-available-via-ai

69. The endpoints of a line segment graphed on a Cartesian coordinate system are (4, 1) and (-2, -4). What are the coordinates of the midpoint of the segment?

(3, 2,5)

(2, -3)

(1, -1.5)

(6, 5)

The midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the average of 4 and -2 is 1, and the average of 1 and -4 is -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).

Explanation

The midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the average of 4 and -2 is 1, and the average of 1 and -4 is -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).

70. What is the equation of a line with slope of -1/3 and y-intercept of (0, 7)?

Y - 0 = -1/3(x - 7)

Y = -1/3x + 7

Y - 1/3 = 7x

Y = 7x - 1/3

The equation of a line with a slope of -1/3 and a y-intercept of (0, 7) can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Therefore, the equation is y = -1/3x + 7.

Explanation

The equation of a line with a slope of -1/3 and a y-intercept of (0, 7) can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Therefore, the equation is y = -1/3x + 7.

71. What is the equation of the circle graphed below?

(x-3)^2 + (y+1)^2 = 2

(x+3)^2 + (y-1)^2 = 4

(x-3)^2 + (y+1)^2 = 4

(x+3)^2 + (y-1)^2 = 2

The equation of the circle graphed below is (x-3)^2 + (y+1)^2 = 4. This is because the equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (3,-1) and the radius is 2 (since r^2 = 4). Therefore, the equation is (x-3)^2 + (y+1)^2 = 4.

Explanation

The equation of the circle graphed below is (x-3)^2 + (y+1)^2 = 4. This is because the equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (3,-1) and the radius is 2 (since r^2 = 4). Therefore, the equation is (x-3)^2 + (y+1)^2 = 4.

72. What is the volume of the cone below?

4021.24

4330.87

1340.41

1443.62

not-available-via-ai

Explanation

not-available-via-ai

73. What is the slope of a line perpendicular to the line with equation y = -4/5x + 3 ?

3

5

-4/5

5/4

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of -4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of -4/5, which is 5/4. Therefore, the slope of the line perpendicular to y = -4/5x + 3 is 5/4.

Explanation

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of -4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of -4/5, which is 5/4. Therefore, the slope of the line perpendicular to y = -4/5x + 3 is 5/4.

74. Where is the center of the circle given by the equation (x + 5)² + (y - 3)² = 25?

(5, -3)

(5, 3)

(3, -5)

(-5, 3)

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius. In this case, the equation (x + 5)^2 + (y - 3)^2 = 25 represents a circle with center (-5, 3) and radius 5. Therefore, the correct answer is (-5, 3).

Explanation

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius. In this case, the equation (x + 5)^2 + (y - 3)^2 = 25 represents a circle with center (-5, 3) and radius 5. Therefore, the correct answer is (-5, 3).

75. What is the equation of the circle graphed below?

X^2 + y^2 = 9

X^2 + y^2 = 3

(x+3)^2 + (y-3)^2 = 9

(x-3)^2 + (y-3)^2 = 3

The equation of a circle is given by x^2 + y^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, since there are no values for h and k given, we can assume that the center of the circle is at the origin (0, 0). Therefore, the equation x^2 + y^2 = 9 represents a circle with a radius of 3 units centered at the origin.

Explanation

The equation of a circle is given by x^2 + y^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, since there are no values for h and k given, we can assume that the center of the circle is at the origin (0, 0). Therefore, the equation x^2 + y^2 = 9 represents a circle with a radius of 3 units centered at the origin.