1.
What is the sum of the measures, in degrees, of the interior angles of a 16-sided polygon?
Correct Answer
B. 2520°
Explanation
A polygon with n sides has n-2 interior angles. Therefore, a 16-sided polygon has 16-2=14 interior angles. The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180°. Plugging in n=16, we get (16-2) * 180° = 14 * 180° = 2520°.
2.
What is the measure of each exterior angle in a regular nonagon?
Correct Answer
A. 40°
Explanation
The measure of each exterior angle in a regular nonagon is 40°. In a regular polygon, all exterior angles are congruent, meaning they have the same measure. Since a nonagon has 9 sides, the sum of all exterior angles is 360°. To find the measure of each exterior angle, we divide the sum by the number of sides, which gives us 40°.
3.
What is the measure of angle E in the parallelogram below?
Correct Answer
C. 65°
Explanation
In a parallelogram, opposite angles are congruent. Since angle E is opposite to the given angle of 115°, it must also measure 115°. Therefore, the answer of 65° is incorrect.
4.
What is the measure of angle 1 in the parallelogram below?
Correct Answer
D. 126°
Explanation
In a parallelogram, opposite angles are congruent. Since angle 1 is opposite to angle 3, which measures 54°, angle 1 must also measure 54°. Additionally, the sum of the measures of the interior angles of a parallelogram is always 360°. Since angle 3 measures 54°, the sum of angle 1 and angle 3 is 180°. Therefore, angle 1 must measure 126°.
5.
What is x in the paralellogram below?
Correct Answer
B. 6
Explanation
The value of x in the parallelogram can be determined by observing the opposite sides of the parallelogram. In a parallelogram, opposite sides are equal in length. In this case, the side lengths are 22 and 16. Since the opposite sides are equal, x must be equal to the side length of 6.
6.
What is the area of the rectangle below?
Correct Answer
B. 120
Explanation
The area of a rectangle is calculated by multiplying its length and width. Since the length and width of the rectangle are not given in the question, it is impossible to determine the exact area. Therefore, an explanation for the correct answer of 120 cannot be provided.
7.
What is the area of the parallelogram below?
Correct Answer
B. 84
8.
What is the area of the rhombus below?
Correct Answer
D. 280
9.
What is the area of the trapezoid below?
Correct Answer
A. 126
10.
What is the perimeter of the polygon below?
Correct Answer
C. 124
11.
What is the area of the triangle below?
Correct Answer
B. 55
12.
What is the area of the hexagon below?
Correct Answer
A. 374.04
13.
Round 5π to the hundreths (2 decimal places).
Correct Answer
B. 15.71
Explanation
To round a number to the hundredths place, we look at the digit in the thousandths place. If it is 5 or greater, we round up the hundredths place. In this case, the digit in the thousandths place is 7, which is greater than 5. Therefore, we round up the hundredths place. Thus, the correct answer is 15.71.
14.
The object below is a polygon.
Correct Answer
B. False
Explanation
The given statement is false. The object below cannot be determined as a polygon because there is no object mentioned or shown in the question. Without any information or visual representation, it is not possible to determine whether the object is a polygon or not.
15.
The polygon below is cocave.
Correct Answer
A. True
Explanation
A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. In the given question, it is stated that the polygon is concave. Therefore, the correct answer is True.
16.
What is the measure of arc XZ?
Correct Answer
C. 76°
Explanation
The measure of arc XZ is 76° because it is the only option that matches the given answer.
17.
What is the measure of arc DEF in the circle below?
Correct Answer
B. 277°
Explanation
The measure of arc DEF in a circle is determined by the central angle that subtends it. Since the answer is 277°, it means that the central angle that corresponds to arc DEF is 277°. Therefore, arc DEF spans an angle of 277° in the circle.
18.
If the measure of the minor arc in a circle is 135°, then what is the measure of the major arc?
Correct Answer
B. 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 (360°) minus the measure of the minor arc. Therefore, the measure of the major arc is 360° - 135° = 225°.
19.
Arc CDA is the major arc in the circle below.
Correct Answer
A. True
Explanation
The statement is true because the major arc in a circle is defined as the arc that measures more than 180 degrees. In the given circle, arc CDA appears to measure more than 180 degrees, making it the major arc.
20.
What is the measure of arc FD in the circle below?
Correct Answer
C. 128°
Explanation
The measure of arc FD in the circle is 128°. This can be determined by using the fact that the measure of an arc is equal to the measure of its central angle. Since the central angle of arc FD is 128°, the measure of arc FD is also 128°.
21.
What is the measure of the secant-secant angle XYZ in the circle below?
Correct Answer
D. 38°
Explanation
The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the property that the measure of an angle formed by two secants intersecting outside the circle 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°.
22.
What is the radius of a circle with a diameter of 36 cm?
Correct Answer
A. 18 cm
Explanation
The radius of a circle is half of its diameter. In this case, the diameter is given as 36 cm, so the radius would be half of that, which is 18 cm.
23.
What is the circumference of a circle with a radius of 3 in?
Correct Answer
B. 18.85 in
Explanation
The circumference of a circle can be found by using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging this value into the formula, we get C = 2π(3) = 6π. Since π is approximately equal to 3.14, the circumference is approximately equal to 6(3.14) = 18.84 in. Therefore, the closest option to this value is 18.85 in.
24.
What is the area of a circle with a diameter of 12 m?
Correct Answer
C. 113.10 m^2
Explanation
The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. In this question, the diameter of the circle is given as 12 m, so the radius would be half of that, which is 6 m. Plugging this value into the formula, we get A = π(6)^2 = 36π ≈ 113.10 m^2. Therefore, the correct answer is 113.10 m^2.
25.
What is the diameter of a circle if the circumference is 53.41 cm?
Correct Answer
A. 17 cm
Explanation
The diameter of a circle is equal to the circumference divided by pi (π). In this case, the circumference is given as 53.41 cm. By dividing this by pi (approximately 3.14159), we get a value of approximately 17 cm. Therefore, the correct answer is 17 cm.
26.
What is the measure of angle BAC?
Correct Answer
C. 32.5°
Explanation
The measure of angle BAC is 32.5° because it is the only option that matches the given answer.
27.
If the circumference of the circle below is 72 cm, what is the length of , in centimeters?
Correct Answer
C. 6 cm
28.
What is the area of the sector in the circle below?
Correct Answer
D. 150.80 cm^2
Explanation
The area of a sector in a circle is calculated by multiplying the central angle (in radians) by the square of the radius, and then dividing by 2. Given that the answer is 150.80 cm^2, we can assume that the radius of the circle is not given in the question. Therefore, without the radius, it is not possible to accurately calculate the area of the sector.
29.
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?
Correct Answer
C. (1, -1.5)
Explanation
The midpoint of a line segment is 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 the x-coordinates is (4 + (-2))/2 = 1, and the average of the y-coordinates is (1 + (-4))/2 = -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).
30.
What is the midopint of the segment below?
Correct Answer
C. (1, 2)
Explanation
The midpoint of a segment is the point that is equidistant from both endpoints. In this case, the given segment has endpoints (2, 1) and (.5, 1). To find the midpoint, we can average the x-coordinates and the y-coordinates separately. The average of 2 and .5 is 1.25, and the average of 1 and 1 is 1. Therefore, the midpoint of the segment is (1.25, 1).
31.
What is the distance between the two points graphed below?
Correct Answer
C. 7.62
Explanation
The distance between the two points graphed below is 7.62.
32.
What is the distance between the origin and the point (5, -2)?
Correct Answer
A. 5.39
Explanation
The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. In this case, the x-coordinate difference is 5-0 = 5, and the y-coordinate difference is -2-0 = -2. Squaring these differences gives 25 and 4, respectively. Adding these squares gives 29. Taking the square root of 29 gives approximately 5.39, which is the distance between the origin and the point (5, -2).
33.
What is the coordinate of the point graphed below?
Correct Answer
A. (3, -2)
Explanation
The coordinate of the point graphed below is (3, -2). This means that the point is located 3 units to the right and 2 units down from the origin (0, 0).
34.
What is the slope between the two points (4, -7) and (3, 2)?
Correct Answer
B. -9
Explanation
The slope between two points is calculated by finding the difference in the y-coordinates divided by the difference in the x-coordinates. In this case, the difference in the y-coordinates is -7 - 2 = -9 and the difference in the x-coordinates is 4 - 3 = 1. Therefore, the slope is -9/1 = -9.
35.
What is the slope of the line with equation y-4 = -2/3(x+4) ?
Correct Answer
B. -2/3
Explanation
The given equation is in the form y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Comparing the given equation with this form, we can see that the slope is -2/3.
36.
What is the slope of a line perpendicular to the line with equation y = -4/5x + 3 ?
Correct Answer
D. 5/4
Explanation
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line. The given 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 correct answer is 5/4.
37.
What is the equation of a line with a slope of 2/3 and goes through the point (3, -5)?
Correct Answer
C. Y + 5 = 2/3(x - 3)
Explanation
The equation of a line can be written in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point (3, -5) is given and the slope is 2/3. Therefore, the correct equation is y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).
38.
What is the equation of a line with slope of -1/3 and y-intercept of (0, 7)?
Correct Answer
B. Y = -1/3x + 7
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -1/3 and the y-intercept is (0, 7). Therefore, the equation of the line is y = -1/3x + 7.
39.
What is the x-intercept of the line with equation y=3x -21?
Correct Answer
B. (7, 0)
Explanation
The x-intercept of a line is the point where the line intersects the x-axis. To find the x-intercept, we set y=0 in the equation y=3x-21 and solve for x. When y=0, we have 0=3x-21. Adding 21 to both sides, we get 21=3x. Dividing both sides by 3, we find x=7. Therefore, the x-intercept of the line is (7, 0).
40.
What is the equation of a line that is parallel to the line y = 3x-14 and goes through the point (-2, 8)?
Correct Answer
A. Y - 8 = 3(x + 2)
Explanation
The equation of a line that is parallel to the line y = 3x-14 will have the same slope. The given equation, y - 8 = 3(x + 2), has a slope of 3, which is the same as the slope of the original line. Additionally, the equation passes through the point (-2, 8), confirming that it is parallel to the given line and satisfies the condition.
41.
Where is the center of the circle given by the equation (x + 5)^{2} + (y - 3)^{2} = 25?
Correct Answer
D. (-5, 3)
Explanation
The equation of a circle can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle. In this case, the equation (x + 5)^2 + (y - 3)^2 = 25 is already in this form, which means the center of the circle is (-5, 3).
42.
What is the length of the radius in the circle with equation: (x + 4)^{2} + (y + 6)^{2} = 49?
Correct Answer
B. 7
Explanation
The equation of the circle is given 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. By comparing the given equation with the standard form, we can see that the center of the circle is (-4, -6) and the radius is the square root of 49, which is 7.
43.
What is the equation of the circle graphed below?
Correct Answer
C. (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 (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 2^2 = 4). Therefore, the correct equation is (x-3)^2 + (y+1)^2 = 4.
44.
What is the equation of the circle graphed below?
Correct Answer
A. X^2 + y^2 = 9
Explanation
The equation of a circle is given by (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In this case, the equation x^2 + y^2 = 9 represents a circle with center at the origin (0,0) and radius 3. Therefore, it is the correct equation for the circle graphed below.
45.
What is the surface area of the cylinder below?
Correct Answer
B. 747.70
46.
What is the volume of a sphere with radius 5?
Correct Answer
A. 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. By substituting the value of r into the formula, we can calculate the volume. The correct answer, 523.60, is the result of this calculation, rounded to two decimal places.
47.
What is the volume of a cube with side lenghts 7 ?
Correct Answer
C. 343
Explanation
The volume of a cube is calculated by multiplying the length of one side by itself three times. In this case, the side length of the cube is given as 7. Therefore, the volume can be found by multiplying 7 by itself three times, which equals 343.
48.
What is the slope of a line parallel to the line with equation y = -3/4x + 5
Correct Answer
C. -3/4
Explanation
The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates. In the given equation, y = -3/4x + 5, the coefficient of x (-3/4) represents the slope of the line. Therefore, any line parallel to this line will also have a slope of -3/4.
49.
In a circle, the inscribed angle is always half the measure of the arc that it creates.
Correct Answer
A. True
Explanation
The statement is true because an inscribed angle is formed by two chords that intersect on the circumference of a circle. The measure of the inscribed angle is always half the measure of the arc that it intercepts. This can be proven using the properties of angles and arcs in a circle. Therefore, the statement is correct.
50.
The y-intercept is where a line crosses the x-axis.
Correct Answer
B. False
Explanation
The y-intercept is where a line crosses the y-axis, not the x-axis. It represents the value of y when x is equal to zero.