Exam For The Second Semester Of Geometry
This is your final exam for the second semester of Geometry. You may use the formula sheet provided to you to answer any of the questions, but you may not use any notes or the internet.
Questions and Answers
- 1.
What is the sum of the measures, in degrees, of the interior angles of a 16-sided polygon?
- A.
360°
- B.
2520°
- C.
2880°
- D.
22.5°
Correct Answer
B. 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°.Rate this question:
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- 2.
What is the measure of each exterior angle in a regular nonagon?
- A.
40°
- B.
360°
- C.
0°
- D.
1260°
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. 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.Rate this question:
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- 3.
What is the measure of angle E in the parallelogram below?
- A.
115°
- B.
295°
- C.
65°
- D.
180°
Correct Answer
C. 65°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.Rate this question:
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- 4.
What is the measure of angle 1 in the parallelogram below?
- A.
180°
- B.
306°
- C.
54°
- D.
126°
Correct Answer
D. 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°.Rate this question:
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- 5.
What is x in the parallelogram below?
- A.
22
- B.
6
- C.
16
- D.
10
Correct Answer
B. 6Explanation
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.Rate this question:
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- 6.
What is the area of the rectangle below?
- A.
60
- B.
120
- C.
46
- D.
240
Correct Answer
B. 120 -
- 7.
What is the area of the parallelogram below?
- A.
168
- B.
84
- C.
42
- D.
38
Correct Answer
B. 84 -
- 8.
What is the area of the rhombus below?
- A.
140
- B.
560
- C.
96
- D.
280
Correct Answer
D. 280 -
- 9.
What is the area of the trapezoid below?
- A.
126
- B.
252
- C.
108
- D.
144
Correct Answer
A. 126 -
- 10.
What is the perimeter of the polygon below?
- A.
142
- B.
106
- C.
124
- D.
143
Correct Answer
C. 124 -
- 11.
What is the area of the triangle below?
- A.
220
- B.
55
- C.
110
- D.
21
Correct Answer
B. 55Explanation
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.Rate this question:
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- 12.
What is the area of the hexagon below?
- A.
374.04
- B.
748.08
- C.
72
- D.
124.68
Correct Answer
A. 374.04 -
- 13.
Round 5π to the hundreths (2 decimal places).
- A.
15.70
- B.
15.71
- C.
15.81
- D.
15.80
Correct Answer
B. 15.71Explanation
The number 5π is approximately 15.71 when rounded to the nearest hundredth.Rate this question:
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- 14.
The object below is a polygon.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
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.Rate this question:
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- 15.
The polygon below is concave.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
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.Rate this question:
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- 16.
What is the measure of arc XZ?
- A.
284°
- B.
104°
- C.
76°
- D.
152°
Correct Answer
C. 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°.Rate this question:
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- 17.
What is the measure of arc DEF in the circle below?
- A.
83°
- B.
277°
- C.
97°
- D.
166°
Correct Answer
B. 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°.Rate this question:
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- 18.
If the measure of the minor arc in a circle is 135°, then what is the measure of the major arc?
- A.
135°
- B.
225°
- C.
270°
- D.
67.5
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 minus the measure of the minor arc. Since a circle has 360°, the measure of the major arc would be 360° - 135° = 225°.Rate this question:
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- 19.
Arc CDA is the major arc in the circle below.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
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.Rate this question:
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- 20.
What is the measure of arc FD in the circle below?
- A.
64°
- B.
32°
- C.
128°
- D.
180°
Correct Answer
C. 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°.Rate this question:
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- 21.
What is the measure of the secant-secant angle XYZ in the circle below?
- A.
150°
- B.
75°
- C.
76°
- D.
38°
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 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°.Rate this question:
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- 22.
What is the radius of a circle with a diameter of 36 cm?
- A.
18 cm
- B.
36 cm
- C.
72 cm
- D.
113.1 cm
Correct Answer
A. 18 cmExplanation
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.Rate this question:
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- 23.
What is the circumference of a circle with a radius of 3 in?
- A.
9.42 in
- B.
18.85 in
- C.
6 in
- D.
28.27 in
Correct Answer
B. 18.85 inExplanation
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.Rate this question:
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- 24.
What is the area of a circle with a diameter of 12 m?
- A.
452.39 m^2
- B.
37.70 m^2
- C.
113.10 m^2
- D.
18.85 m^2
Correct Answer
C. 113.10 m^2Explanation
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.Rate this question:
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- 25.
What is the diameter of a circle if the circumference is 53.41 cm?
- A.
17 cm
- B.
8.5 cm
- C.
167.79 cm
- D.
12 cm
Correct Answer
A. 17 cmExplanation
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.Rate this question:
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- 26.
What is the measure of angle BAC?
- A.
130°
- B.
65°
- C.
32.5°
- D.
38°
Correct Answer
C. 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°.Rate this question:
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- 27.
If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?
- A.
21.6 cm
- B.
864 cm
- C.
6 cm
- D.
30 cm
Correct Answer
C. 6 cmExplanation
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.Rate this question:
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- 28.
What is the area of the sector in the circle below?
- A.
26 cm^2
- B.
4 cm^2
- C.
1357.17 cm^2
- D.
150.80 cm^2
Correct Answer
D. 150.80 cm^2 -
- 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?
- A.
(3, 2,5)
- B.
(2, -3)
- C.
(1, -1.5)
- D.
(6, 5)
Correct Answer
C. (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).Rate this question:
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- 30.
What is the midpoint of the segment below?
- A.
(2, 1)
- B.
(2, 4)
- C.
(1, 2)
- D.
(.5, 1)
Correct Answer
C. (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).Rate this question:
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- 31.
What is the distance between the two points graphed below?
- A.
4.53
- B.
1.41
- C.
7.62
- D.
3.16
Correct Answer
C. 7.62Explanation
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.Rate this question:
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- 32.
What is the distance between the origin and the point (5, -2)?
- A.
5.39
- B.
7
- C.
2.65
- D.
1.73
Correct Answer
A. 5.39Explanation
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.Rate this question:
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- 33.
What is the coordinate of the point graphed below?
- A.
(3, -2)
- B.
(-3, -2)
- C.
(-2, 3)
- D.
(3, 2)
Correct Answer
A. (3, -2)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.Rate this question:
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- 34.
What is the slope between the two points (4, -7) and (3, 2)?
- A.
-1/9
- B.
-9
- C.
-3
- D.
-5/7
Correct Answer
B. -9Explanation
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.Rate this question:
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- 35.
What is the slope of the line with equation y-4 = -2/3(x+4) ?
- A.
4
- B.
-2/3
- C.
3
- D.
3/2
Correct Answer
B. -2/3Explanation
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.Rate this question:
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- 36.
What is the slope of a line perpendicular to the line with equation y = -4/5x + 3 ?
- A.
3
- B.
5
- C.
-4/5
- D.
5/4
Correct Answer
D. 5/4Explanation
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.Rate this question:
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- 37.
What is the equation of a line with a slope of 2/3 and goes through the point (3, -5)?
- A.
Y - 5 = 2/3(x - 3)
- B.
Y = 2/3x - 5
- C.
Y + 5 = 2/3(x - 3)
- D.
Y = 2/3(x - 3)
Correct Answer
C. 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).Rate this question:
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- 38.
What is the equation of a line with slope of -1/3 and y-intercept of (0, 7)?
- A.
Y - 0 = -1/3(x - 7)
- B.
Y = -1/3x + 7
- C.
Y - 1/3 = 7x
- D.
Y = 7x - 1/3
Correct Answer
B. Y = -1/3x + 7Explanation
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.Rate this question:
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- 39.
What is the x-intercept of the line with equation y=3x -21?
- A.
(-21, 0)
- B.
(7, 0)
- C.
(3, 0)
- D.
(0, -21)
Correct Answer
B. (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).Rate this question:
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- 40.
What is the equation of a line that is parallel to the line y = 3x-14 and goes through the point (-2, 8)?
- A.
Y - 8 = 3(x + 2)
- B.
Y = 2x - 8
- C.
Y - 8 = 3x
- D.
Y = 3x + 2
Correct Answer
A. 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).Rate this question:
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- 41.
Where is the center of the circle given by the equation (x + 5)2 + (y - 3)2 = 25?
- A.
(5, -3)
- B.
(5, 3)
- C.
(3, -5)
- D.
(-5, 3)
Correct Answer
D. (-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).Rate this question:
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- 42.
What is the length of the radius in the circle with equation: (x + 4)2 + (y + 6)2 = 49?
- A.
49
- B.
7
- C.
4
- D.
6
Correct Answer
B. 7Explanation
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.Rate this question:
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- 43.
What is the equation of the circle graphed below?
- A.
(x-3)^2 + (y+1)^2 = 2
- B.
(x+3)^2 + (y-1)^2 = 4
- C.
(x-3)^2 + (y+1)^2 = 4
- D.
(x+3)^2 + (y-1)^2 = 2
Correct Answer
C. (x-3)^2 + (y+1)^2 = 4Explanation
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.Rate this question:
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- 44.
What is the equation of the circle graphed below?
- A.
X^2 + y^2 = 9
- B.
X^2 + y^2 = 3
- C.
(x+3)^2 + (y-3)^2 = 9
- D.
(x-3)^2 + (y-3)^2 = 3
Correct Answer
A. X^2 + y^2 = 9Explanation
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.Rate this question:
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- 45.
What is the surface area of the cylinder below?
- A.
140
- B.
747.70
- C.
1539.38
- D.
2111.15
Correct Answer
B. 747.70 -
- 46.
What is the volume of a sphere with radius 5?
- A.
523.60
- B.
104.72
- C.
580.49
- D.
314.16
Correct Answer
A. 523.60Explanation
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.Rate this question:
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- 47.
What is the volume of a cube with side lengths of 7 ?
- A.
42
- B.
49
- C.
343
- D.
276
Correct Answer
C. 343Explanation
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.Rate this question:
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- 48.
What is the slope of a line parallel to the line with equation y = -3/4x + 5
- A.
4
- B.
3/4
- C.
-3/4
- D.
5
Correct Answer
C. -3/4Explanation
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.Rate this question:
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- 49.
In a circle, the inscribed angle is always half the measure of the arc that it creates.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
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.Rate this question:
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- 50.
The y-intercept is where a line crosses the x-axis.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The y-intercept is actually where a line crosses the y-axis, not the x-axis.Rate this question:
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.bmp "What is the area of the hexagon below?")
.bmp "What is the measure of arc XZ?")
.bmp "Arc CDA is the major arc in the circle below.")
.bmp "What is the measure of arc FD in the circle below?")
.bmp "If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?")
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.bmp "What is the distance between the two points graphed below?")
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