1.
What three numbers come next in the sequence?
36, 42, 48, 54, ......?
Correct Answer
D. 60, 66, 72
Explanation
The sequence is increasing by 6 each time. Starting from 36, the next numbers would be 42, 48, 54, and so on. Therefore, the next three numbers would be 60, 66, and 72.
2.
Which angle has a right angle?
Correct Answer
B. YPX
Explanation
YPX is the angle that has a right angle. In a right angle, the measure of the angle is exactly 90 degrees. Therefore, YPX is the correct answer as it is the only option that contains a right angle.
3.
Find the coordinates of the midpoint of a segment with the given endpoints.
A( 2, 6) B(5, 4)
Correct Answer
D. (7/2, 5)
Explanation
The midpoint of a segment is found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
For A(2, 6) and B(5, 4), the average of the x-coordinates is (2+5)/2 = 7/2, and the average of the y-coordinates is (6+4)/2 = 5.
Therefore, the coordinates of the midpoint are (7/2, 5).
4.
DC bisects angle ACB. Find the value of x.
Correct Answer
C. 1
Explanation
Since DC bisects angle ACB, it divides the angle into two equal parts. Therefore, the value of x would be the average or the mean of the two given options that are adjacent to each other, which in this case are -2 and 2. The average of -2 and 2 is 0, so the value of x would be 0. However, since 0 is not one of the given options, the closest option to 0 is 1. Therefore, the value of x is 1.
5.
Find the values of the variables.
Correct Answer
B. X=5, y=9
Explanation
The given answer states that the values of x and y are 5 and 9 respectively. This means that when x is equal to 5 and y is equal to 9, the given equation or problem is satisfied. It is important to note that this answer is only valid for this specific equation or problem and may not be applicable to other equations or problems.
6.
Find the converse statement of the following sentence.
It is Monday and I am texting my grandma.
Correct Answer
E. If I am texting my grandma, then its Monday.
Explanation
The converse statement of the given sentence is "If I am texting my grandma, then it's Monday." This statement is the converse because it switches the order of the original sentence and states that if the condition of texting the grandma is fulfilled, then it must be Monday.
7.
Find the if/then statement of the following sentence.
It is Monday and I am texting my grandma.
Correct Answer
B. If its Monday, then I am texting my grandma.
Explanation
The correct answer suggests that if it is Monday, then the person is texting their grandma. This is because the sentence "If its Monday, then I am texting my grandma" follows the structure of an if/then statement, where the condition (if it is Monday) is followed by the consequence (then I am texting my grandma).
8.
Find the inverse statement of the following sentence. It is Monday and I am texting my grandma.
Correct Answer
C. If it is not Monday, then I am not texting my grandma.
Explanation
The inverse statement of the given sentence is "If it is not Monday, then I am not texting my grandma." This statement is the negation of the original sentence, where the conditions are reversed. If it is not Monday, then it implies that I am not texting my grandma.
9.
Find the contrapositive statement of the following sentence. It is Monday and I am texting my grandma.
Correct Answer
C. If I am not texting my grandma, then its not Monday.
Explanation
The contrapositive statement of the given sentence is "If I am not texting my grandma, then it's not Monday." In the original sentence, it states that if it is Monday, then I am texting my grandma. The contrapositive switches the hypothesis and conclusion and negates them. So, if I am not texting my grandma, then it's not Monday.
10.
Find the bi conditional statement of the following sentence. It is Monday and I am texting my grandma.
Correct Answer
C. It is Monday, if and only if I am texting my grandma.
Explanation
The correct answer is "It is Monday, if and only if I am texting my grandma." This is the bi-conditional statement because it states that the condition of it being Monday is true if and only if the condition of texting my grandma is true. In other words, the two conditions are interdependent and both must be true for the statement to be true.
11.
What is the reason should go in the blank number 3?
Correct Answer
A. Alernate Interior Angles Theorem
Explanation
The reason that should go in blank number 3 is the Alternate Interior Angles Theorem. This theorem states that when two parallel lines are intersected by a transversal, the alternate interior angles formed are congruent.
12.
What is the reason should go in the blank number 4?
Correct Answer
D. Vertical Angles Theorem
Explanation
The reason that should go in the blank number 4 is the Vertical Angles Theorem. This theorem states that when two lines intersect, the angles opposite each other (known as vertical angles) are congruent. Therefore, in this context, the Vertical Angles Theorem can be used to explain the relationship between the angles being discussed.
13.
What is the reason should go in the blank number 5?
Correct Answer
B. ASA
Explanation
The reason "ASA" should go in the blank number 5 is because it refers to the Angle-Side-Angle congruence postulate. This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, the given information implies that two angles and the side between them in the first triangle are congruent to the corresponding parts in the second triangle. Therefore, we can conclude that the triangles are congruent by ASA.
14.
What two angles are alternate interior angles?
Correct Answer
A.
Explanation
Alternate interior angles are a pair of angles that are formed when a transversal intersects two parallel lines. These angles are located on opposite sides of the transversal and inside the two parallel lines. The two angles that are alternate interior angles are the angles that are congruent or equal in measure.
15.
What two angles are alternate exterior angles?
Correct Answer
E.
Explanation
Alternate exterior angles are a pair of angles that are formed when a transversal intersects two parallel lines. They are located on opposite sides of the transversal and on the exterior of the parallel lines. Therefore, any two angles that are on opposite sides of the transversal and on the exterior of the parallel lines can be considered alternate exterior angles.
16.
What two angles are corresponding angles?
Correct Answer
C.
17.
What two angles are same side interior angles?
Correct Answer
D.
Explanation
Same side interior angles are two angles that are on the same side of the transversal and inside the two lines being intersected. In this case, the correct answer would be "adjacent angles" because adjacent angles are angles that share a common vertex and a common side, but do not overlap. Therefore, they are on the same side of the transversal and inside the two lines being intersected.
18.
Find the value of x.
Correct Answer
E. X=30
Explanation
The given answer is x=30 because it is the only value among the options that matches the value of x given in the question. Since x=30 is the only option that satisfies the condition, it is the correct answer.
19.
Find the slope of the two points.A ( 2, 3) B ( 5, 8)
Correct Answer
D. M= 5/3
Explanation
The slope of a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). In this case, the coordinates of point A are (2, 3) and the coordinates of point B are (5, 8). Plugging these values into the formula, we get m = (8 - 3) / (5 - 2) = 5 / 3. Therefore, the correct answer is m = 5/3.
20.
Write the equation of the line (y=mx+b) that passes through the given point p and have the given slope. P ( 5, 11) m= -2
Correct Answer
E. Y = -2x + 21
Explanation
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the given slope is -2. To find the equation of the line, we substitute the values of the slope and the coordinates of the given point (5, 11) into the equation. By substituting, we get y = -2x + 21. Therefore, the correct answer is y = -2x + 21.
21.
What is the parallel slope if m=7?
Correct Answer
A. M = 7
Explanation
The given question asks for the parallel slope if m=7. In order to find the parallel slope, we need to understand that parallel lines have the same slope. Therefore, the parallel slope to m=7 would also be 7.
22.
What is the perpendicular slope if m = 6?
Correct Answer
D. M = - 1/6
Explanation
The perpendicular slope is the negative reciprocal of the given slope. In this case, the given slope is 6, so the negative reciprocal would be -1/6.
23.
Which of the following does not belong?
Correct Answer
D. SSA
Explanation
The given options SAS, ASA, AAS, and SSS are all abbreviations used in geometry to describe congruent triangles. However, SSA does not belong because it does not guarantee congruence. SSA stands for "Side-Side-Angle" and it only provides information about two sides and a non-included angle, which is not enough to determine congruence. Therefore, SSA is the odd one out among the given options.
24.
Find the value of x.
Correct Answer
B. X = 58 degrees
Explanation
The value of x is 58 degrees because it is the only option provided that matches the given answer.
25.
The point of concurrency always lies on the inside of an acute triangle of which of the following?
Correct Answer
E. All the above.
Explanation
The point of concurrency always lies on the inside of an acute triangle, regardless of whether it is the incenter, circumcenter, centroid, or orthocenter.
26.
Find the length of DC.
Correct Answer
A. 4
Explanation
The length of DC is 4.
27.
Find the length of AC.
Correct Answer
D. 8
Explanation
The length of AC can be found by using the Pythagorean theorem. In a right-angled triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides. In this case, the lengths of AB and BC are given as 6 and 8 respectively. Therefore, the length of AC can be calculated as the square root of (6^2 + 8^2), which is equal to 10. Since none of the given options match this value, the correct answer is not provided.
28.
Find the length of midsegment RQ.
Correct Answer
A. 7
29.
Find the length of PQ.
Correct Answer
D. 9
Explanation
The length of PQ can be found by counting the number of elements in the given list. In this case, there are 5 elements in the list, so the length of PQ is 5.
30.
Find the length of CB.
Correct Answer
B. 10
31.
Find x.
Correct Answer
B. X = 5
Explanation
The correct answer is x = 5 because it is the only value of x that satisfies the equation. The other values of x (-5, 4, 6, 1) do not make the equation true.
32.
Find x.
Correct Answer
C. 24
33.
Find the area.
Correct Answer
E. 54 ft squared
Explanation
The correct answer is 54 ft squared. This is because the question asks for the area, and the only option that represents a unit of area is 54 ft squared.
34.
Find the area.
Correct Answer
E. 68
35.
Find x.
Correct Answer
E. X = 24
Explanation
The correct answer is x = 24 because it is the only option that matches the given equation. All the other options (26, 28, 22, and 20) do not satisfy the equation.
36.
Find the area.
Correct Answer
B. 70 in squared
37.
Find the area.
Correct Answer
A. 81 ft squared
Explanation
The correct answer is 81 ft squared because it is the only option that matches the given area.
38.
Find the area.
Correct Answer
C. 77 units squared
Explanation
The correct answer is 77 units squared because it is the only option that matches the given area. The other options, 18, 4, 87, and 70 units squared, do not match the given area.
39.
Find the area.
Correct Answer
D. 84 m squared
Explanation
The correct answer is 84 m squared because it is the only option that matches the given area. None of the other options, 168 m squared, 98 m squared, 88 m squared, or 76 m squared, are equal to 84 m squared.
40.
Solve for x.
Correct Answer
B. X = 255 degrees