1.
What percent of a circle is 75 degrees?
Correct Answer
B. 20.83%
Explanation
The measure of an angle in a circle is directly proportional to the percentage of the circle it represents. Since 75 degrees is 20.83% of 360 degrees (a full circle), the correct answer is 20.83%.
2.
Which expression represents the use of the distributive property on 3(a + b)?
Correct Answer
D. 3a + 3b
Explanation
The expression 3(a + b) represents the use of the distributive property because the 3 is being multiplied to both terms inside the parentheses. This means that the 3 is being distributed or distributed across both a and b. Therefore, the correct answer is 3a + 3b.
3.
What is the greatest common factor of 9x, 3y, and 12z?
Correct Answer
C. 3
Explanation
The greatest common factor (GCF) is the largest number that divides evenly into all of the given terms. In this case, the GCF of 9x, 3y, and 12z is 3 because it is the largest number that can divide evenly into all of them. Each term has a factor of 3, so it is the common factor among them. Therefore, the correct answer is 3.
4.
What value of x makes "-6x = -42" a true statement?
Correct Answer
A. 7
Explanation
To find the value of x that makes "-6x = -42" a true statement, we need to solve the equation. By dividing both sides of the equation by -6, we get x = 7. Substituting x = 7 back into the equation, we have -6(7) = -42, which is true. Therefore, the correct answer is 7.
5.
What is the slope of y = -4x + 1?
Correct Answer
C. -4
Explanation
The slope of a linear equation in the form y = mx + b represents the rate at which y changes with respect to x. In this equation, the coefficient of x is -4, which means that for every increase of 1 in x, y decreases by 4. Therefore, the slope of y = -4x + 1 is -4.
6.
What value of x makes 4x - 2 = 2(x + 1) a true statement?
Correct Answer
D. 2
Explanation
To find the value of x that makes the equation true, we need to solve for x. By distributing 2 to (x + 1), we get 4x - 2 = 2x + 2. Combining like terms, we have 2x = 4. Dividing both sides by 2, we find that x = 2. Therefore, the value of x that makes the equation true is 2.
7.
What is the square root of 28 in simplified form?
Correct Answer
C. 2 Times The Square Root of 7
Explanation
The square root of 28 can be simplified as 2 times the square root of 7. This is because 28 can be factored into 2 times 2 times 7, and the square root of 2 times 2 is 2, while the square root of 7 remains as it is. Therefore, the simplified form of the square root of 28 is 2 times the square root of 7.
8.
What is the solution of 4x - 7(x - 1) > 3(x + 1)?
Correct Answer
A. X < 2/3
Explanation
To solve the given inequality, we first distribute the -7 and 3 to the terms inside the parentheses. This gives us 4x - 7x + 7 > 3x + 3. Simplifying further, we combine like terms to get -3x + 7 > 3x + 3. Next, we subtract 3x from both sides to isolate the variable. This gives us -6x + 7 > 3. Then, we subtract 7 from both sides to further isolate the variable. This gives us -6x > -4. Finally, we divide both sides by -6, remembering to flip the inequality sign since we are dividing by a negative number. This gives us x < 2/3 as the solution to the inequality.
9.
What value of x makes "2x + 3 = 15" a true statement?
Correct Answer
D. 6
Explanation
To find the value of x that makes the equation "2x + 3 = 15" true, we need to solve for x. Subtracting 3 from both sides of the equation gives us 2x = 12. Dividing both sides by 2 gives us x = 6. Therefore, the value of x that makes the equation true is 6.
10.
What kind of slope does the line 3x - 2y = 6 have?
Correct Answer
D. Positive
Explanation
The line 3x - 2y = 6 can be rewritten as y = (3/2)x - 3. In this form, the coefficient of x is positive, indicating that the line has a positive slope. This means that as x increases, y also increases, and as x decreases, y decreases. Therefore, the correct answer is positive.
11.
What kind of slope does the line "3x + 2y = 6" have?
Correct Answer
B. Negative
Explanation
The line "3x + 2y = 6" has a negative slope. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. By isolating y, we get y = -3/2x + 3. The negative coefficient of x indicates that the slope is negative.
12.
If x = 4, what is 3^x (3 to the power of x)?
Correct Answer
B. 81
Explanation
When x = 4, 3^x (3 to the power of x) can be calculated by raising 3 to the power of 4. This can be done by multiplying 3 by itself 4 times. Therefore, 3^4 equals 81.
13.
What kind of slope does y = 4 have?
Correct Answer
D. Zero
Explanation
The equation y = 4 represents a horizontal line that is parallel to the x-axis. Since the slope of a horizontal line is always zero, the correct answer is zero.
14.
What is the y-intercept of 4x + 2y = -8?
Correct Answer
D. (0, -4)
Explanation
The y-intercept is the point where the graph of a function crosses the y-axis. To find the y-intercept of the equation 4x + 2y = -8, we set x = 0 and solve for y. When x = 0, the equation becomes 2y = -8, which gives us y = -4. Therefore, the y-intercept is (0, -4).
15.
What is the midpoint of the line segment with endpoints at (-1, 1) and (7, -3)?
Correct Answer
B. (3, -1)
Explanation
The midpoint of a line segment is the point that is equidistant from both endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (-1 + 7)/2 = 3 and the y-coordinate is (1 + -3)/2 = -1. Therefore, the midpoint of the line segment with endpoints at (-1, 1) and (7, -3) is (3, -1).