1.
What value of x makes 8x - 5(x - 2) = x + 26 a true statement?
Correct Answer
C. 8
Explanation
To find the value of x that makes the equation true, we need to simplify both sides of the equation. Starting with the left side, we distribute the -5 to the terms inside the parentheses: 8x - 5x + 10. Simplifying further, we combine like terms: 3x + 10. Now we have the equation 3x + 10 = x + 26. To isolate x, we subtract x from both sides: 2x + 10 = 26. Then, we subtract 10 from both sides: 2x = 16. Finally, we divide both sides by 2 to solve for x: x = 8. Therefore, the correct answer is 8.
2.
What is the Greatest Common Factor of 14 and 24?
Correct Answer
A. 2
Explanation
The greatest common factor (GCF) is the largest number that divides evenly into both 14 and 24. In this case, the GCF of 14 and 24 is 2 because it is the largest number that can divide evenly into both 14 (2 x 7) and 24 (2 x 2 x 2 x 3).
3.
If you can drive 390 miles in 6 hours, how many miles can you drive in 9 hours?
Correct Answer
D. 585
Explanation
If you can drive 390 miles in 6 hours, it means that your average speed is 65 miles per hour (390 miles divided by 6 hours). To find out how many miles you can drive in 9 hours, you can multiply your average speed by the number of hours. Therefore, 65 miles per hour multiplied by 9 hours equals 585 miles.
4.
What is 3x + (-3x)?
Correct Answer
C. 0
Explanation
The expression 3x + (-3x) simplifies to 0 because the terms 3x and -3x cancel each other out. When we add a positive quantity and its negative counterpart, the result is always zero. Therefore, the correct answer is 0.
5.
What is -2 + (-8)?
Correct Answer
A. -10
Explanation
To find the sum of -2 and -8, we add the two numbers together. Since both numbers are negative, their sum will also be negative. When we add -2 and -8, we get -10.
6.
What is 0.14 - (-0.13)?
Correct Answer
D. 0.27
Explanation
The expression 0.14 - (-0.13) can be simplified by changing the double negative into a positive. Therefore, -(-0.13) becomes 0.13. Subtracting 0.13 from 0.14 gives us a final answer of 0.27.
7.
What kind of equation is "4^2 = 16"?
Correct Answer
C. Exponential
Explanation
The equation "4^2 = 16" is an example of an exponential equation. In this equation, the base is 4 and the exponent is 2. The equation represents the exponential growth of 4 raised to the power of 2, which equals 16. Exponential equations involve a variable raised to a power, where the variable represents the quantity that is growing or decaying exponentially.
8.
What is the reciprocal of 1/3?
Correct Answer
B. 1-Mar
Explanation
The reciprocal of a fraction is obtained by flipping the numerator and denominator. In this case, the reciprocal of 1/3 would be 3/1, which is equivalent to 3. Therefore, the correct answer is 3.
9.
What is "x + 5"?
Correct Answer
A. An Expression
Explanation
The expression "x + 5" represents a mathematical statement that combines the variable x with the constant 5 using the addition operation. It does not equate to a specific value, but rather represents a general mathematical relationship. Therefore, the correct answer is "An Expression."
10.
What does "ASA" stand for in geometry?
Correct Answer
D. Angle-Side-Angle
Explanation
"ASA" stands for Angle-Side-Angle in geometry. This refers to a postulate or a rule that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. This means that the two triangles have the same shape and size.
11.
What value of x makes "3x = x" a true statement?
Correct Answer
B. 0
Explanation
The value of x that makes "3x = x" a true statement is 0. This is because when we substitute x with 0 in the equation, we get 3(0) = 0, which simplifies to 0 = 0. Since both sides of the equation are equal, the statement is true.
12.
For what values of x does the absolute value of x-1 equal 2?
Correct Answer
B. 3, -1
Explanation
The absolute value of a number is always positive, so to find the values of x that make the absolute value of x-1 equal to 2, we need to find the values of x that are 2 units away from 1. This means that x can be either 3 or -1, as both of these values are 2 units away from 1 on the number line.
13.
What is -2(6)?
Correct Answer
B. -12
Explanation
To find -2(6), we multiply -2 by 6. When we multiply a negative number by a positive number, the result is always negative. Therefore, -2(6) equals -12.
14.
What types of numbers are greater than zero?
Correct Answer
A. Positive
Explanation
Positive numbers are greater than zero because they are numbers that are greater than zero and do not have a negative sign. Positive numbers can be whole numbers, decimal numbers, or fractions as long as they are greater than zero. Real numbers include both positive and negative numbers, so they are not exclusively greater than zero. Integer numbers include both positive and negative whole numbers, so they are also not exclusively greater than zero. Negative numbers are less than zero, so they are not greater than zero.
15.
What power does scientific notation deal with?
Correct Answer
C. 10
Explanation
Scientific notation deals with expressing numbers in the form of a coefficient multiplied by 10 raised to a power. The correct answer is "10" because it represents the power in scientific notation.