1.
What is (2^4)(2^0)?
Correct Answer
A. 2^4
Explanation
The given expression (2^4)(2^0) can be simplified by using the rule of exponents which states that when multiplying two numbers with the same base, you add the exponents. In this case, 2^4 represents 2 raised to the power of 4, which is 16. Since any number raised to the power of 0 is equal to 1, 2^0 equals 1. Therefore, (2^4)(2^0) simplifies to 16 * 1, which is equal to 16.
2.
What is the y-intercept of y = -4x + 1?
Correct Answer
B. 1
Explanation
The y-intercept of a linear equation is the point where the line intersects the y-axis. In the given equation, y = -4x + 1, the y-intercept can be found by setting x = 0 and solving for y. When x = 0, the equation becomes y = 1. This means that the line intersects the y-axis at the point (0, 1). Therefore, the correct answer is 1.
3.
What is 5!?
Correct Answer
C. 120
Explanation
The correct answer is 120 because 5! (read as "5 factorial") means multiplying all positive integers from 1 to 5. Therefore, 5! is equal to 5 x 4 x 3 x 2 x 1, which equals 120.
4.
What value of x will make "2x + 5 = 3x" a true statement?
Correct Answer
C. 5
Explanation
To make the equation "2x + 5 = 3x" true, we need to find the value of x that satisfies the equation. By subtracting 2x from both sides of the equation, we get 5 = x. Therefore, the value of x that makes the equation true is 5.
5.
What is the equation of a line with a slope of -2 and passing through (4, -1)?
Correct Answer
C. Y = -2x + 7
Explanation
The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2. Since the line passes through the point (4, -1), we can substitute these values into the equation. By solving for b, we find that b = 7. Therefore, the equation of the line is y = -2x + 7.
6.
What is the degree of -9x^4?
Correct Answer
C. 4
Explanation
The degree of a term in a polynomial is determined by the exponent of the variable. In this case, the term is -9x^4, where the exponent of x is 4. Therefore, the degree of -9x^4 is 4.
7.
What is the factored form of w(x + y) - z(x + y)?
Correct Answer
A. (w - z)(x + y)
Explanation
The given expression can be factored by using the distributive property. By factoring out the common factor of (x + y), we get (w - z)(x + y).
8.
What is the y-intercept of y = 3x?
Correct Answer
C. 0
Explanation
The y-intercept of a linear equation represents the point where the line intersects the y-axis. In the equation y = 3x, when x is 0, the value of y will also be 0. Therefore, the y-intercept is 0.
9.
What is (y^5)(y^0)?
Correct Answer
C. Y^5
Explanation
When multiplying variables with the same base, you add their exponents. In this case, y is raised to the power of 5 and y is raised to the power of 0. Any number raised to the power of 0 is equal to 1. Therefore, y^0 equals 1. So, when multiplying y^5 and y^0, the result is y^5.
10.
What is the equation of a line with a slope of -3 and a y-intercept of -1?
Correct Answer
A. Y = -3x - 1
Explanation
The equation of a line with a slope of -3 and a y-intercept of -1 is y = -3x - 1. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -3 and the y-intercept is -1, so the equation becomes y = -3x - 1.
11.
What kind of slope does y = 3x + 1 have?
Correct Answer
D. Positive
Explanation
The equation y = 3x + 1 represents a line with a positive slope. This means that as the value of x increases, the value of y also increases. The positive slope indicates that the line is ascending from left to right.
12.
What is the degree of 2x^2 - x - 1?
Correct Answer
A. 2
Explanation
The degree of a polynomial is determined by the highest power of the variable in the expression. In this case, the highest power of x is 2, so the degree of 2x^2 - x - 1 is 2.
13.
What is (3^5)/(3^3)?
Correct Answer
B. 3^2
Explanation
To find the value of (3^5)/(3^3), we can use the rule of exponents which states that when dividing two numbers with the same base, we subtract the exponents. In this case, we have 3^5 divided by 3^3. Subtracting the exponents, we get 3^(5-3) which simplifies to 3^2. Therefore, the correct answer is 3^2.
14.
If x = -28 and y = -61, what is " -x + 3(x - y) "?
Correct Answer
D. 127
Explanation
The given expression is "-x + 3(x - y)". Substituting the given values of x and y, we get "-(-28) + 3((-28) - (-61))". Simplifying this expression further, we have "28 + 3(33)". Multiplying 3 with 33 gives us 99. Adding 28 and 99 together results in 127. Therefore, the answer is 127.
15.
What is the slope of the line y = 2x - 3?
Correct Answer
C. 2
Explanation
The slope of a line is the coefficient of the x-term in its equation when it is in the form y = mx + b. In this equation, y = 2x - 3, the coefficient of the x-term is 2. Therefore, the slope of the line is 2.