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Correct Answer C. 3x<sup style="color: rgb(0, 0, 0); font-family: 'Times New Roman';">2 + 10x - 8
Explanation The given expression is a product of two binomials, (3x - 2) and (x + 4). To find the equivalent trinomial, we need to multiply these binomials. Using the distributive property, we multiply each term of the first binomial by each term of the second binomial. This gives us 3x * x + 3x * 4 - 2 * x - 2 * 4. Simplifying this expression, we get 3x^2 + 12x - 2x - 8. Combining like terms, we have 3x^2 + 10x - 8, which matches the correct answer.
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4.
What is the value of y in the equation 2(3y - 4) = 10
A.
1
B.
0
C.
3
D.
7
Correct Answer C. 3
Explanation To find the value of y in the given equation, we need to solve for y. We can start by simplifying the equation. Distributing the 2 on the left side of the equation gives us 6y - 8 = 10. Next, we can isolate the y term by adding 8 to both sides of the equation, resulting in 6y = 18. Finally, by dividing both sides of the equation by 6, we find that y = 3.
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5.
The additive inverse of -10 is 10.
A.
True
B.
False
Correct Answer A. True
Explanation The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. In this case, the additive inverse of -10 would be a number that, when added to -10, gives a sum of zero. Since 10 + (-10) equals zero, 10 is the additive inverse of -10. Therefore, the statement is true.
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6.
"x is at most equal to 9" is written mathematically as x < 9.
A.
True
B.
False
Correct Answer B. False
Explanation The statement "x is at most equal to 9" means that x can be equal to 9 or any value less than 9. However, the mathematical representation of this statement should be x ≤ 9, not x < 9. The symbol ≤ represents "less than or equal to" while < represents "less than". Therefore, the given statement is incorrect.
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7.
The _______ of a line is a number that measures its "steepness", usually denoted by letter m.
Correct Answer slope
Explanation The slope of a line is a number that measures its "steepness", usually denoted by letter m. It indicates how much the y-coordinate changes for every unit increase in the x-coordinate. A positive slope means the line is increasing from left to right, while a negative slope means the line is decreasing. The slope can also be used to determine whether a line is horizontal (slope = 0), vertical (undefined slope), or diagonal.
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8.
A set of points in a space is ________ if all the points lie in the same plane.
Correct Answer coplanar
Explanation A set of points in a space is considered coplanar if all the points lie in the same plane. This means that the points can be contained within a flat, two-dimensional surface, and there are no points that are outside of this plane. Therefore, the term "coplanar" is used to describe this arrangement of points in space.
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9.
Which property is illustrated by the equation (a + b) + c = c + (a + b) ?
A.
Associative
B.
Commutative
C.
Distributive
D.
Identity
Correct Answer B. Commutative
Explanation The equation (a + b) + c = c + (a + b) demonstrates the commutative property. This property states that the order of addition does not affect the result. In this case, regardless of whether we add a and b first or c first, the result will be the same.
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10.
Which ordered pair is not in the solution set of y > 2x + 1 ?
A.
(1,4)
B.
(1,6)
C.
(3,8)
D.
(2,5)
Correct Answer D. (2,5)
Explanation The equation y > 2x + 1 represents a line with a slope of 2 and a y-intercept of 1. The ordered pair (2,5) does not satisfy this inequality because when x = 2, y = 5, which is not greater than 2(2) + 1 = 5. Therefore, (2,5) is not in the solution set of y > 2x + 1.
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