1.
Write an algebraic expression for the verbal expression: the sum of the square of a number and 34.
Correct Answer
C. X^2+34
Explanation
The verbal expression states that we need to find the sum of the square of a number and 34. The algebraic expression x^2+34 represents this. The term x^2 represents the square of the number, and the term 34 represents the constant value that needs to be added to it. Therefore, the correct answer is x^2+34.
2.
Evaluate the expression when w = 4, n = 8, v = 5, and t = 2: 2nt - v^2
Correct Answer
B. 7
Explanation
The expression 2nt - v^2 can be evaluated by substituting the given values for w, n, v, and t. When w = 4, n = 8, v = 5, and t = 2, the expression becomes 2(8)(2) - 5^2. Simplifying this gives us 32 - 25, which equals 7. Therefore, the correct answer is 7.
3.
(5x^3y) (12x^2y^3z)
Correct Answer
A. 60x^5y^4z
Explanation
The given expression is a product of two terms: (5x^3y) and (12x^2y^3z). To simplify the expression, we multiply the coefficients (5 and 12) to get 60. Then, we combine the variables by adding their exponents. For x, we have x^3 * x^2 = x^5. For y, we have y * y^3 = y^4. And for z, we have no z in the first term, so we keep it as z. Therefore, the simplified expression is 60x^5y^4z.
4.
What are the two possible values of 0 if x^2 - 36 = 0?
Correct Answer
B. {-6,6}
Explanation
The equation x^2 - 36 = 0 can be rewritten as (x - 6)(x + 6) = 0. This means that either (x - 6) = 0 or (x + 6) = 0. Solving for x in each case, we find that x can be either -6 or 6. Therefore, the two possible values of 0 are -6 and 6.
5.
Factor completely using integers: 4ax - 14bx = 35by - 10ay
Correct Answer
C. (2x - 5y) (2a - 7b)
Explanation
The given expression can be factored as (2x - 5y) (2a - 7b). We can see that both terms in the first factor have a common factor of 2, and both terms in the second factor have a common factor of -7. By factoring out these common factors, we can rewrite the expression in the form of (2x - 5y) (2a - 7b). This is the correct factorization of the given expression.
6.
Define two variables, write two equations, and solve: A movie theater sold 450 tickets, receiving a total of $1800. If each adult ticket was $5 and each child ticket was $2, how many adult tickets were sold?
Correct Answer
D. 300
Explanation
Let's assume that x represents the number of adult tickets sold and y represents the number of child tickets sold. We can write two equations based on the given information: x + y = 450 (equation 1) and 5x + 2y = 1800 (equation 2). By solving these equations simultaneously, we can find the values of x and y. Multiplying equation 1 by 2 and subtracting it from equation 2, we get 5x + 2y - 2x - 2y = 1800 - 900, which simplifies to 3x = 900. Dividing both sides by 3, we find that x = 300. Therefore, 300 adult tickets were sold.
7.
Solve -z/5 - 3 < 4
Correct Answer
C. Z > -35
Explanation
The given inequality is solved by isolating the variable z. By adding 3 to both sides of the inequality, we get -z/5 < 7. Multiplying both sides by -5, we get z > -35. Therefore, the correct answer is z > -35.
8.
Determine the slope of the line passing through the pair of points: (6,-4) and (-3,7)
Correct Answer
B. -11/9
Explanation
To determine the slope of a line passing through two points, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (6, -4) and (-3, 7). Plugging in the values, we get: slope = (7 - (-4)) / (-3 - 6) = 11 / (-9) = -11/9. Therefore, the correct answer is -11/9.
9.
A price increased from $35 to $36.40. What was the percent of increase?
Correct Answer
A. 4%
Explanation
The price increased by $1.40 ($36.40 - $35). To find the percent increase, we divide the increase by the original price ($1.40 / $35) and multiply by 100. This gives us a percent increase of 4%.