SAT practice Test 3

Question 1

If three times a number is equal to that number minus 7, what is the number?

Accepted Answer

-3.5</label></li>

Answer

Let 'x' represent the unknown number. The problem states 'three times a number is equal to that number minus 7,' which translates into the algebraic equation 3x = x - 7. To solve for x, subtract 'x' from both sides: 2x = -7. Finally, divide both sides by 2: x = -7/2, which is -3.5.

Question 2

>The amount of skin samples that David needs for an experiment must be greater than 11 but less than or equal to 27. Which of the following represents an acceptable range for David's experiment?

Accepted Answer

11<s<27</label></li>

Answer

The problem states that the number of skin samples, 's', must be 'greater than 11', which is represented by the inequality 11 < s. It also states that 's' must be 'less than or equal to 27', which is represented by s <= 27. Combining these two conditions into a single compound inequality gives the acceptable range as 11 < s <= 27.

Question 3

If 2x+2y=0, which of the following must be equivalent to 2x-2y?

Accepted Answer

-4y</label></li>

Answer

Given the equation 2x + 2y = 0, we can isolate 2x by subtracting 2y from both sides, resulting in 2x = -2y. The question asks for an equivalent expression for 2x - 2y. By substituting -2y for 2x in the expression, we get (-2y) - 2y. This simplifies to -4y.

Question 4

Which of the following is equivalent to 4x²-4x-48?

Accepted Answer

4(x-3)(x+4)

Answer

To check which option is equivalent to 4x^2 - 4x - 48, we can expand the given correct answer, 4(x-3)(x+4). First, multiply the binomials: (x-3)(x+4) = x^2 + 4x - 3x - 12 = x^2 + x - 12. Then, distribute the 4: 4(x^2 + x - 12) = 4x^2 + 4x - 48. This shows that 4(x-3)(x+4) is equivalent to 4x^2 + 4x - 48. (Note: There is a discrepancy in the sign of the middle term between the question's expression and the provided correct answer's expansion.)

Question 5

If 2a+3b=26 and 5a+4b=51, what is the value of a+b?

Accepted Answer

11</label></li>

Answer

We are given a system of two linear equations: 2a + 3b = 26 and 5a + 4b = 51. To find the value of a + b, a straightforward method is to add the two equations together. Adding the left sides gives (2a + 3b) + (5a + 4b) = 7a + 7b. Adding the right sides gives 26 + 51 = 77. So, 7a + 7b = 77. Dividing the entire equation by 7 yields a + b = 11.

SAT Practice Test

SAT Practice Test

SAT practice Test 3