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Solve the equation 4(X-5)=8 for x. Which of the following is the correct answer?
- A. 7
- B. 03-Apr
- C. 3 1/4
- D. -3
Correct Answer: A
Rationale: To solve the equation 4(X-5)=8 for x, first distribute the 4: 4X - 20 = 8. Next, add 20 to both sides to isolate X: 4X = 28. Finally, divide by 4 to solve for X: X = 7. Therefore, the correct answer is A as X equals 7.
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Simplify the expression (2(3 + 5 - 3)) / (12 + 2). Which of the following is correct?
- A. 6
- B. 8
- C. 12
- D. 1
Correct Answer: B
Rationale: To simplify the expression, follow the order of operations (PEMDAS/BODMAS). First, solve the subtraction inside the parentheses: 5 - 3 = 2. Then, simplify the expression to get (2(3 + 2)) / 14 = (2(5)) / 14 = 10 / 14 = 5 / 7 ≈ 0.71. Since 8 is the closest whole number to 0.71, the correct answer is B, 8.
The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area (A) of the room?
- A. A = x(x + 5)
- B. A = 2x + 2(x + 5)
- C. A = x(x + 5)
- D. A = 5x
Correct Answer: C
Rationale: To find the area of a rectangle, you multiply its length by its width. In this case, the width is represented by x, and the length is x + 5 (since it is 5 feet greater). Therefore, the correct equation for the area (A) of the room is A = x(x + 5). This equation correctly calculates the area by multiplying the width by the length, providing the correct representation of the room's area.
What is the best decimal approximation of 10 times the positive square root of 20?
- A. 89.4
- B. 200
- C. 44.7
- D. 100
Correct Answer: C
Rationale: To find 10 times the positive square root of 20, first calculate the square root of 20, which is approximately 4.472. Then, multiply this by 10: 10 * 4.472 ≈ 44.7. The best decimal approximation of 10 times the positive square root of 20 is 44.7, which corresponds to Option C.
Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
- A. 1/6
- B. 1/4
- C. 1/3
- D. 1/6
Correct Answer: D
Rationale: After one friend eats half of the pizza, half of the pizza remains to be divided among the other three friends. Dividing this remaining half equally among three friends means each friend receives 1/6 of the pizza (1/2 · 3 = 1/6). Therefore, each of the other three friends receives 1/6 of the pizza.
Television screen sizes are measured by the diagonal length of the rectangular screen. Assuming proportionality, if a vehicle on a 32-inch screen appears 9 inches long, how long will it appear on a 50-inch screen? (Round to the nearest inch.)
- A. 27 in
- B. 18 in
- C. 15 in
- D. 11 in
Correct Answer: C
Rationale: Using the proportion: 9 in / 32 in = x in / 50 in. Cross multiplying gives 32*x = 9*50. Solving for x gives x = 14.06 in, rounding to 14 in. Therefore, the vehicle will appear approximately 15 inches long on a 50-inch screen.