GED Math Test #7 2 Flashcards

Factor completely: x² − 9

Answer: (x − 3)(x + 3)

x² − 9 is a difference of two squares: a² − b² = (a − b)(a + b). Here a = x and b = 3, so x² − 9 = (x − 3)(x + 3).

A right triangle has legs of 6 and 8. What is the length of the hypotenuse?

Answer: 10

Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100. So c = √100 = 10. This is a classic 3-4-5 Pythagorean triple scaled by 2.

If f(x) = 2x² − 3x + 1, what is f(−2)?

Answer: 15

f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15. Substitute −2 for x and follow order of operations.

A store offers a 15% discount on a $120 item. After the discount, sales tax of 8% is applied. What is the final price?

Answer: $110.16

Discounted price = $120 × (1 − 0.15) = $120 × 0.85 = $102. Then apply 8% sales tax: $102 × 1.08 = $110.16. The final price after the 15% discount and 8% tax is $110.16.

What is the perimeter of a regular hexagon with a side length of 7 cm?

Answer: 42 cm

A regular hexagon has 6 equal sides. Perimeter = 6 × 7 = 42 cm.

The equation y = −3x + 6 represents a line. What is its y-intercept?

Answer: 6

In slope-intercept form y = mx + b, m is the slope and b is the y-intercept. Here b = 6, so the line crosses the y-axis at (0, 6).