Math Algebra Flashcards

A store sells pens for $1.50 each and notebooks for $3.00 each. Maria spent $18.00 buying a total of 8 items. How many pens did she buy?

Answer: 4

Let p = pens and n = notebooks; p + n = 8 and 1.5p + 3n = 18, solving gives p = 4.

Which expression is equivalent to (3x² + 5x - 2) - (x² - 3x + 4)?

Answer: 2x² + 8x - 6

Distributing the minus sign and combining like terms: (3-1)x² + (5+3)x + (-2-4) = 2x² + 8x - 6.

If 2(a + b) = 14 and a - b = 1, what is the value of a?

Answer: 4

From the first equation a + b = 7; adding a - b = 1 gives 2a = 8, so a = 4.

The function g(x) = -2x + 7 represents a line. What is the x-intercept?

Answer: (3.5, 0)

Set g(x) = 0: -2x + 7 = 0 → x = 3.5, so the x-intercept is (3.5, 0).

Which inequality is represented by a dashed line with slope -1 and y-intercept 4, shaded below the line?

Answer: y < -x + 4

A dashed line means strict inequality, and shading below means y is less than the line, giving y < -x + 4.

If 4^(x+1) = 64, what is the value of x?

Answer: 2

Since 64 = 4³, we have 4^(x+1) = 4³, so x + 1 = 3 and x = 2.

A quantity decreases from 200 to 50. By what percentage did it decrease?

Answer: 75%

Percent decrease = (200 - 50)/200 × 100 = 150/200 × 100 = 75%.