Math 5 Flashcards

A gym charges a one-time enrollment fee plus a monthly membership rate. The total cost in dollars after m months is represented by the expression 30m + 50. What does the value 50 represent in this context?

Answer: The one-time enrollment fee

In the expression 30m + 50, the term 30m represents the monthly cost (rate × months), so the constant 50 is the fixed, one-time enrollment fee added regardless of how many months are purchased.

A student buys pencils for $0.50 each and notebooks for $2.00 each. She purchases 12 items total and spends exactly $15.00. How many notebooks did she buy?

Answer: 6

Setting up the system: p + n = 12 and 0.50p + 2n = 15. Substituting p = 12 − n gives 0.50(12 − n) + 2n = 15 → 6 + 1.5n = 15 → n = 6.

Which equation represents a parabola with a vertex at (−2, 5)?

Answer: y = (x + 2)² + 5

Vertex form is y = (x − h)² + k, where (h, k) is the vertex. For vertex (−2, 5), h = −2 and k = 5, giving y = (x − (−2))² + 5 = (x + 2)² + 5.

A store purchases a jacket for $80 and marks it up by 35% before selling it. What is the selling price of the jacket?

Answer: $108.00

A 35% markup means the selling price is 80 × 1.35 = $108.00. Multiplying by 1.35 adds 35% of the original price to itself in one step.

What is the slope of the line that passes through the points (3, 7) and (9, 19)?

Answer: 2

Slope = (y₂ − y₁) / (x₂ − x₁) = (19 − 7) / (9 − 3) = 12 / 6 = 2. The line rises 2 units for every 1 unit it moves to the right.

A delivery driver earns $0.22 per mile driven plus a flat daily base pay. His total earnings for one day are represented by the expression 0.22m + 64, where m is the number of miles driven. If the driver drove 200 miles in one day, how much did he earn?

Answer: $108.40

Substitute m = 200 into 0.22m + 64: 0.22(200) + 64 = 44 + 64 = $108.40.