Keystone Algebra

Four expressions are shown. Which inequality comparing two of the expressions is true when 0.1 < x < 0.4?

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The greatest common factor (GCF) of x³y^k and x^2ky⁴ is x³y³. What is the value of k?

• 1

• 2

• 3

• 4

Which equation correctly shows that (x²)⁴ = x⁸

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When factored completely, which is a factor of 6x³ - 12x² - 48x?

• (x + 2)

• (x + 4)

• (2x - 3)

• (2x - 4)

Anna's Baker charges a delivery fee of $10.95 for one delivery order of cupcakes. Each cupcake in the order costs $1.15. Which equation describes the relationship between the number of cupcakes ordered (x) and the total cost (y), in dollars, of the deliver order?

• y = 1.15x

• y = 12.10x

• y = 1.15x + 10.95

• y = 10.95x + 1.15

Darlene is collecting prize tickets. The equation y = 2x + 1 describes the relationship between the number of days (x) since she began collecting and the number of prize tickets (y) she has collected. Which statement correctly describes a solution to the system?

• Darlene has collected 2 prize tickets at the end of 1 day.

• Darlene has collected 4 prize tickets at the end of 9 days.

• Darlene has collected 22 prize tickets at the end of 10 days.

• Darlene has collected 25 prize tickets at the end of 12 days.

Mary measured the heights of two different plants every day. Plant A was 1 inch tall when Mary began her measuring, and it grew 0.5 inch per day. Plant B was 3 inches tall, and it grew 0.25 inch per day. On which day were plant A and plant B the same height?

• day 5

• day 8

• day 12

• day 16

Which graph shows the solution set of the inequality |2x - 7| > 3?

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The solution set of an inequality is shown. Which inequality has the solution set shown in the graph?

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A T-shirt company has a goal to earn a monthly profit of more than $3,500. The company charges $20 per T-shirt. The company has $1,500 in monthly costs. The inequality 20x - 1,500 > 3, 500 models this situation. Which BEST describes the meaning of x in the inequality?

• the profit made from the sale of 20 T-shirts

• the profit made from 1 month of T-shirt sales

• the number of T-shirts that need to be sold for the company to meet its goal

• the number of T-shirts that need to be sold for the company to recover its monthly costs