Keystone Algebra

The greatest common factor (GCF) of 2 monomials is 3x²y. One of the monomials is 3x⁴y. Which could be the other monomial?

• 3xy²

• 6x²y³

• 9x⁶y²

• 18x⁶y²

Simplify: (3x² + 2x - 8) - (-x² + 6x + 4)

• 2x² + 8x - 4

• 2x² + 8x - 12

• 4x² + 8x - 4

• 4x² - 4x - 12

In an experiment, a plant grows 0.05 centimeter per day. The plant had a height of 2 centimeters when the experiment started. Which equation describes the relationship between the number of days (d) the experiment lasts and the height (h), in centimeters, of the plant?

• h = 0.05d + 2

• h = 0.05(2) + d

• h = 2d + 0.05

• h = 2.05d

Juanita used the steps shown below to correctly solve an equation. A step is missing. Which shows the equation that is most likely a missing step and the property that justifies the step?

• -3c - 6 + 4c = 10c + 9; associative property of addition

• -3c + 18 + 4c = 10c + 45; associative property of addition

• -3c - 6 + 4c = 10c + 9; distributive property

• -3c + 18 + 4c = 10c + 45; distributive property

Christine sells a total of 50 tickets to a school play. Student tickets sell for $1.50 each, and adult tickets sell for $4.00 each. Christine made a total of $112.50 in ticket sales. Christine writes a system of equations to represent this information. Which statement BEST describes the solution to the system of equations?

• Christine sells 35 student tickets and 15 adult tickets.

• Christine would earn $200.00 by selling 50 tickets.

• Christine sells a pair of tickets between $3.00 and $8.00.

• Christine could not earn $112.50 by selling 50 student tickets.

A cleaning service offers its customers a choice between two plans. Plan A costs $3,000 and includes 1 year of an unlimited number of cleanings. Plan B costs $75 per cleaning. Henry wants to choose the less expensive plan. He uses the inequality 3,000 < 75c to decide which plan to choose based on the number of cleanings (c) he expects to need. Based on the solution of the inequality, which statement about Henry's choice of plan is true?

• Henry should choose Plan A only if he expects to need fewer than 40 cleanings in 1 year.

• Henry should choose Plan A only if he expects to need more than 40 cleanings in 1 year.

• Henry can choose either plan and pay the same amount if he expects to need fewer than 40 cleanings in 1 year.

• Henry can choose either plan and pay the same amount if he expects to need more than 40 cleanings in 1 year.

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Ms. Bernard monitored the growth of a fish. The fish originally weighed 27 ounces. The fish grew at a rate of 5 ounces per month. The equation below can be used to describe the weight, in ounces, of the fish. Ms. Bernard correctly determined that x = 9. What does the solution of the equation mean?

• The fish grew at a rate of 9 ounces per month for 72 months.

• The fish grew at a rate of 72 ounces per month for 9 months.

• It took 9 months for the fish to grow to a weight of 72 ounces.

• It took 72 months for the fish to grow to a weight of 9 ounces.

A system of equations is shown below. What is the solution of the system of equations?

• (-2. -7)

• (2, 7)

• (2, 3)

• (3, 2)