Math 1 MVPA Asst 2 Units 1-5 (2023-24)

A fence building company is designing a fence for a client’s rectangular yard that maximizes the enclosed yard’s area with 120 feet of fence. The fence will connect to the back of the house, which provides one side of the rectangle. The company’s graph modeling the area, A(w), of the yard with width w, in feet, is shown. Which statement about the fence building company’s model is true?

• The area of the enclosed yard increases for fence widths between 0 feet and 1,800 feet.

• The width of the enclosed yard should be 30 feet to maximize the area of the enclosed yard.

• There is only one width of the enclosed yard that creates an area of 1,200 square feet.

• To maximize the area of the enclosed yard, the client needs 1,800 feet of fence.

Which expression is equivalent to √81m¹²n⁴, when m > 0, and n > 0?

• 3m³n²

• 3m⁶n²

• 9m³n²

• 9m⁶n²

The equation 6x + 2y = 76 represents the total amount of money a family spends at a grocery store when buying x packages of hot dogs and y packages of hot dog buns. Which represents the equation when solved for y?

• y = -3x + 38

• y = -1/3x + 38

• y = 1/3x + 38

• y = 3x + 38

Tags

CCSS.6.EE.C.9

A student is saving money to go on a school field trip. The student needs to earn at least $110 from two jobs next week. The student can work at most 20 hours. The first job pays $7 per hour, and the second job pays $9 per hour. If x is the number of hours worked at the first job, and y is the number of hours worked at the second job, which system of linear inequalities models the situation?

• x + y ≤ 20, 7x + 9y ≥ 110

• x + y ≥ 20, 7x + 9y ≤ 110

• x + y ≤ 110, 7x + 9y ≥ 20

• x + y ≥ 110, 7x + 9y ≤ 20

Which function is best represented by the graph?

• x - 4y = -4

• x - 4y = 4

• x + 4y = -4

• x + 4y = 4

What value of x makes the equation 4x + 2(x - 8) = 14 - 5(2 - x) true?

• x = 3.5

• x = 20

• x = 5

• x = 6

A homeowner association president determines a location for a pool. Entrance 1 is located at (-4, 5), and Entrance 2 is located at (6, -7). If the pool is located halfway between Entrance 1 and Entrance 2, what is the y-coordinate of the pool’s location?

• -1

• 0

• -2

• -3

What is the midpoint formula used to find the halfway point between two coordinates on a plane?

• (x1 + x2, y1 + y2)

• ((x1 + x2) / 2, (y1 + y2) / 2)

• (x1 - x2, y1 - y2)

• ((x1 - x2) / 2, (y1 - y2) / 2)

If the x-coordinate of the pool’s location is halfway between Entrance 1 at (-4, 5) and Entrance 2 at (6, -7), what is the x-coordinate of the pool’s location?

• 0

• 1

• 2

• -1

An architect determines the location of a window on a wall by mapping out the window on a coordinate plane. The window forms a triangle with vertices located at (4, -2) , (8, -2) , and (8, 6) . What is the area of the triangle, in square units?

• 12 square units

• 16 square units

• 24 square units

• 32 square units