Question

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length which is three more than seven times x and the width is four times x minus 2.

a.) What are the dimensions of your mowing plot? (2 points)

Length: ______________________________________

Width: ______________________________________

b.) What is the area of your plot (remember area = length x width)? (2 points)

Area: _________________________________________

c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)

Area: _________________________________________

2.) Factor by grouping: (4 points)

xy − 4y + 7x − 28

Answer 1

1a) Length = 7x + 3 & Width = 4x - 2

1b) Area = 28x^2 -2x -6

1c) Area = 2774 sq. m

2. (x-4)(y+7)

Explanation:

Answer 2

1a) Length = 7x + 3 & Width = 4x - 2

1b) Area =
`28x^2 -2x -6`

1c) Area = 2774 sq. m

2.
`(x-4)(y+7)`

Explanation:

1a)

The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)

The area is length * width

Since we already know the algebraic expressions for length and width from part (a) above, we use the formula:

Area = (7x+3)(4x-2) = 28x^2 -14x + 12x - 6 = 28x^2 -2x -6

Area =
`28x^2 -2x -6`

1c)

Given x = 10, we put this into the area expression we found in (b) above.Let's see:

`28x^2 -2x -6\\=28(10)^2 -2(10) -6\\=2774`

Area = 2774 sq. m

2.

We can group the first two terms and next two terms and write up:

`xy-4y+7x-28\\(xy-4y)+(7x-28)\\y(x-4)+7(x-4)\\(x-4)(y+7)`

That's the factored form.