Write a simplified polynomial expression in standard form to represent the area of the rectangle below.A picture of a rectangle is shown with one side labeled as 5 x plus 2 and another side labeled as x minus 4.

5x2 + 18x − 2

5x2 + 13x + 2

5x2 − 18x − 8

5x2 + 13x + 8

Answers

Answer 1

Answer: Given:
Rectangle shape.
One side: 5x + 2
other side: x - 4

Area = length * width
Area = (5x+2)(x-4)
A = 5x(x-4) +2(x-4)
A = 5x² - 20x + 2x - 8
A = 5x² - 18x - 8

Answer 2

Answer:

The polynomial expression that represents the area of the rectangle is: C. 5x² - 18x - 8

What is the Area of a Rectangle?

Area = (length)(width)

Given the dimensions of the rectangle as:

Length = 5x + 2
Width = x - 4

Area of the rectangle = (5x + 2)(x - 4)

5x(x - 4) + 2(x - 4)

5x² - 20x + 2x - 8

Add like terms together

5x² - 18x - 8

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Show that the system of rational expressions is closed under addition, or give an example showing the contrary.

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Jamie, John, and Jake are on the prom committee. They are responsible for blowing up the balloons for prom night. John can blowup a balloon every 15 seconds while it takes Jamie and Jake 20 seconds per balloon. If 1 out of 80 balloons are found to be defected after they are inflated, Identify the expression which represents the number of balloons inflated per hour.A) 592.5x
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D) 600 - 1/80x

Answers

First, pass all the rate of inflation to ballons/hour

John: 1 b/15s * 3600 s/h = 240 b/h
Jamie: 1 b/20s * 3600 s/h = 180 b/h
Jake: 180 b/h

Then sum the rates to obtain the total rate

Total ballons per hour: 240 b/h + 180 b/h + 180b/h = 600 b/h

If it passes x hours the number of ballons inflated is 600*x

The number of ballon defective are 600*x/80

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Answer: option A)

Suppose you need to minimize the cost of fencing in a rectangular region with a total area of 450 square feet. The material that will be used for three sides costs $15 per linear foot, and the material that will be used for the fourth side costs $18 per linear foot. Write a function that expresses the cost of fencing the region in terms of the length, x, of the two opposite sides of the region with material costs of $15 per linear foot.

Answers

Answer:

30*x + 14850/x

Step-by-step explanation:

Let x be the length of the two opposite sides of the region with material costs of $15 per linear foot.

Let y be the length of the other two sides

Now, we have the following equations

Area of the rectangular región = x * y = 450 ft2

Total cost of fencing = 15*x + 15*x + 15 *y + 18*y

Total cost of fencing = 30*x + 33 *y

We now that area is equal to 450 ft2 = x*y

So y = 450/x

Now we can substitute y in equation for Total cost of fencing and obtain a function that expresses the cost of fencing the region in terms of the length, x

Total cost of fencing = 30*x + 33 *(450/x)

Total cost of fencing = 30*x + 14850/x

PLZ HELP, GIVING BRAINLIEST!! Which of these choices are equivalent to the expression i^85? a. i^7 b. i^26 c. i^41 d. i^99