Appreciate any help!!

The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length

Artemon [7]

Answer:

Width = 10 inches

Step-by-step explanation:

Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.

We can establish the following values to help us solve for the width of a rectangle:

Perimeter (P) = 68 inches

Length (L) = 14 + W inches

Width (W) = unknown

<h3 /><h3><u>Solve for the Width (W)</u></h3>

P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.

Divide both sides by 2:

$\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}$

$\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}$

Substitute the value of the Perimeter and the length (L) into the formula:

$\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}$

Combine like terms on the right-hand side, and simplify the left-hand side of the equation:

$\displaystyle\mathsf{34\:=14\:+2W}$

Subtract 14 from both sides:

34 - 14 = 14 - 14 + 2W

20 = 2W

Divide both sides by 2 to solve for the width (W):

$\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}$

W = 10 inches

Therefore, the width of the rectangle is 10 inches.

<h3 /><h3><u>Double-check:</u></h3>

Verify whether the derived value for the width is correct:

P = 2L + 2W

68 = 2(14 + 10) + 2(10)

68 = 2(34) + 20

68 = 48 + 20

68 = 68 (True statement).

Thus, the length of the rectangle is 34 inches, and the width is 10 inches.

4 0

3 years ago

Fiona deposits $2,000 into a savings account. If the Fed requires a 20 percent reserve ratio, how much of Fiona’s money can the

sesenic [268]

The amount the the fed require =

20/100 x 2,000 = 400

The amount of money that Fiona's bank can lend is : $ 2,000 - $ 400
= $ 1,600

6 0

3 years ago

Read 2 more answers

Question 2 Mr. Smith is buying two types of gift cards to give as prizes to employees at a company picnic. He will buy restauran

ella [17]

Answer: He can buy 5 restaurant gift cards and 7 movie gift cards

Step-by-step explanation:

7 0

3 years ago

A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One

vodka [1.7K]

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that <u>the trip can cost exact $90</u> so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

7 0

2 years ago

Decide whether the equations is a trigonometric function identity, EXPLAIN.

hodyreva [135]

(1) Answer: Identity true

$\cos^2x(1+\tan^2x)=\cos^2x(1+\frac{sin^2x}{cos^2x})=\\= \cos^2x\frac{cos^2x+sin^2x}{cos^2x}=1$