Let x=-11/4 and y=-11/8

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

How would you also do this??

Vesna [10]

4(5x + 7) = 128

First, I'd do distributive property and get:

20x + 28 = 128

Then, subtract 28 from each side.

20x = 100

Next, I'd divide 100 by 20 = 5

x = 5

4 *(5(5) + 7) = 128

5 * 5 = 25

4 * (25 + 7)

4 * 32 = 128

Therefore, the perimeter = 2l + 2w

l = 4

w = 5x + 7

BUT we know that x = 5

w = 5(5) + 7 = 32

2(4) + 2(32)

8 + 64 = 72

Therefore, the perimeter would be 72 inches.

5 0

4 years ago

Find the area of a circle with a diameter of 4.

Oliga [24]

area of circle =22/7×4=12.56

6 0

3 years ago

Read 2 more answers

Tell weather the figures are similar.Explain<br>

monitta

No the figures aren’t similar. According to the Angle Angle Similarity Theorem- they should have the same angle degree.

8 0

3 years ago

(3 points) Blades of grass Suppose that the heights of blades of grass are Normally distributed and independent, with each heigh

NemiM [27]

The final answer is:

a) P( Y < 42.5 ) = 0.8541

b) P( 39.5 < Y < 40.5 ) = 0.1670.

What is the normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

If x follows a normal distribution with mean μ and standard deviation σ then the distribution of

$\sum_{i =1}^{n}x_{i}$ follows an approximately normal distribution with a mean $n\mu$ and standard deviation $\sqrt{n }\sigma$

let x be the height of blades of grass

x follows normal distribution with mean = μ = 4 and standard deviation = σ = 0.75.

Y = x1 + x2 +...........+x10

$Y = \sum_{i =1}^{10}x_{i}$

Distribution of Y is normal with,

Mean = $\mu _{y}=10*4 = 40$ and standard deviation $= \sigma _{y}=\sqrt{10}*0.75 = 2.3717$

a)

P( Y < 42.5 )

Using normal distribution formmula,

$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}$

=NORMDIST( x, mean, SD , 1 )

=NORMDIST(42.5, 40, 2.3717, 1 )

=0.8541

P( Y < 42.5 ) = 0.8541

b)

P( 39.5 < Y < 40.5 ) = P( Y < 40.5 ) - P( Y < 39.5 )

Using normal distribution formmula,

$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}$

P( Y < 40.5 ) =NORMDIST(40.5, 40, 2.3717, 1 ) = 0.5835

P( Y < 39.5 ) = NORMDIST(39.5, 40, 2.3717, 1 ) = 0.4165

P( 39.5 < Y < 40.5 ) = 0.5835 - 0.4165 = 0.1670

P( 39.5 < Y < 40.5 ) = 0.1670

Hence, the final answer is:

a) P( Y < 42.5 ) = 0.8541

b) P( 39.5 < Y < 40.5 ) = 0.1670.

To learn more about the normal distribution visit,

brainly.com/question/4079902

#SPJ4

5 0

2 years ago