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NeTakaya
3 years ago
5

The length of a rectangle is twice it’s width.The perimeter of the rectangle in 162 inches.How long is the rectangle?

Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0
The perimeter of a rectangle is all sides added  up, so length + length + width + width.

L = length

W = width

then the perimeter is L+L+W+W, or 2L + 2W, or 2(L+W).

\bf \textit{perimeter of a rectangle}\\\\
P=2(L+W)~~
\begin{cases}
P=162\\
L=\stackrel{\textit{twice W}}{2W}
\end{cases}\implies 162=2(2W+W)
\\\\\\
\cfrac{162}{2}=3W\implies 81=3W\implies \cfrac{81}{3}=W\implies 27=W

what's the length?  well, is just 2(27).
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56 points for whoever answers correctly !
vladimir2022 [97]

We need to use what we know about rectangles to get:

1)

  • Total length = 2*W + 8ft
  • Total width = W + 8ft

2) area = 2*W^2 + 24ft*W + 64ft^2

<h3>Working with rectangles:</h3>

We know that rectangles are defined by two measures, width W and length L.

Here we do know that the length of the pool is twice the width, and the width is W, then the length of the pool is:

L = 2*W

And we also have a sidewalk of 4ft all around the pool, now we want to get:

1) The total length and the total width.

This will be equal to the length/width of the pool <u>plus twice the width of the sidewalk</u> (we add it twice because is in both ends) then we have:

  • Total length = L + 2*4ft = 2*W + 8ft
  • Total width = W + 2*4ft = W + 8ft

2) Now we want to get an expression for the total area of the pool.

Remember that for a rectangle the area is just the product between the width and the length, so to get the area of the pool with the sidewalk we just take:

area = (total length)*(total width)

area = (2*W + 8ft)*(W + 8ft) = 2*W^2 + 3*W*8ft + 64ft^2

area = 2*W^2 + 24ft*W + 64ft^2

This is the equation that gives the total area as a function of W, the width of the pool.

If you want to learn more about rectangles, you can read:

brainly.com/question/17297081

6 0
3 years ago
Find the value of the expression below for x=10<br><br> x ^2 - 2 (x + 5)
Thepotemich [5.8K]

Answer:

20

Step-by-step explanation:

your welcome!!

7 0
3 years ago
Read 2 more answers
Which line(s) intersect the parabola y = x^2 − 3x + 4 at two points? Select all that apply. A. y = –3x + 2 B. y = –3x + 3 C. y =
TEA [102]

Answer:

C and D

Step-by-step explanation:

Equating the line A and the parabola, we get

-3x + 2 = x² - 3x + 4

0 = x² - 3x + 4 +3x - 2

0 = x² + 2

-2 = x²

which has no real solutions. Then, the line A and the parabola don't intersect each other.

Equating the line B and the parabola, we get

-3x + 3 = x² - 3x + 4

0 = x² - 3x + 4 + 3x - 3

0 = x² + 1

-1 = x²

which has no real solutions. Then, the line B and the parabola don't intersect each other.

Equating the line C and the parabola, we get

-3x + 5 = x² - 3x + 4

0 = x² - 3x + 4  + 3x - 5

0 = x² - 1

1 = x²

√1 = x

which has 2 solutions, x = 1 and x = -1. Then, the line C and the parabola intersect each other.

Equating the line D and the parabola, we get

-3x + 6 = x² - 3x + 4

0 = x² - 3x + 4  + 3x - 6

0 = x² - 2

2 = x²

√2 = x

which has 2 solutions, x ≈ 1.41 and x ≈ -1.41. Then, the line D and the parabola intersect each other.

4 0
3 years ago
P(x) = 2x^2 - 4x - 6
raketka [301]

Answer:

p(x) =2(x-1) ^2-8

Step-by-step explanation:

  • Add the same value to both sides
  • Add 1 to the expression
  • Add 2×1 to the left side
  • Simplify factors
  • Move constant to the right
  • Then calculate
7 0
3 years ago
The points -13 and 6 are plotted on a number line. What is the distance, in units, between the two points?
joja [24]

19 units

Use the absolute value to find the difference between the values. This ensures that no matter which way round the calculation is done the result is the same

| - 13 - 6 | = | - 19 | = 19

or

| 6 - (- 13) | = | 6 + 13 | = | 19 | = 19


8 0
3 years ago
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