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3 years ago

The area of a square rug is 169ft^2. How long is each side of the rug?

Mathematics

1 answer:

jek_recluse [69]3 years ago

6 0

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{13 \: ft}}}}}$

Step-by-step explanation:

$\star{ \sf{ \: Area \: of \: a \: square \: rug \: ( \: A \: ) \: = \: 169 \: {ft}^{2} }}$

$\sf{ \underline{Finding \: the \: length \: of \: a \: square \: ( \: l \: )}}$

$\boxed{ \sf{Area \: of \: a \: square \: = \: {l}^{2} }}$

$\hookrightarrow{ \sf{169 = {l}^{2} }}$

$\hookrightarrow{ \sf{ {l}^{2} = 169}}$

$\hookrightarrow{ \sf{ \sqrt{ {(l)}^{2} } = \sqrt{169} }}$

$\hookrightarrow{ \text{length \: = \: 13 \: ft}}$

$\text{Hope \: I \: helped!}$

$\text{Best \: wishes !!}$

~ $\text{TheAnimeGirl}$

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John goes to a bookstore. he wants to buy at. most 25 books and spend at most $75. paperback books cost 1.75 and har cover books

Yanka [14]

Answer:

x + y ≤ 25
1.75x + 2.50y ≤ 75

Step-by-step explanation:

Paperback books = x
Hard cover books = y

Number of books:

x + y ≤ 25

Cost of books:

1.75x + 2.50y ≤ 75

The system above is the one we need

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2 years ago

Which equations could you use to solve the following problem? Fifty-six is 85% of what number? 56 = (0.85)w = = p = (0.85)56

Sidana [21]

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

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6 0

3 years ago

Solve for s. 4s + 6s - 4 = 6

UkoKoshka [18]

Answer:

s = 1

Step-by-step explanation:

4s + 6s - 4 = 6

10s - 4 = 6

+ 4 +4

10s = 10

10s/10=

s = 1

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2 years ago

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Delvig [45]

Answer:

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Step-by-step explanation:

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2 years ago

Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

algol13

9514 1404 393

Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

Given:

x/(1 -x) = 1/x

Find:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

Solution:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

5 0

2 years ago