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soldi70 [24.7K]
3 years ago
8

A new youth activity center is being built in safe harbor. The perimeter of the rectangular playing field is 282 yards. The leng

th of the field is 6 yards less thank double the width. What are the dimensions of the playing field
Mathematics
1 answer:
lara [203]3 years ago
4 0
Answer:
length=92yd
width=49yd

Step by step:
2l+2w=282
l=2w-6
Plug in l
2(2w-6)+2w=282
4w-12+2w=282
6w-12=282
6w=282+12
w=294/6
w=49
Then plug in w
2l+2(49)=282
2l+98=282
2l= 184
l=92
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If f(x) = 7+ 4x and g(x) = 1/2,
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270

<h3>Further explanation</h3>

<u>Given:</u>

  • \boxed{ \ f(x) = 7 + 4x \ }
  • \boxed{ \ g(x) = \frac{1}{2x} \ }

<u>Question:</u>

What is the value of \boxed{ \ \bigg( \frac{f}{g} \bigg)(5)? \ }

<u>The Process:</u>

The form of \boxed{ \ \bigg( \frac{f}{g} \bigg)(x) \ } means that f(x) is divided by g(x).

\boxed{\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) \ } \rightarrow \boxed{ \ \frac{f(x)}{g(x)} \ }}

Let us solve the problem.

\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) = \frac{7 + 4x}{\frac{1}{2x}} \ }

\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) = (7 + 4x) \times \frac{2x}{1} \ }

Thus, we get \boxed{{ \ \bigg( \frac{f}{g} \bigg)(x) = 14x + 8x^2 \ }}

And now, we can calculate the value of \bigg( \frac{f}{g} \bigg)(5).

\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 14(5) + 8(5)^2 \ }

\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 70 + 200 \ }

Thus, the value is 270.

- - - - - - - - - - -

Alternative thinking

\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = \frac{7 + 4(5)}{\frac{1}{2(5)}} \ }

\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = (7 + 20) \times 10} \ }

\boxed{\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 270 \ }}

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