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Kipish [7]
3 years ago
5

Problem solving your family has a rectangular pool that measures 18 feet by 9 feet. your family wants to put a deck around the p

ool but is not sure how wide to make the deck. determine how wide the deck should be when the total area of the pool and deck is 400 square feet. what is the width of the deck?
Mathematics
1 answer:
tester [92]3 years ago
7 0
Let w be the width of the deck. Then, using the total area, we get:
(9+2w)(18+2w)=400
4w²+54w-238=0
2w²+27w-119=0
(2w-7)(w+17)=0
w=-17 or 7/2
Using the positive value, we get a width of 3&1/2 ft. for the deck
☺☺☺☺
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<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%20x%5E%7B2%7D-10x%2B25%7D%2B25%2B12%5Csqrt%7Bx%7D%20%3D15%5Csqrt%7Bx%7D" id="TexFor
vodomira [7]

Step-by-step explanation:

\sqrt{ x^{2}-10x+25}+25+12\sqrt{x} =15\sqrt{x} \\  \\  \therefore \: \sqrt{ x^{2}-10x+ {5}^{2} }+25 =15\sqrt{x} - 12\sqrt{x}\\  \\  \therefore \: \sqrt{( x - 5)^{2}}+25 =3\sqrt{x}  \\  \\ \therefore \:  x - 5+ 25 = 3 \sqrt{x}  \\  \\ \therefore \: x + 20 = 3 \sqrt{x}  \\  \\ squaring \: both \: sides \\ (x + 20)^{2}  = ( {3 \sqrt{x} })^{2}  \\ \therefore \:  {x}^{2}  + 40x + 400 = 9x \\ \therefore \:  {x}^{2}  + 40x + 400  - 9x = 0 \\  \therefore \:  {x}^{2}  + 31x + 400  = 0 \\

8 0
4 years ago
Evaluate.<br> 18.65 -52/11=
professor190 [17]
The answer is about 13.9927.

You would divide 52/11 and then subtract that decimal by 18.65.

18.65-4.7272=13.9927.
6 0
4 years ago
Triangle RST is shown below. What is the length of ST?
Tju [1.3M]

Answer:

A: 12

Step-by-step explanation:

Using the pythagoreom theorem, a^2+b^2=c^2. We can plug in the lengths of 5 and 13 which is 5^2+b^2=13^2. Now we can square the numbers to get 25+b^2=169. Subtract 25 from 169 to get 144. Now find the square root of 144 which is 12.

3 0
3 years ago
find a model for simple harmonic motion if the position at t = 0 is 6, the amplitude is 6 centimeters, and the period is 4 secon
Y_Kistochka [10]

Answer:

y = 6cos(π/2)t

Step-by-step explanation:

Given in the question that,

in a simple harmonic motion in which

at t=0 the amplitude is 6 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at t=0 is 0.  

And,

the period is given as 4 sec

We know that model equation of simple harmonic motion is

<h3>y = a. cosb(t + c) + d</h3>

here,

a is amplitude

c is Horizontal shift or phase shift

d is Vertical shift

<h3>Step1</h3><h3>Find b</h3>

Period = 2 π / b

4 = 2π / b

b = 2π/4

b = 1π/2

<h3>Step2</h3><h3>Find shifts</h3>

Horizontal and vertical shifts are 0.

So, c = 0 and d = 0

<h3>Step3</h3><h3>Plug those values in the above in the equation</h3>

y = 6cos π/2 (t + 0) + 0

y = 6cos(π/2)t

4 0
4 years ago
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Bond [772]

Answer: BCE

Step-by-step explanation:

The angle has a vertex at N, so the correct options are B, C, and E.

4 0
3 years ago
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