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katovenus [111]

3 years ago

11

You spend 10 minutes playing video games. You then spend 1-hour doing homework. Write the ratio of the amount of time spent play

ing video games to the amount of time spent doing homework as a fraction in simplest form.

1 answer:

brilliants [131]3 years ago

4 0

here u go

hope you can understand my handwriting

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Andru [333]

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◉ $\large\bm{ -4}$

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Before performing any calculation it's good to recall a few properties of integrals:

$\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}$

$\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }$

So we apply the first property in the first expression given by the question:

$\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}$

And we solve the second integral:

$\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }$

Then we take the last equation and we subtract 10 from both sides:

$\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}$

And we divide both sides by 2:

$\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}$

Then we apply the second property to this integral:

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}$

Then we use the other equality in the question and we get:

$\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}$

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}$

We substract 8 from both sides:

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}$

• $\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}$

7 0

2 years ago

Solve the following for y:<br> p(t + 4) = 2y

dimulka [17.4K]

Answer:

the answer is y =p(t + 4)/2

6 0

3 years ago

7(x-2)=28 Can somebody help me and show the steps?

olya-2409 [2.1K]

Since the 7 is in front of the parentheses you must multiply it by everything inside the parentheses. 7 times X is 7X and 7 times -2 is -14. Then you need to make the X be by itself on one side, to do that you have to add 14 to -14 to make it disappear, and also add 14 to the other side, to 28. Then you divide both sides by 7 to make X be by itself.

7(x-2)=28
7X-14=28
7x=42
X=6

6 0

2 years ago

F(x) = 3x - 3 <br> g(x) = 4x+5 <br> find (f•g) (3) <br><br> only numerical answers work

Andreas93 [3]

Answer:

48 bcoz u do 4(3)+5 do f(g) than for f(17) u do 3(17)-3

6 0

3 years ago

Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 ti

stiv31 [10]

2.5(12.75x + 24.50) = 188.75
31.875x + 61.25 = 188.75
31.875x = 188.75 - 61.25
31.875x = 127.50
x = 127.50 / 31.875
x = 4....they worked 4 hrs

5 0

3 years ago

Read 2 more answers