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Sergeeva-Olga [200]

3 years ago

14

One month salma rented 3 movies and 2 video games for a total of $19 . the next month she rented 5 movies and 6 video games for

a total of $47 . find the rental cost for each movie and each video game.

1 answer:

Doss [256]3 years ago

7 0

6$ and 8$ boiiiiiiiiiiiiii

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Andru [333]

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

◉ $\large\bm{ -4}$

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

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

1 year ago

Can anyone please help with this question?

vitfil [10]

The middle section is n(n+1)

The top row is n+2

The bottom row is 2n+1

So the rule for the total number of tiles will be the sum of the above rules...

s(n)=n(n+1)+n+2+2n+1

s(n)=n^2+n+n+2+2n+1

s(n)=n^2+4n+3

6 0

3 years ago

40 POINTS is (4,7) a solution of equations? Explain your answer 2x+4y=36 3x-4y=-6

dsp73

<span>2x + 4y = 36
3x - 4y = -6
--------------add
5x = 30
x = 6

</span>2x+4y=36
2(6)+4y=36
12 + 4y = 36
4y = 24
y = 6

answer
<span>(6, 6) is a solution of equations
</span><span>(4,7) is NOT a solution of equations</span>

6 0

3 years ago

Read 2 more answers

Given:<br> f(x)=x^2<br> g(x)=x-1<br> Find f(g(2))+g(f(-1))

Marina CMI [18]

Answer:

-1

Step-by-step explanation:

First, we need to work out the left-hand side.

find g(2) → g(2) = 2 - 1 which is 1
next, find f(1) → f(1) = 1³ which is 1

Now, we can work out the right hand side.

find f(-1) → f(-1) = -1³ which is -1
then, find g(-1) → g(-1) = -1 - 1 = -2

Finally we can work out the full sum: 1 + -2 = -1.

Hope this helps!

8 0

2 years ago

1+1 abcdefghijklmnopqrstuvwxyandz

skad [1K]

Answer:2

Step-by-step explanation: two 1 equal one 2

3 0

2 years ago

Read 2 more answers