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3 years ago

Let f(x) = x2 + x + 2 and g(x) = 2x + 5. Find f(g(x)). Show each step of your work. (10 points)

Mathematics

1 answer:

DaniilM [7]3 years ago

6 0

We were given;

f(x) = x² + x + 2

and

g(x) = 2x + 5

f(g(x)) = f(2x+5)

= (2x+5)²+(2x+5)+2

Expanding brackets gives;

=(2x)²+2(2x)(5) +5²+(2x+5)+2

Simplifying gives;

= 4x² +20x+25+ 2x+5+2

f(g(x))= 4x² +22x +32

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The ratio of snails to fish in the fishtank is 2:5

Elina [12.6K]

There are 6 snails and 5 fish.
6:15, because
2:5
2+5=7
21/7=3
2:5(3)= 6:15

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3 years ago

1-58. Mr. Wright was making a table to figure out how much it costs to send a certain numt

Drupady [299]

A table of values can be used to represent variables that are directly proportional.

The complete table of proportions is:

$\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]$

Given that

$\left[\begin{array}{ccccccccc}Letters&10&2&[\ ]&7&1&500&[\ ] \\Cost&0.45&0.90&6.75&[\ ]&[\ ]&[\ ] & 18.90\end{array}\right]$

Let:

$L \to$ Letters

$C \to$ Cost

Using proportional reasoning, we have:

$C = kL$

Where

$k \to$ ratio of proportion

For the first values of C and L, we have:

$C = kL$

$0.45 = k \times 10$

Divide both sides by 10

$k = 0.045$

So, the equation of proportion is:

$C = 0.045L$

When C = 6.75, we have:

$C = 0.045L$

$6.75 = 0.045L$

Solve for L

$L = \frac{6.75}{0.045}$

$L = 150$

When L = 7, we have:

$C = 0.045L$

$C = 0.045 \times 7$

$C = 0.315$

When L = 1, we have:

$C = 0.045L$

$C = 0.045 \times 1$

$C = 0.045$

When L = 500, we have:

$C =0.045L\\$

$C =0.045 \times 500$

$C =22.5$

When C = 18.90, we have:

$C = 0.045L$

$18.90 = 0.045L$

Solve for L

$L=\frac{18.90}{0.045}$

$L=420$

Hence, the complete table is:

$\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]$

Read more about proportions at:

brainly.com/question/21126582

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2 years ago

4(-2d-3)=12, someone please solve this for me asap

wlad13 [49]

4(-3 + -2d) = 12

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-12 + -8d = 12

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0 + -8d = 12 + 12

-8d = 12 + 12

12 + 12 = 24

-8d = 24

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5 0

3 years ago

X/2.5=20 what does x equal?

sesenic [268]

This is a one-step equation. All you need to do is multiply the 2.5 over to the 20 to get x by itself. x=50 Hope this helps!

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3 years ago

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Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.

Lina20 [59]

Answer:

Step-by-step explanation:

$(8,9)=(x1,y1) \\ m=7 \\ y−y1=m(x−x1) \\ y−9=7(x−8)$

$y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47$

8 0

3 years ago