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lubasha [3.4K]
2 years ago
15

(2x³+4x²-x+8) / (x² + 3x + 2)

Mathematics
1 answer:
a_sh-v [17]2 years ago
3 0

\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\

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In planning her retirement, Liza deposits some money at 2% interest, twice as much deposited at 2.5%. What is the amount deposit
harkovskaia [24]
She deposited two amounts, let's say "a" and "b"
"a" earning 2% interest
"b" earning 2.5% interest

the 2.5% one, is twice as much as the 2% one
so.. one can say that, whatever "a" is, "b" is twice as much,
or b = 2*a -> b = 2a

now.. .the sum of both earned interest, was $1190

so.. one can say that (2% of a) + (2.5% of b) = 1190
let' us use the decimal notation then
\frac{2}{100}a+\frac{2.5}{100}b=1190\implies 0.02a+0.025b=1190
\\ \quad \\
\textit{however, we know "b" is 2a thus}
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0.02a+0.025\boxed{b}=1190\implies 0.02a+0.025(\boxed{2a})=1190

solve for "a" to find what the "a" amount is,
to find "b", well, "b" is "2a", so just do a 2*a to get "b"

5 0
3 years ago
Is the following relation a function?<br> Yes or No question
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6.<br> How many columns are in a 5 x 4 matrix?
bearhunter [10]
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4 0
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Need help asap! Tyy
Oksi-84 [34.3K]

Answer:

27 feet squared

Step-by-step explanation:

the formula for the area of a triangle is b(h)/2 so u just plug in the numbers into the formula from the question. we know that the base is 6ft long and the height is 9ft long.

A = b(h)/2

A = 6(9)/2

A = 27

therefore the area of the sail is 27 feet squared.

7 0
3 years ago
Read 2 more answers
Help me. Im actually so serious ​
Leviafan [203]

Answer:

<em>Answer in explanation</em>

Step-by-step explanation:

<u>Linear Modeling</u>

It's given a situation where a student has two summer jobs and wants to collect $750 to pay for a down payment on a car. He gets paid $25 for each lawn mowed and $15 for each pool cleaned

  • Create a model in standard form

Let

x = number of lawns mowed

y = number of pools cleaned

He wants to make $750, thus:

25x + 15 y = 750

Dividing by 5, we have the model that represents the linear relationship:

5x  + 3y = 150

  • Identify the x-intercept

The x-intercept can be found by setting y=0:

5x  + 3(0) = 150

5x = 150

Dividing by 5:

x = 150/5 = 30

x = 30

This represents the situation where the student gets his $750 by only mowing 30 lawns, no pools cleaned.

  • Identify the y-intercept

The y-intercept can be found by setting x =0:

5(0)  + 3y = 150

3y = 150

y = 150/3 = 50

y = 50

This represents the situation where the student gets his $750 by only cleaning 50 pools, no lawns mowed.

  • Identify two combinations that are solutions to the equation

Starting from the basic equation

5x  + 3y = 150

We can give x some arbitrary value (less than 30) and find the value for y.

For example, for x=12

5*12 + 3y = 150

60 + 3y = 150

3y = 150 - 60 = 90

y = 90/3=30

This solution corresponds to the case where the student gets $750 by mowing 12 lawns and cleaning 30 pools.

For example, for x=21

5*21 + 3y = 150

105 + 3y = 150

3y = 150 - 105 = 45

y = 45/3=15

This solution corresponds to the case where the student gets $750 by mowing 21 lawns and cleaning 15 pools.

5 0
3 years ago
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