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3 years ago

What is the simplified form of the quantity y−squared minus y minus 12 over the quantity y−squared plus 8y plus 15?

Mathematics

1 answer:

kkurt [141]3 years ago

6 0

Y^2-y-12/y^2+8y+15=

(y-4)(y+3)/(y+3)(y+5)=

The y+3 cancel out. Therefore: (y-4)/(y+5)

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Partial fraction decomposition<br> 20x+9/25x^2+20x+4

ozzi

Step-by-step explanation:

We have

$\frac{20x + 9}{25 {x}^{2} + 20x + 4 }$

Let's factor the denomiator first,

the denomaitor is a perfect square so we get

$\frac{20x + 9}{(5x + 2) {}^{2} }$

Now, we must think of two fractions that

$\frac{a}{(5x + 2) {}^{2} } + \frac{b}{5x + 2}$

We use a perfect square term for one fraction, then a linear one for the next, because if we set both of the denomiator to the same factor, we would get a inconsistent system.

So right now, we have

$\frac{a}{(5x + 2) { }^{2} } + \frac{b}{5x + 2} = \frac{20x +9 }{25 {x}^{2} + 20x + 4 }$

$a + (5x + 2)b = 20x + 9$

$5b (x)= 20$

$a + 2b = 9$

$b = 4$

so that means that a is

$a + (2)(4) = 9$

$a + 8 = 9$

$a = 1$

So our equation is

$\frac{1}{(5x + 2) {}^{2} } + \frac{4}{5x + 2}$

6 0

2 years ago

Which problem is not represented by the

trasher [3.6K]

Answer:

d the other equations the total is 35. this one the total would be 55

8 0

3 years ago

a pond at a hotel holds 4290 gallons. the groundskeeper drains the pond at a rate of 78 gallons per hour. how long will it take

Studentka2010 [4]

55 hours to drain it

5 0

3 years ago

Which sign makes the statement true?<br>8.9 8 68100

Lyrx [107]

Well i would say it would be 8.9

3 0

3 years ago

You buy tomato sauce for $0.37 per ounce. One portion of potato gnocchi requires 2 ounces of tomato sauce. How much does the sau

Novay_Z [31]

Answer:

$0.74 = 74 cents

Step-by-step explanation:

The cost of one ounce of tomato = $0.37

1 portion of potato gnocchi requires 2 ounces of tomato sauce.

To find the cost of one portion of the potato gnocchi, we have to simply find the cost of 2 ounces of tomato sauce.

That is:

Cost = 2 * 0.37 = $0.74

Hence, one portion of potato gnocchi costs $0.74

Since $1 = 100 cents, the cost in cents will be:

0.74 * 100 = 74 cents

6 0

3 years ago