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Vladimir79 [104]
3 years ago
6

Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

Mathematics
1 answer:
rusak2 [61]3 years ago
7 0
Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form ax^2+bx+c. To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
x^2+2x-8=(x+4)(x-2)
In the denominator we have a difference of squares:
x^2-9=x^2-3^2=(x+3)(x-3)

Now we can rewrite our function:
y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at x=3 and x-3

We can conclude that the graphic of our rational function is: 

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Factoring expressions 9+36w
alexdok [17]

Answer:

9( 1 + 4w)

Step-by-step explanation:

So if you're simplifying then you need to find the greatest common factor. The GCF is 9.

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3 years ago
If we get the 100 from number 1 each year for ten years and invest each payment in an account that earns 8% how much will be the
blsea [12.9K]

Answer:

$1,448.66

Step-by-step explanation:

The future value of an annuity with yearly deposits 'P' at an interest rate of 'r' invested for 'n' years is determined by:

FV = P[\frac{(1+r)^n-1}{r}]

For P = $100, r = 0.08 and n = 10 years:

FV = 100[\frac{(1+0.08)^{10}-1}{0.08}]\\FV=\$1,448.66

The amount at the end of the ten years is $1,448.66

4 0
3 years ago
Compute the measures of center for both the boys and girls data. Describe their differences. Use the terms mean and median to ju
polet [3.4K]

Answer:boys: median=50, mean=46

Girls: median= 33, mean=34

Step-by-step explanation:

Mean is the average. Median is the middle number. Both groups had 10 scores. Boys ranged from 15-81. Girls from 0-75; their mean & median would be less because their scores are less.

6 0
3 years ago
What value of a makes the equation true?<br> a+29=-63<br><br> I need help!!
irakobra [83]

Answer:

a = -92

Step-by-step explanation:

<u>Step 1:  Subtract 29 from both sides</u>

a + 29 = -63

a + 29 - 29 = -63 - 29

<em>a = -92</em>

<em />

Answer:  a = -92

7 0
3 years ago
Read 2 more answers
What is the length of RU?
marta [7]

Answer:

Length of RU is 20 units.

Step-by-step explanation:

In ΔRSt and ΔRUT,

ST ≅ TU [Given]

RT ≅ RT [Reflexive property]

∠RTS ≅ ∠RTU [Both the angles are the right angles]

ΔRTS ≅ ΔRTU [By SAS property of congruence]

Therefore, RS ≅ RU [By CPCTC (corresponding parts of the congruent triangles are congruent]

8x = 6x + 5

8x - 6x = 5

2x = 5

x = 2.5

Length of RU = (6x + 5)

                      = 6(2.5) + 5

                      = 15 + 5

                      = 20

Length of RU is 20 units.

7 0
3 years ago
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