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3 years ago

What is the area of this shape?

Mathematics

1 answer:

expeople1 [14]3 years ago

7 0

Answer: the link you posted is the area of the shape

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%20%2B4x-4%7D%7Bx%5E%7B2%7D%20-2x-8%7D" id="TexFormula1"

givi [52]

i) The given function is

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

We can rewrite in factored form to obtain;

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

$f(x)=\frac{(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)}{(x-4)(x+2)}$

The domain is

$(x-4)(x+2)\ne0$

$(x-4)\ne0,(x+2)\ne0$

$x\ne4,x\ne-2$

ii) To find the vertical asymptotes equate the denominator to zero.

$(x-4)(x+2)=0$

$(x-4)=0,(x+2)=0$

$x=4,x=-2$

iii) To find the roots, equate the numerator to zero.

$(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)=0}$

$(x+2\sqrt{2}+2)=0,(x-2\sqrt{2}+2)=0}$

$(x=-2\sqrt{2}-2,x=2\sqrt{2}-2)}$

iv) To find the y-intercept, substitute $x=0$ into the equation.

$f(0)=\frac{0^2+4(0)-4}{0^2-2(0)-8}$

We simplify to obtain;

$f(0)=\frac{-4}{-8}$

$f(0)=\frac{1}{2}$

v) The horizontal asymptote is

$lim_{\to \infty}\frac{x^2+4x-4}{x^2-2x-8}=1$

The equation of the horizontal asymptote is y=1

vi) The function does not have a variable factor that is common to both the numerator and the denominator.

The function has no holes in it.

vii) The given function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

7 0

3 years ago

Joni has two U.S coins in her pocket. One of the coins is not a dime. If the total value of coins in her pocket is 11 cents, wha

Snezhnost [94]

There is one dime and i penny

because it says one coin is not a dime
that does dot mean the other coin is not a dime

6 0

3 years ago

2/3 x 21=? find the product then write it in simplest form.

Nadusha1986 [10]

The product of 2/3 X 21 is 14 and that is in simplest form

5 0

3 years ago

THe equation of the graph line is 2x-3y=12 what is the x-intercept of the graph

katrin2010 [14]

2x-3y=12

Make y substitute 0

2x-3(0)=12

2x= 12

X= 12-2

X= 10

X-intercept is 10

5 0

3 years ago

PLEASE ANSWER ASAP WILL GIVE BRAINLIEST.

lara31 [8.8K]

Answer:

C) The cost increases $2.50 for every additional pair of shoes rented.

Step-by-step explanation:

Notice a pattern. When you buy a new pair of shoes, the total gets increased by $2.50 depending on how many pairs of shoes you buy. For example, starting with 1 pair of shoes, it costs $2.50, but when you buy another pair, the cost is $2.50+$2.50=2*$2.50=$5.00, and so on...

Therefore, the correct choice is C

7 0

2 years ago