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Rom4ik [11]
3 years ago
12

Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6

Mathematics
2 answers:
lora16 [44]3 years ago
8 0

Answer:

The answer is the option C

graph of 3x minus 3, with discontinuity at negative 2, negative 9

Step-by-step explanation:

we have

f(x)=\frac{9x^{2}+9x-18}{3x+6}

Simplify

f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}

Step 1

Convert to a factored form the numerator

x^{2}+x-2=0    

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+x=2

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+x+0.25=2+0.25

x^{2}+x+0.25=2.25

Rewrite as perfect squares

(x+0.5)^{2}=2.25

Square root both sides

x+0.5=(+/-)1.5

x=-0.5(+/-)1.5

x=-0.5+1.5=1

x=-0.5-1.5=-2

so

x^{2}+x-2=(x-1)(x+2)  

Step 2

Simplify the function f(x)

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}=3\frac{(x-1)(x+2)}{(x+2)}

The domain of the function f(x) is all real numbers except the number x=-2

Because the denominator can not be zero

f(x)=3\frac{(x-1)(x+2)}{(x+2)}=3(x-1)=3x-3  

f(x)=3x-3  ------> with a discontinuity at x=-2

f(-2)=3(-2)-3=-9

The discontinuity is at point (-2,-9)

the answer in the attached figure

Iteru [2.4K]3 years ago
7 0
Hello,

y=(9x²+9x-18)/(3x+6)=(9(x-1)(x+2))/(3(x+2))
If x≠-2 then y=3(x-1)==>y=3x-3
So we must exclude (-2,-9)

Answer C (graph n°3)
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Question and choices are in the photo please explain the answer
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Answer:

\text{A) }68\:\mathrm{cm}

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.

Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.

To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a 90^{\circ}, creating right triangles \triangle TOP and \triangle SOP.

The Pythagorean Theorem states that the following is true for any right triangle:

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Thus, we have:

10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24

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What we know:

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What are the zeroes of f(x) = x2 + 5x + 6?
Vera_Pavlovna [14]

Answer:

Zeros are x = −2, −3 .

Step-by-step explanation:

Given : f(x) = x² + 5x + 6.

To find : What are the zeroes of f(x).

Solution : We have given that

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To find the zeros of the function we need to set f(x) = 0.

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Therefore, Zeros are x = −2, −3 .

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