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solong [7]
3 years ago
5

One x-intercept of the graph of the of the cubic function f(x) = x^3 – 2x^2 – 111x – 108 is –9.

Mathematics
1 answer:
katrin2010 [14]3 years ago
3 0

Answer:

The zeros of the given function are -9,-1 and 12.

Step-by-step explanation:

The given function is

f(x)=x^3-2x^2-111x-108

It is given that the x-intercept of the graph is -9, therefore -9 is a zero of the function.

Since -9 is the zero of the function, therefore (x+9) is a factor of f(x). Use synthetics method or long division method to divide the function by (x+9).

f(x)=(x+9)(x^2-11x-12)=0

f(x)=(x+9)(x^2-12x+x-12)=0

f(x)=(x+9)(x(x-12)+(x-12))=0

f(x)=(x+9)(x-12)(x+1)=0

Use zero product property and quote each factor equal to 0.

x=-9,-1,12

Therefore zeros of the given function are -9,-1 and 12.

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4 0
2 years ago
PLEASE HELP!! Find the coordinates.
Mazyrski [523]

Answer:

Option (D)

Step-by-step explanation:

Coordinates of the points J, E and V are,

J → (-4, -5)

E → (-4, -3)

V → (-1, -1)

This triangle is translated by the rule T_{} given in the question.

Coordinates of the image will follow the rule,

(x, y) → [(x + 2), (y + 4)]

following this rule coordinates of the image triangle will be,

J(-4, 5) → J'(-2, -1)

E(-4, -3) → E'(-2, 1)

V(-1, -1) → V'(1, 3)

Therefore, points given in the option (D) will be the answer.

7 0
3 years ago
A line with a slope of -7 passes through the points (u,0) and (8,-7) what is the value of u?
laila [671]

Answer:

u = 7

Step-by-step explanation:

Using the slope intercept formula:

\frac{y2 - y1}{x2 - x1}  = slope

Substitute our values from the points and the known slope:

\frac{-7 - 0}{8 - u} = -7

Now we multiply both sides by (8 - u) to isolate the x:

(8-u) x \frac{-7}{8 - u} = -7 (8 - u)

Next we add 56 to both sides:

-7 = -56 + 7u

Finish off by dividing both sides by 7:

7u = 49

u = 7

6 0
3 years ago
Solve this x²+8/10 -x = 10/2
AysviL [449]
x^2+\frac{8}{10}-x=\frac{10}{2}\\
x^2-x+\frac{8}{10}-\frac{10}{2}=0\\
x^2-x+\frac{8}{10}-\frac{50}{10}=0\\
x^2-x-\frac{42}{10}=0\\
x^2-x+\frac{1}{4}-\frac{1}{4}-\frac{42}{10}=0\\
(x-\frac{1}{2})^2=\frac{1}{4}+\frac{42}{10}\\
(x-\frac{1}{2})^2=\frac{5}{20}+\frac{84}{20}\\
(x-\frac{1}{2})^2=\frac{89}{20}\\
x-\frac{1}{2}=\sqrt{\frac{89}{20}} \vee x-\frac{1}{2}=-\sqrt{\frac{89}{20}}\\
x=\frac{1}{2}+\frac{\sqrt{89}}{\sqrt{20}} \vee x=\frac{1}{2}-\frac{\sqrt{89}}{\sqrt{20}}\\



x=\frac{1}{2}+\frac{\sqrt{89}}{2\sqrt{5}} \vee x=\frac{1}{2}-\frac{\sqrt{89}}{2\sqrt5}}\\
x=\frac{1}{2}+\frac{\sqrt{445}}{10} \vee x=\frac{1}{2}-\frac{\sqrt{445}}{10}}\\
x=\frac{5+\sqrt{445}}{10} \vee x=\frac{5-\sqrt{445}}{10}}\\
7 0
3 years ago
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