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Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

3 years ago

Write an equation in point-slope form for the line that has a slope of 4/5 and contains the point (−5, −3).

ankoles [38]

y = mx + b, where m = slope, and b = y-intercept.

Since you are not given the y-intercept, you have to solve for it through the equation, y = (4/5)x (which is the slope you are given) + b, and replace x and y with values given, which are (-5,-3)

y = (4/5)x + b

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

-3 = -4 + b

1 = b

Then replace b in the first equation to get the answer

y = (4/5)x + 1

5 0

3 years ago

Invent measurements that would show triangle XYZ is similar to triangle NLM using the Side-Angle-Side Triangle Similarity Theore

IRINA_888 [86]

Answer:

The answer is that when you put the LMN. You can rotate it. Then we know it is similar.

6 0

2 years ago

The graph of F(x) = x^2 is shown.

max2010maxim [7]

Answer:

B

Step-by-step explanation:

Given a function of a parabola (quadratic) in the form f(x) = x^2, we have a translated function as:

g(x) = a(x-b)^2

Where

a is the vertical compression or stretch. If a > 1, it is a vertical stretch and if 0 < a < 1, it is a vertical compression.

b is the horizontal translation b units to the right

The function given is p(x) = 3(x-8)^2

So it means that it is a vertical stretch with a factor 3 and the graph is shifted horizontally 8 units right

the correct answer is B

4 0

2 years ago

Find the circumference of a circle if the area is 300 square centimeters.

Blababa [14]

The answer is: [C]: 61.38 cm .
_______________________________________________

Note: A = $\pi *r$ ²

300 = (3.14) * r² ;
______________________
Divide each side by "3.14" ;

r² = 300/3.14 ;

r² = 95.5414012738853503 ;

√r² = √(95.5414012738853503) ;

r = 9.7745281867661188048

Circumference, "C" = $\pi$ * d ; (d = diameter = 2*r);

C = 2* $\pi$ *r ;

C = 2*(3.14)*(9.7745281867661188048)

C = 61.384037012891226094144 ; which rounds to answer choice:
[C]: 61.38 cm .
________________________________________________________

8 0

2 years ago

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