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2 years ago

The graph represents a cubic function. Write the function.

Mathematics

2 answers:

Norma-Jean [14]2 years ago

7 0

Zeros are

(0,0)
(-3,0)
(-4,0)

Write in factor form and solve

(x-0)(x-(-3))(x-(-4))=0
x(x+3)(x+4)=0
x[x(x+4)+3(x+4)]=0
x(x²+4x+3x+12)=0
x(x²+7x+12)=0
x³+7x²+12x=0

Points given (-2,16)

Solve for n

n(x³+7x²+12x)=y

On solving we get

n=-4

So the function is

y=-4(x³+7x²+12x)
y=-4x³-28x²-48x

TiliK225 [7]2 years ago

4 0

Answer:

-4x³ - 28x²- 48x

Explanation:

x-intercept: (-4, 0), (-3, 0), (0, 0)

→ so equation: a(x+4)(x+3)(x+0)

point given: (-2, 16)

→ substitute these points to find a

a(-2+4)(-2+3)(-2) = 16

a = -4

so the graphed cubic equation:

-4(x+4)(x+3)(x+0)

-4x³ -28x²-48x

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Find z such that 97.5% of the standard normal curve lies to the left of z. (Enter a number. Round your answer to two decimal pla

fomenos

Answer:

z=1.96

Step-by-step explanation:

Using normal distribution table or technology, 97.5% corresponds to z=1.959964, generally denoted z=1.96, or 1.96 standard deviations above the mean.

(above value obtained from R)

6 0

3 years ago

Plz help, I'm taking an Advanced class (Algebra) Will give brainliest ✔✔✔✔✔✔✔✔✔

bija089 [108]

Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$(x_1, y_1)$ and $(x_2, y_2)$ are points on the function

You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

$h(0) = 3(5)^0 = 3 \cdot 1 = 3$

$h(1) = 3(5)^1 = 3 \cdot 5 = 15$

$h(2) = 3(5)^2 = 3 \cdot 25 = 75$

$h(3) = 3(5)^3 = 3 \cdot 125 = 375$

Now, let's find the slopes for each of the sections of the function:

Section A

$m = \dfrac{15 - 3}{1 - 0} = \boxed{12}$

Section B

$m = \dfrac{375 - 75}{3 - 2} = \boxed{300}$

Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

$\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25$

It is 25 times greater. This is because $3(5)^x$ is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.

7 0

3 years ago

Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFraction right-parenthes

Alina [70]

Answer:

$y-\frac{1}{3}=\frac{3}{4}(x-4)$

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

In this problem we have

$point\ (4,\frac{1}{3})$

$m=\frac{3}{4}$

substitute the given values

$y-\frac{1}{3}=\frac{3}{4}(x-4)$

y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

7 0

3 years ago

Read 2 more answers

What is the solution to this equation 2/3x+1=1/6×-7

Alika [10]

Answer:

A . x= -16

Step-by-step explanation:

$\\\frac{2}{3}x+1=\frac{1}{6}x-7\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\\frac{2}{3}x+1-1=\frac{1}{6}x-7-1\\\\\frac{2}{3}x=\frac{1}{6}x-8\\\\\mathrm{Subtract\:}\frac{1}{6}x\mathrm{\:from\:both\:sides}\\\\\frac{2}{3}x-\frac{1}{6}x=\frac{1}{6}x-8-\frac{1}{6}x\\\\= \frac{1}{2}x=-8\\\\\mathrm{Multiply\:both\:sides\:by\:2}\\\\2\times \frac{1}{2}x=2\left(-8\right)\\\\x=-16$

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3 years ago

Classify the triangle by its angles and sides

postnew [5]

Answer; A: Right scalene. Square on the corner tells you it's a right triangle. It's a scalene triangle because none of the sides are equal.

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2 years ago