MATHEMATICS MIDDLE SCHOOL

Which of the following functions best represents the graph?f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Answers

Answer 1

Answer:

Answer:

$f(x)=x^3+x^2-4x-4$

Step-by-step explanation:

From the graph, the x-intercepts are;

$x=-2$

$x=-1$

$x=2$

These are root of the polynomial function represented by the given graph.

By the remainder theorem;

$f(-2)=0,f(-1)=0,f(2)=0$

According to the factor theorem, if $(x-a)$ is a factor of $f(x)$ , then $f(a)=0$

This implies that;

$(x+2),(x+1),(x-2)$ are factors of the required function.

Hence; $f(x)=(x+1)(x-2)(x+2)$

We expand using difference of two squares to obtain;

$f(x)=(x+1)(x^2-4)$

We expand using the distributive property to get;

$f(x)=x^3-4x+x^2-4$

Rewrite in standard form to obtain;

$f(x)=x^3+x^2-4x-4$

Answer 2

Answer:

Answer:

Choice A: f(x) = x^3 + x^2 − 4x − 4

Step-by-step explanation:

Here's a great and simple answer.

Ok first we need to take the x intercepts to solve.

If we look at the graph we see the x ints are -2,+1 and +2.

To solve we need to put them into factor form

= (x-2) (x+2) and (x+1)

Simplify: (x-2) (x+2) = (x^2-4) and (x+1)

Now we take (x^2-4) and (x+1) and multiply them to find our answer

(x^2-4) (x+1)

= x^2(x) and x^2(1) = x^3 and x^2.

now the other: -4(x) and -4(+1) = -4x and -4

We have nothing common here so we just join them

= x^3 + x^2 - 4x - 4, and that is the same as choice A.

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A pillow that usually costs $18 is marked down 25%. Which expressions can be used to find the new price of the pillow?

Answers

Answer:

x = 18-(0.25×18)

Step-by-step explanation:

The price of the pillow = $18.00

cost is marked down = 25% = $(25)/(100)$ = 0.25

Let the new price be x

The expression that can be used to find the new price of the pillow will be

x = 18-(0.25×18)

n= new price

n=18-(18*0.25)

What is the rate of change of the linear function that has a graph that passes through the points (2,9) and (-1,3)?

Answers

Answer:

Step-by-step explanation:

The rate of change is just the slope, which is -6/-3 or 2.

Final answer:

The rate of change of the linear function can be determined by calculating the slope of the line passing through the given points. The slope of the line passing through the points (2,9) and (-1,3) is 3. Therefore, the rate of change of the linear function is 3.

Explanation:

The rate of change of the linear function can be determined by calculating the slope of the line passing through the given points.

To find the slope, we can use the formula: slope = (change in y) / (change in x). By substituting the coordinates of the points (2,9) and (-1,3), we get a slope of 3.

Therefore, the rate of change of the linear function is 3.

Learn more about rate of change here:

brainly.com/question/29181502

#SPJ3

What is the cost of an 8-ounce salad without soup? How do you know?

Answers

Answer:

Picture?

Step-by-step explanation:

PLEASEEE HELPP The water usage at a car wash is modeled by the equation W(x) = 3x3 + 4x2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 2x3 + 2x2 − 18x − 11
C(x) = 3x3 + 2x2 − 18x + 11
C(x) = 3x3 + 2x2 − 18x − 11
C(x) = 2x3 + 2x2 − 18x + 11

Answers

We have been given that the water usage at a car wash is modeled by the equation $W(x) = 3x^3+4x^2-18x + 4$ , where W is the amount of water in cubic feet and x is the number of hours the car wash is open.

The amount of decrease in water used is modeled by $D(x) = x^3 + 2x^2 + 15$ , where D is the amount of water in cubic feet and x is time in hours.

The function C(x) will be difference of W(x) and D(x) that is $C(x)=W(x)-D(x)$ .

Upon substituting both function values in above formula, we will get:

$C(x)=3x^3+4x^2-18x + 4-(x^3 + 2x^2 + 15)$

Let us remove parenthesis.

$C(x)=3x^3+4x^2-18x + 4-x^3-2x^2-15$

Combine like terms.

$C(x)=3x^3-x^3+4x^2-2x^2-18x+4-15$

$C(x)=2x^3+2x^2-18x-11$

Therefore, the function $C(x)=2x^3+2x^2-18x-11$ represents the water used by the car wash on a shorter day and option A is the correct choice.

Answer:

Step-by-step explanation:

If sin 0 = 4/5 then what is cos(90-0)

Need answer in fraction

Answers

The result would be back to 4/5.

You can test this by finding the solving for theta when sin(theta) = 4/5. Then, enter that value into the expression cos(90 - theta). You will be back to just 4/5.

What is the answer to 68.20 ÷ 3.1