Help me please I’m dumb

Let $f(x)$ be a quadratic polynomial such that $f(-4) = -22,$ $f(-1)=2$, and $f(2)=-1.$ Let $g(x) = f(x)^{16}.$ Find the sum of

Murrr4er [49]

Answer:

The sum of the coefficients of the terms in (-1.5·x² + 0.5·x + 4)¹⁶ that have even degree is -4273411167.501

Step-by-step explanation:

The parameters given are;

f(-4) = -22

f(-1) = 2

f(2) = -1

g(x) = f(x)¹⁶

The function f(x) is presented as follows;

f(x) = a·x² + b·x +c

We have;

-22 = a·(-4)² + b·(-4) +c

-22 = a·16 - 4·b +c ..............(1)

2 = a·(-1)² + b·(-1) +c

2 = a - b +c...........................(2)

-1 = a·(2)² + b·(2) +c

-1 = 4·a + 2·b +c...................(3)

Solving the equations (1), (2), and (3) by using an online linear systems solver, we get;

a = -1.5, b = 0.5, c = 4

Therefore, f(x) = -1.5·x² + 0.5·x + 4

f(x)¹⁶ = (-1.5·x² + 0.5·x + 4)¹⁶ which gives the coefficients of the even terms as follows;

656.841 - 19267.331 + 248302.054 - 1772904.419 + 6735603.932 - 2868054.635 - 119602865.901 + 750783340.827 + -2542435585.611 + 5338903756.992 - 6048065910.25 -1031335136 + 17223697920 - 32238338048 + 32107397120 - 17716740096 = -4273411167.501.

3 0

3 years ago

Find the area and perimeter of this irregular shape: picture #8

8090 [49]

Answer:

Perimeter: 14.2

Area: 9.2

Step-by-step explanation:

Simple times for area

simple plus for perimeter

3 0

2 years ago

Read 2 more answers

When Mrs. Stewart makes pie dough, she uses 2/3 cup of shortening for every 2 1/2 cups of flour which proportion could be used t

zloy xaker [14]

Answer:

The amount of flour Mrs.Stewart needs for 5 cups of shortening $=\frac{75}{4} =18\tfrac{3}{4}$ cups.

Step-by-step explanation:

Mrs.Stewart pie dough needs $\frac{2}{3}$ cups of shortening for $2\tfrac{1}{2}=\frac{5}{2}$ cups of flour.

Now we assume that the shortening needed for $x$ cups of flour is $y$ cups.

Accordingly we can arrange the ratios.

So for one cup of shortening how many cups of flour is needed we have to use the unitary method:

$\frac{cups\ of flour\ (x)}{cups\ of\ shortening\ (y)} =\frac{x}{y} =\frac{5/2}{2/3}$

Plugging the value of $y=5$ as it is number of cups of shortening Mrs.Stewart have used.

And multiplying both sides with $5$ .

Number of cups of flour needed when $5$ cups of shortenings are used $(x) =\frac{x}{y} =\frac{5/2}{2/3}$ .

So, $(x)=\frac{5\times 3\times 5}{2\times 2} =\frac{75}{4} = 18\tfrac{3}{4}$

The amount of floor Mrs.Stewart needed for $5$ cups of shortening $= 18\tfrac{3}{4}\$ cups of floor.

3 0

2 years ago

Solve the inequality. Graph the solution set and write it in interval notation. .

STALIN [3.7K]

Answer:

-4

Step-by-step explanation:

8 0

2 years ago

Multiply: 4(−5 2/3) Enter your answer as a fraction in simplest form, like this: 42/53

8_murik_8 [283]

Answer:

The amount that came is $\frac{-68}{3}$

Step-by-step explanation:

The computation is shown below:

According to the question, it is mentioned that

Multiply 4 by $-5\frac{2}{3}$

First open the equation in a fraction it would be $\frac{-17}{3}$

Now multiplied the above fraction by a 4

That gives the result of $\frac{-68}{3}$

Hence, the amount that came is $\frac{-68}{3}$

We simply multiply the 4 with the given fraction

Thus the above represents the simplest form of the fraction

5 0

2 years ago