Solve the problems. Write the complete proof in your homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it.

This is an interesting problem. The underlying solution is to solve a system of equations.

First we need to define what's a cubic polynomial function :

f(x) = [tex]ax^{3}+bx^{2}+cx+d[/tex], where a,b,c,d are constant values.

We assume from the problem that f(-1) = 40, and that the zeros of our unknown function are -6,-5 and -2.

This gives us a system of equation to solve :

[tex]-216a +36b-6c+d=0\\-125a+25b-5c+d=0\\-8a+4b-2c+d=0\\-a+b-c+d = 40\\[/tex]

Good luck

Using the Factor Theorem, it is found that the function is given by:

[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

From the graph, the zeroes are [tex]x_1 = -8, x_2 = -3, x_3 = 10[/tex], hence:

[tex]f(x) = a(x + 8)(x + 3)(x - 10)[/tex]

[tex]f(x) = a(x^2 + 11x + 33)(x - 10)[/tex]

[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]

From the y-intercept, that is, when [tex]x = 0, y = -13.5[/tex], we find a.

[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]

[tex]-330a = -13.5[/tex]

[tex]330a = 13.5[/tex]

[tex]a = \frac{13.5}{330}[/tex]

[tex]a = 0.0409[/tex]

Hence:

[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]

To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382

Answer:

first guy is wrong

Step-by-step explanation:

my teacher said it's wrong, when I find out the right answer ill put it here

Answer:

Choose 1/25 as the common denominator

Step-by-step explanation:

1/25 is the lowest number that both existing denominators can be factored into.

6/25 would remain the same....  6/25

4/5 would become 20/25.....  multiply the top and bottom by 5

So 6/25 - 20/25 = - 14/25

Answer:

well the answer would be 45?

Step-by-step explanation:

Answer:

[tex]f(x) = - 2 {x}^{3} \\ g(x) = 3x - 5 \\ h(x) = x - 1 \\ g(h(x)) = 3(x - 1) - 5 \\ = 3x - 3 - 5 = 3x - 8 \\ f(g(h(x)) )= - 2 {(3x - 8)}^{3} \\ f(g(h(3)) )=- 2 {(3(3) - 8)}^{3} \\ = - 2 {(9 - 8)}^{3} \\ f(g(h(3)) )=- 2[/tex]

Answer:

It would be 74 remainder 2, the first one

The answer is 3/16f-12/8g

Answer:

8/27 ft cubed

Step-by-step explanation:

2/3 cubed = 8/27

8/27 ft cubed

4173

Hope this helped you- have a good day bro cya)

Hundreds place = 1

Ones place = 3

Thousands place = 4

Tens place = 7

Number: 4173

Hope this helps!! :)

Given the graph and the table of functions, f(x) and g(x), the following evaluated:

a. f(0) = 9

b. g(2) = -3

c. f(-1) = 5

Given the functions, f(x) and g(x), the following can be evaluated:

a. Find f(0):

Using the table given, what we need to determine is the of the output, f(0) that an input value, x = 0, will give.

Therefore,

f(0) = 9

b. Find g(2):

From the graph, find the corresponding value of g(x) that corresponds with x = 2.

Therefore,

g(2) = -3

c. Find f(-1):

From the table, find the corresponding value of f(x) that corresponds with x = -1.

Therefore,

f(-1) = 5

Learn more here:

https://brainly.com/question/19639627

Answer:

35 : w = 1 : 2

obviously w = 70

Step-by-step explanation:

Hopefully this helps you :)

Have a nice day.

apokibunnyavatar

Answer:

x ≤ -9 and x ≤ 5

Step-by-step explanation:

2x² + 4x - 85 ≤ -4x +5

2x² + 8x - 85 ≤ 5

2x² + 8x - 90 ≤ 0

x² + 8x -180 ≤ 0

(x + 18)(x - 10) ≤ 0

(x + 9)(x - 5) ≤ 0

x + 9 ≤ 0

x ≤ -9

x - 5 ≤ 0

x ≤ 5

Answer:

You have been directed to trim $10,000 from the monthly warehouse

told that you cannot reduce the costs for HVAC, refrigeration, and ligh

expense must be cut significantly?

A. Water

B. Copiers

C. Computers

D. Lights

Answer:

aaaaaaaa nad its by

Step-by-step explanation:

Answer:

[tex]f'( x ) = \frac{f(b) - f(a)}{b - a} \\ = \frac{f(6) -f(a)}{6 - 1} \\ 3\leqslant \frac{f(6) - 10}{5} \\ 15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25[/tex]

Answer:

25

Step-by-step explanation:

Our "best" case is when [tex]f'(x) = 3[/tex] everywhere - if it changes it means [tex]f(x)[/tex] will grow faster. But if [tex]f'(x)[/tex] is constant, it means [tex]f(x)[/tex] is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)

Answer:

4+2=6-3

Step-by-step explanation:

Answer:

y=-0.5x+3.5

Step-by-step explanation:

Answer:

4 and 1/2 cups of flour

Step-by-step explanation:

First, you need to divide 2 by 1/3, which will give you 6. Then multiply 6 by 3/4, which gives you 4 1/2. Hope this helped!

Answer:

x = 12

y = 4

Step-by-step explanation:

x + y = 16

x - y = 8

y + 8 = x

Replace x with y + 8 in the new equation

8 + 2y = 16 ----> we can minus 8 on both sides

2y = 8 -----> divide both sides by 2

y = 4

Now for the x value

x + 4 = 16 ----> minus 4 on both sides

x = 12

Answer:

12 and 4

Step-by-step explanation:

Answer:

Georgia's brother  > 176 Ounces

Step-by-step explanation:

He weighed LESS THAN 11 pounds, which is equal to 176 ounces. He must have weighed 175 ounces or less.

Answer:

0<x<176

Step-by-step explanation:

Answer: Use the distributive property to multiply 3 by y−4.

3y−12−2(y−4)

Use the distributive property to multiply −2 by y−4.

3y−12−2y+8

Combine 3y and −2y to get y.

y−12+8

Add −12 and 8 to get −4.

Anwser:

y−4

Step-by-step explanation:

Hope this helps!

Answer:

a) 9/11 = 0.8181...

b) 4/5 = 8/10 = 0.8

c) -17/5 = -34/10 = -3.4

d) 5/9 = 0.5555...

Answer:

are you cheating again?

Step-by-step explanation:

cuz I wanna know the answer too

Answer: 270 inches squared

Answer: 14:26

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Answer:

15) 104 lbs

16) 263 miles

Step-by-step explanation:

15)  

4/7 of their weight (182) = the water weight

4/7 × 182 = 104 lbs

16)

3.5 months = 920 miles

1 month = 920 ÷ 3.5

= 262.8571429 ≈ 263 miles

Answer:

15) 104 lb

16) 262 6/7 miles/month

Step-by-step explanation:

15)

4/7 * 182 lb = 4/7 * 182/1 lb = (4 * 182)/(7 * 1) lb = (4 * 7 * 26)/7 lb = 104 lb

Answer: 104 lb

16)

(920 miles)/(3 1/2 months) = (920 miles)/(7/2 months) =

= 920/1 miles * 2/(7 months) = (920 * 2 miles)/(7 months) =

= 1840/7 miles/month = 262 6/7 miles/month

Answer:

Answer A

Step-by-step explanation:

Alt Interior angles make two angles parallel

The cost of pen and colored pencils per piece is =10.85

The new total length of both Betty and Beth is =227.2cm

Total number of pens Randy needs to buy = 5

Total number of colored pencils Randy needs to buy= 3

The both items are bought at the same prize = a

The cost of five pens is = 5× a = 5a

The cost of colored pencils is = 3 × a= 5a

The money needed to spend on the items= 86.78

To find the cost of each item which is a ,

5a + 3a = 86.78

(5+3) a= 86.78

8a = 86.78

therefore a = 86.78/8

= 10.85

Therefore the prize of each item is = 10.85. That is option B

Betty's height = 119.2 cm

Beth's height = 105.6cm ( which remained the same)

But Betty's height after 6 months = (6× 0.4) + 119.2

= 2.4 + 119.2

= 121.6 cm

Therefore, the total new height= 121.6 + 105.6

= 227.2cm

That is option A.

Hello!

11 weeks plus 12 weeks equals the total number of weeks.

23 weeks

Hope this helps!

#HaveAnAmazingDay

[tex]GraceRosalia :)[/tex]