Find the geometric mean between each pair of numbers

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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:

4+2=6-3

Step-by-step explanation:

Answer:

y=-0.5x+3.5

Step-by-step explanation:

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.

Answer:

8/27 ft cubed

Step-by-step explanation:

2/3 cubed = 8/27

8/27 ft cubed

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:

1 Large Salad uses 10 cherry tomatoes.

1 Small Salad uses 6 cherry tomatoes.

Jorge wants to make 6 large salads: 6 x 10 = 60 cherry tomatoes for the large salads.

4 small salads: 4 x 6 = 24 cherry tomatoes.

Now we add them together to find the total amount: 60 + 24 = 84 Cherry Tomatoes.

I hope this has helped! :)

Answer:

He needs 84 cherry tomatoes.

Step-by-step explanation:

6 * 10 = 60 cherry tomatoes

6 * 4 = 24 cherry tomatoes

60 + 24 = 84 cherry tomatoes

Hope this helps!

Answer: 270 inches squared

Answer:

shorter piece = 6. longer piece = 12

Step-by-step explanation:

short piece = s

long piece = l

l+s= 18

l= 6+s , substitute

6+s+s = 18

6+2s= 18

2s= 18-6

2s= 12

s=12/2

s= 6= shorter piece

l= 6+s

l= 6+6= 12 = longer piece

Answer:

It would be 74 remainder 2, the first one

Hello!

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

23 weeks

Hope this helps!

#HaveAnAmazingDay

[tex]GraceRosalia :)[/tex]

Answer:

The correct answer I think is D

Step-by-step explanation:

The explanation of the other person is right, but you do 3-7, which gives u -4

Answer: 14:26

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

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:

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

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:

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:

-13, 11, 19

Step-by-step explanation:

You will plug in the numbers for x in each equation so you will have three equations:

1. 8(-1)-5

2. 8(2)-5

3. 8(3)-5

Solve these equations and you will get

1. -13

2. 11

3. 19

Answer:

7/12

1/6 to 2/12 add 5/12 to get 7/12

Answer:

5

Step-by-step explanation:

f(-1) = -3(-1)^3 + 2(-1)^2

f(-1) = -3(-1) + 2(1)

f(-1) = 3 + 2

f(-1) = 5

Hope this helps! Pls give brainliest!

Answer:

5

Step-by-step explanation:

plug in -1 for x

so

[tex] -3 ({ - 1})^{3} + 2 ({ - 1})^{2} [/tex]

went we solve we get

[tex]3 + 2 \\ = 5[/tex]

so 5 is ur answer

pls give brainlist

if any questions ask

have a great day thanks :)

Answer:

-25

Step-by-step explanation:

When you owe someone something, in integers, your answer is in the negative.

Answer:

are you cheating again?

Step-by-step explanation:

cuz I wanna know the answer too

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!

Nominal data, derived from the Latin word 'name,' is just that: a name. Republicans, Democrats, Independents, and so on. You have no idea who or why you're voting for, but you do have a party name, so that's something, right? To make this more quantitative, give each a random number of your choosing (usually small sequential numbers like 1, 2, or 3 but it could be anything). The kinds of statistical analysis you can do with nominal data are severely restricted since the value of the number has no relevance in your environment; it's simply a placeholder.

Ordinal data gives a numerical order to a prior category, such as 'Republican,' although that order does not have to signify anything. Let me explain: suppose you're questioned on a poll to rank your preferred candidate on a scale of 1 to 5. Obviously, a value of '5' is better than a value of '1,' but what does it mean? I'm glad you asked.

Interval data takes ordinal ideas and couples them with schemata that make sense. Using our prior 1-5 scale, for example, 1 degree Fahrenheit is cooler than 5 degrees. Interval data lacks a point of origin, which makes sense when discussing temperatures since 0 degrees Fahrenheit does not indicate a lack of temperature.

Ratio data combines the preceding three ideas and adds a point of origin, or '0' value. The greatest example I could think of was speed. We all realize that 5 mph is quicker than 1 mph, precisely since we all know that 0 mph implies we're not moving at all.

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:

[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)

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

Answer:

h=23

Step-by-step explanation:

triangle equals 180 degrees

180-40=140

140/4=35