Please help me i'm struggling!

The polynomial function of degree 7 with the given zeros and multiplicities is: f(x) = x³(x + 2)³(x - 2)

To find a polynomial function with the specified zeros and multiplicities, we can construct it using the factors that correspond to each zero and multiplicity.

Since -2 has a multiplicity of 3, it means it appears three times as a zero. Similarly, 0 has a multiplicity of 3, and 2 has a multiplicity of 1.

A polynomial function with these zeros and multiplicities can be written as:

f(x) = (x + 2)³ × x³ × (x - 2)

To make it a polynomial of degree 7, we can multiply it by an additional linear factor:

f(x) = (x + 2)³ × x³ × (x - 2) × (x - r)

Where "r" is a constant representing the last factor. This factor ensures the degree of the polynomial is 7.

Now, we need to find the value of "r" to complete the polynomial. Since we already have three factors with multiplicity 3 and one factor with multiplicity 1, the polynomial has already reached its degree of 7.

Therefore, we don't need to include the "x - r" factor, and the final polynomial is:

f(x) = (x + 2)³ × x³ × (x - 2)

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The polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 2 as a zero of multiplicity 1 is f(x) = x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2.

To find a polynomial function of degree 7 with the given zeros and multiplicities, we can start by constructing the factors of the polynomial.

Since -2 is a zero of multiplicity 3, we have the factor (x + 2)^3. Similarly, since 0 is a zero of multiplicity 3, we have the factor x^3. Lastly, since 2 is a zero of multiplicity 1, we have the factor (x - 2).

Multiplying these factors together, we obtain:

(x + 2)^3 * x^3 * (x - 2)

Expanding this expression, we get:

(x^3 + 6x^2 + 12x + 8) * x^3 * (x - 2)

To simplify further, we multiply the terms:

(x^6 + 6x^5 + 12x^4 + 8x^3) * (x - 2)

Expanding again, we obtain:

x^7 - 2x^6 + 6x^6 - 12x^5 + 12x^4 - 24x^3 + 8x^3 - 16x^2

Combining like terms, we get:

x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2

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Answer: [tex]20,706\ m^3[/tex]

Step-by-step explanation:

Given

The warehouse has the following dimension

Height is [tex]h=8\frac{1}{2}\ m[/tex]

[tex]h=\dfrac{17}{2}\ m[/tex]

Length is [tex]l=120\ m[/tex]

Width is [tex]w=20\frac{3}{10}\ m[/tex]

[tex]w=\dfrac{203}{10}\ m[/tex]

Volume of the warehouse is the product of height, length and width

[tex]\Rightarrow V=h\times l\times w\\\\\Rightarrow V=\dfrac{17}{2}\times 120\times \dfrac{203}{10}\\\\\Rightarrow V=20,706\ m^3[/tex]

Therefore, the length of the warehouse is [tex]20,706\ m^3[/tex].

Answer:

Line C.

Step-by-step explanation:

Negatives are supposed to be on the left side of the 0, not the right side, so we can determine that lines B and D are wrong. On line A, -3/5 is on -2 which is wrong, so line C is the correct answer.

Answer:

[tex]n=9[/tex]

Step-by-step explanation:

[tex]3n-18=9[/tex]

[tex]3n+18=[/tex] +18

[tex]3n=27[/tex]

[tex]3(9)=27[/tex]

[tex]n=9[/tex]

Answer:

[tex]g(-3)=42[/tex]

Step-by-step explanation:

Given:

[tex]g(x)=4x^2+6[/tex]

Let's substitute -3 for [tex]x[/tex]

[tex]g(-3)=4(-3)^2+6[/tex]

Now, let's solve

[tex]g(-3)=4(9)+6[/tex]

[tex]g(-3)=36+6[/tex]

[tex]g(-3)=42[/tex]

Hope this helps

Answer:

c = 12

Step-by-step explanation:

If c is one side you would need to multiply that side times 4 because that's the way you find the perimeter. In this case, you need to divide 48 by 4 so that you get the centimeters for each side. The answer is 12

Brainliest pls

Answer:

B

[tex]area = 2\pi \: rh \\ = 2 \times 3 \times 5 \times 1 \\ = 30 \: {cm}^{2} [/tex]

Answer:

Hi, your answer is y=[tex]-\frac{1}{2} x[/tex]-3

Step-by-step explanation:

We will use the slope-intercept formula which is

[tex]\frac{y2-y1}{x2-x1}[/tex]

We will use two points in this case I'll use

(-2,-2) and (-8,1)

[tex]\frac{1-(-2)}{-8-(-2)}[/tex]=[tex]-\frac{3}{6}[/tex] which can be simplified as [tex]-\frac{1}{2}[/tex]

Your Y will be -3

which your final answer will be y=-1/2x-3

Hope this helps :)

Answer:

2400 seconds

Step-by-step explanation:

Answer:

40 min = 2400 sec

Step-by-step explanation:

Answer:

your answer would be become 11 feet

Answer:

15

Step-by-step explanation:

Given :

StartAbsoluteValue 8 EndAbsoluteValue + StartAbsoluteValue Negative 7 EndAbsoluteValue

THE ABSOLUTE value of any given number is the positive equivalent of that number ; hence ;

|8| = 8 ;

|-7| = 7

Hence,

|8| + |-7| = 8 + 7 = 15

Answer:

15

Step-by-step explanation:

Answer:

A (x+3)−1=8open paren x plus 3 close paren minus 1 is equal to 8

C 2(x+3)=182 times open paren x plus 3 close paren is equal to 18

E 2x=122 x is equal to 12

Step-by-step explanation:

Given:

2(x+3) − 2 = 16

2x + 6 - 2 = 16

2x = 16 - 6 + 2

2x = 12

x = 12/2

x = 6

A. (x+3)−1=8

x + 3 - 1 = 8

x = 8 - 3 + 1

x = 6

B (x+3)−2=8

x + 3 - 2 = 8

x = 8 - 3 + 2

x = 7

C 2(x+3)=18

2x + 6 = 18

2x = 18 - 6

2x = 12

x = 12/2

x = 6

D x+3=9x

3 = 9x - x

3 = 8x

x = 3/8

E 2x=12

x = 12/2

x = 6

F 2x=15

x = 15/2

x = 7 1/2

Answer:

Line m

Step-by-step explanation:

The line is labeled with an m.

Answer:

Sally is 63

Step-by-step explanation:

Represent Sally's age by x and Sam's by  y.

Then x = 3y and x + y = 84.

Substituting 3y for x in the second equation, we get:

3y + y = 84, or 4y = 84, or y = 21.  Since Sally is 3 times as old as Sam, we multiply 21 by 3:  Sally's age is 3(21 years) = 63 years

the equivalent expression is C

Answer:

P earned $ 718.85.

Step-by-step explanation:

Given that P borrowed $ 16000 from a person at 12% per annum simple interest and lent the whole amount to Q at the same rate of annually compound interest, to determine how much did he gain after 3 years the following calculation must be performed:

16,000 x 0.12 x 3 = X

1,920 x 3 = X

5,760 = X

16,000 x (1 + 0.12 / 1) ^ 3 = X

16,000 x 1.12 ^ 3 = X

16,000 x 1.404928 = X

22,478.85 = X

22,478.85 - 16,000 = 6,478.85

6,478.85 - 5,760 = X

718.85 = X

Therefore, P earned $ 718.85.

Answer:

The area of the image is equal to the area of the pre-image multiplied by the scale factor.

The area of the dilated trapezoid is __54*2/3=36_ square centimeters.

Answer:

80miles

Step-by-step explanation:

Area of a square grid = L²

L is the side length of the grid

Given that Area of the square = 400mi square

400 = L²

L =√400

L = 20miles

To get the number of miles travelled, we will find its perimeter

P = 4L

P = 4(20)

P = 80miles

Hence Jacob's family travels 80miles

4x + 5 = 3x +4

4x - 3x = 4-5

x = -1

value of x is equal to -1

Answer:

x = -1

Step-by-step explanation:

4x + 5 = 3x +4 (subtract 3x from both sides)

-3x        -3x

=1x         =0

rewrite: x + 5 = 4 (subtract 5 from both sides)

                  -5  -5

                  =0  =-1

Therefore x = -1 (Please mark brainliest hope i helped :)

Answer:

S = 62.5%

Step-by-step explanation:

Given the following data;

Ratio of J:S = 3:5 = 3 + 5 = 8

To find what percent of team members are seniors;

[tex] S = \frac {5}{8} * 100 [/tex]

[tex] S = \frac {500}{8} [/tex]

S = 62.5%

Additionally, to find what percent of team members are juniors;

J = 100 - S

J = 100 - 62.5

J = 37.5%

Answer:

B

Step-by-step explanation:

His friends snack was 6 dollars.

15.25+1.25= 16

16+1.25= 17.25

17.25+1.25= 19

1/6 of 30 is 5 because 5x6=30.

30-19=11

He has to have 5 left over so the snack was 6 dollars.

Answer:

6b+16n=178

n=b+7

Step-by-step explanation:

Let b=the number of bracelets made

Let n=the number of necklaces made

​

System of Equations:

​

6b+16n=178

n=b+7

Answer:

The answer is 2(23x+4).

Answer:

D

Step-by-step explanation:

To find the inverse of a function, first replace f(x) with y.

Next, switch all the x's and y's, and then solve for y.

Finally, replace y with f-1(x).

Answer:

-1

Step-by-step explanation:

y2-y1/x2-x1

-4-5/5- -4

-9/9

-1

Answer:

16.6 units

Step-by-step explanation:

Hi there!

We can use the Pythagorean theorem to help us solve this problem: [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle (the hypotenuse) and a and b are the other two sides

It's safe to assume that x is the longest side in this triangle, making it the c value. Plug 14 and 9 into the equation as a and b and solve for x:

[tex]14^2+9^2=x^2\\196+81=x^2\\277=x^2\\x=16.6[/tex]

Therefore, the value of x is 16.6 units when rounded to the nearest tenth.

I hope this helps!

Answer:

[tex] \frac{1}{ {a}^{42} } [/tex]

Step-by-step explanation:

[tex] {( {r}^{ - 7}) }^{6} [/tex]

Since,

[tex] {( {a}^{x}) }^{y} = {a}^{xy} [/tex]

Then,

[tex] = {r}^{ (- 7 \times 6)} = {r}^{ - 42} [/tex]

Since,

[tex] {a}^{ - 1} = \frac{1}{a} [/tex]

Then,

[tex] = {r}^{ - 42} = \frac{1}{ {r}^{42} } [/tex]

Therefore,

2nd Option is correct.