According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function f(x)=(4x3−13x+11)3?

Answer:

164.67 cm

Step-by-step explanation:

The arithmetic mean of height of 5 pupils is 164cm . Let the sum of heights of 5 pupils be x . Then , according to the question ,

[tex]\sf\longrightarrow \dfrac{x}{5}= 164cm [/tex]

On solving ,

[tex]\sf\longrightarrow x = 5*164cm =\bf{820cm}[/tex]

When a student of height 168cm is added ,

[tex]\sf\longrightarrow Mean = \dfrac{820cm+168cm}{6}\\[/tex]

[tex]\sf\longrightarrow Mean = \dfrac{988}{6}\\ [/tex]

[tex]\sf\longrightarrow \boxed{\pink{\sf Mean = 164.66 \approx 164.67 cm }}[/tex]

Answer: B is 11 feet tall

A=x+1 since A is one more than B

C=x+1/2 since C is one half more than B

B=x since B is just B

A+B+C=34.5

x+1+x+x+1/2=34.5

3x+1.5=34.5

3x=33

x=11

B is 11 feet tall

Answer:

$3672

Step-by-step explanation:

3060 x 20% = 612

612 + 3060 = 3672

Answer:

Step-by-step explanation:

Asked:  How many square tables are needed to place 100 pupils?

Given: Square table each has 4 pupils to sit

operation :  Multiplication, subtraction,  Division

Solve:

Number of pupils in 9 rectangular tables = 9*8 = 72 pupils

Remaining pupils = 100 - 72 = 28

Number of square table needed =28 ÷ 4 = 7

7 square tables are needed.

Answer:

0.134

Step-by-step explanation:

"By" means multiplied by, so the question is, what's 0.00536 multiplied by 25?

In the first step, we multiply all the numbers in the decimal by 5, and we get 0.02680. In the second, we multiply all the numbers in the decimal by 20, and we get 0.10720. Then we add the two together and get 0.134.

I hope that helped :)

Lets start by finding the equation.

25 is the constant, .3 is the slope, and 50.2 is the final.

This means that our equation is:

50.2 = .3x + 25

50.2 - 25 = .3x

25.2 = .3x

25.2 / .3 = x

84 = x

This means that Ken travelled 84 miles if his bill was $50.2.

I hope this helps! :)

[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]

[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]

Answer:

12 weeks

Step-by-step explanation:

I will use x to describe the amount of weeks.

200.39 (amount already have) + 80.10x (amount per week) = 1161.59 (total amount needed)

Now, just solve for x.

80.10x = 961.2

x = 12

Answer:

see explanation

Step-by-step explanation:

Under a rotation about the origin of 180°

a point (x, y ) → (- x, - y ) , then

A (- 5, - 8 ) → A' (5, 8 )

B (2, - 3 ) → B' (- 2, 3 )

C (- 2, 9 ) → C' (2, - 9 )

Answer:

No

Step-by-step explanation:

No, because s is less then 2. 7 is not less then 2.

‘Hope that helps! :)

Answer:

no

Step-by-step explanation:

s<2

s=7

7>2

Answer:

m = 5

Step-by-step explanation:

The x-coordinate of A is -2 and that of B is 0.  The increase in this coordinate from A to B is 2.  Similarly, the y-coordinate increases by 10.  The slope is therefore m = rise / run = 10/2, or m = 5

Answer:

$9.68 per Hour, $11.72 per Hour.

Step-by-step explanation:

What you thought of..

10% of original pay wage = $0.80

Sofia's Pay Wage will be incremented by 10% of $8 every 6 Months.

Function:

Sofia's Pay Wage = e

Original Pay Wage = o

Increment = i

6 Months = t

e = o + ti

1 Year = 12 Months

$8 + ($0.80 x 2) = $9.60

In 1 Year, Sofia's Pay Wage will be $9.60 per Hour

$8 + ($0.80 x 4) = $11.20

In 2 Years, Sofia's Pay Wage will be $11.20 per Hour

What I Thought Of..

Sofia's Pay Wage will be incremented by 10% every 6 Months.

Function:

Sofia's Pay Wage = e

Original Pay Wage = o

Increment = i

6 Months = t

e = o + t(ei)

1 Year = 12 Months

($8 + {10% of Sofia's Pay Wage}) = $8.80

($8.80 + {10% of Sofia's Pay Wage}) = $9.68

In 1 Year, Sofia's Pay Wage will be $9.68 per Hour

($9.68 + {10% of Sofia's Pay Wage}) = $10.65

($10.65 + {10% of Sofia's Pay Wage}) = $11.72

In 2 Years, Sofia's Pay Wage will be $11.72 per Hour

Brainly? (I spent a while on this)

Step-by-step explanation:

(a○b)(x) is the same as a(b(x)).

it is really that simple.

first you calculate the result of the inner function, and then that result is the input for the outer function.

that's it.

so,

(w○u)(2) = w(u(2))

u(2) = -2 -1 = -3

w(-3) = 2×(-3)² + 1 = 2×9 + 1 = 19

so, 19 is the first answer.

(u○w)(2) = u(w(2))

w(2) = 2×2² + 1 = 2×4 + 1 = 9

u(9) = -9 - 1 = -10

so, -10 is the second answer.

Answer:

355 ounces

Step-by-step explanation:

Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:

[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]

"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.

[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]

[tex]\frac{352oz}{1} + 3 = x[/tex]

[tex]352+3 = x[/tex]

[tex]x=355[/tex]

So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)

Answer: were you born yesterday

Step-by-step explanation:

Answer:

= -3x +3

Step-by-step explanation:

like terms (7x) -(4x)

or 7x + -4x = -3x

no like terms to condense 3

Hey there!

11x + 3 = 6

SUBTRACT 3 to BOTH SIDES

11x + 3 - 3 = 6 - 3

CANCEL out: 3 - 3 because it gives you 0

KEEP: 6 - 3 because it helps you solve for your x-value

11x = 6 - 3

11x = 3

DIVIDE 11 to BOTH SIDES

11x/11 = 3/11

CANCEL out: 11/11 because that gives you 1

KEEP: 3/11 because it simplifies for the x-value

SOLVE

x = 3/11

Therefore, your answer should bed x = 3/11

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

18⁰

Step-by-step explanation:

As AOB is a line so it's is 180 ⁰

Hence,

5y+3y+2y=180⁰

10y=180⁰

y=180⁰/10

y=18⁰

Answer:

20.63%

Step-by-step explanation:

189-20.63%=150,0093

Answer:

20.63%

Step-by-step explanation:

% change = (New Value - Initial Value)/(Initial Value) * 100

                 = (150-189)/189 * 100

                 = -20.63%

Though the value comes as negative but it only indicates that it is a percentage decrease. As the question mentioned that the value is decreased, the final answer would be only 20.63%.

Hopefully this helps!!

Hello there!

7 14/18 is the mixed number that has not been reduced to simplest form.

We can divide the numerator and denominator by 2 to reduce the fraction:

7 7/9

The answer is Option A. Hope this helps!

~Just a cheerful gal

#CarryOnLearning

[tex]SilentNature[/tex]

Answer:

27360

Step-by-step explanation:

38x40=1520

1520*18=27360

Answer:

Step-by-step explanation:180

Answer:

80

Step-by-step explanation:

i don't know if it is right

Answer: Domain is {-3, -2, -1, 1, 2, 3}. Range is {3, 4, 5}

Step-by-step explanation:

Domain in x values and therefore -3, -2, -1, 1, 2, 3. The range is y-values and you don't have to repeat same values making the range 3, 4, 5

Gustavo used 8 round tables and 6 rectangular tables.

Since Gustavo sets up tables for a caterer on weekends, and each round table can seat 8 people while each rectangular table can seat 10 people, and one weekend, his boss asked him to set up tables for 124 people, and he uses 2 more round tables than rectangular tables, to find the number of round tables and rectangular tables Gustavo used the following calculation must be performed:

Therefore, Gustavo used 8 round tables and 6 rectangular tables.

Learn more in https://brainly.com/question/25443927

Answer:

$50

Step-by-step explanation:

$370 - $120 = $250 ( 5 ballet tickets )

$250 divided by 5 tickets is $50 per ticket

Ratio is 50:40 or 5:4 simplified  

Answer:

7.22 x 10^5

Step-by-step explanation:

Remember that the decimal is always to the right of the ones place.

1. Move it one place to the left and multiply by 10 to compensate.

2. Move it two places to left and multiply by 10^2.

3. Move the decimal point three times and multiply 10^3 to compensate, and the pattern continues until you reach the very last digit, the 7.

4. Numbers after the 7 that are not zeros will be after the decimal point.

so, 7.22 x 10^5

Answer:

Step-by-step explanation:

Wall dimensions: 6 m x 5 m

=> Wall dimensions: 30 m²

Area of window: 0.5 x 2

=> Area of window: 1 m²

Area of door: 3 m × 1.5 m

=> 4.5 m²

Required wall to be painted: 30 - 1 - 4.5

=> Required wall to be painted: 24.5 m²

Therefore, the required paint for the wall to be fully painted is 24.5 m². Hoped this helped.