what is the product? 3x^5 (2x^2+4x+1)

Answers

Answer 1
the answer is C.) 6x^7...
 
Answer 2

Answer:

The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]  is [tex]6x^7+12x^6+3x^5[/tex]

Step-by-step explanation:

Given: Polynomial [tex]3x^5(2 x^2+4x+1)[/tex]

We have to find the product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]

Consider the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]  

Apply distributive rule, [tex]a(b+c)=ab+ac[/tex]

Multiply [tex]3x^5[/tex] with each term in brackets, we have,

[tex]=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1[/tex]

[tex]=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5[/tex]

Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex]

Simplify, we have,

[tex]=6x^7+12x^6+3x^5[/tex]

Thus, The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]  is [tex]6x^7+12x^6+3x^5[/tex]


Related Questions

How many ways are there to select 7 countries in the united nations to serve on a council if 1 is selected from a block of 56, 3 are selected from a block of 63 and 3 are selected from the remaining 70 countries?

Answers

[tex]56\cdot63C3\cdot70C3=\\\\ 56\cdot\dfrac{63!}{3!60!}\cdot\dfrac{70!}{3!67!}=\\\\ 56\cdot\dfrac{61\cdot62\cdot63}{2\cdot3}\cdot\dfrac{68\cdot69\cdot70}{2\cdot3}=\\\\ 121,731,687,840 [/tex]

How do you do this problem?

Answers

[tex]\bf \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\ -------------------------------\\\\ \cfrac{\frac{10}{9}}{\frac{8}{9}}\implies \cfrac{10}{\underline{9}}\cdot \cfrac{\underline{9}}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]

Raina wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 55 feet. Suppose each can of paint will cover 275 square feet. How many cans will she need to paint the ceiling?

Answers

area of the ceiling = 55 x 55 = 3025 square feet

 3025/275 = 11 cans

use any method to solve the equation. If necessary, round to the nearest hundredth. 11x^2=8

Answers

11x^2 = 8
x^2 = 8/11
x = +/- sqrt (8/11)

x =  0.85 , -0.85

Answer:

x = + 0.85 , -0.85

Step-by-step explanation:

Given : 11x² = 8.

To find : use any method to solve the equation. If necessary, round to the nearest hundredth.

Solution : We have given that : 11x² = 8.

First we divide both sides by 11,

x² = [tex]\frac{8}{11}[/tex].

Now taking square root both sides .

x = [tex]\sqrt{\frac{8}{11}}[/tex].

x =± 0.8528.

Therefore, x = + 0.85 , -0.85

NEED ASAP


Which linear inequality is represented by the graph?

y ≤ 1/3x − 1
y ≥ 1/3x − 1
y < 3x − 1
y > 3x − 1

Answers

The slope is 1/3. We know this because the x value increases by 3 each time the y value increases by 1. Slope is always rise over run. It is more than or equal to because the shaded part is above the line.
Answer:B

Answer:

[tex]y\geq \frac{1}{3}x -1[/tex]

Step-by-step explanation:

To find linear inequality, first we find the equation of the line.

LEts pick two points (3,0)  and (0,-1)

To get equation of a line [tex]y=mx+b[/tex], use slope formula to find slope m

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{0+1}{3-0} =\frac{1}{3}[/tex]

y intercept is (0,-1) . so b=-1

The equation of the line becomes

[tex]y=\frac{1}{3}x -1[/tex]

now we look at the shaded region.

the graph is shaded at the top and also we have solid line . so we use >= symbol

[tex]y\geq \frac{1}{3}x -1[/tex]

Two pools are being filled with water. To start, the first pool contains 922 liters of water and the second pool contains 1300 liters of water. Water is being added to the first pool at a rate of 33.75 liters per minute. Water is being added to the second pool at a rate of 20.25 liters per minute.
After how many minutes will the two pools have the same amount of water?
How much water will be in each pool when they have the same amount?

Answers

Final answer:

After 28 minutes, both pools will have the same amount of water, which will be 1653 liters in each pool.

Explanation:

To find out after how many minutes the two pools will have the same amount of water, we can set up an equation where the volume of water in the first pool plus the water added over time equals the volume of water in the second pool plus the water added to it over the same period.

Let x represent the number of minutes after which both pools will have the same amount of water. The equation can be expressed as:

922 + 33.75x = 1300 + 20.25x

To solve for x, we subtract 20.25x from both sides:

922 + 13.5x = 1300

Now, subtract 922 from both sides to isolate the term with x:

13.5x = 378

Divide both sides by 13.5 to solve for x:

x = 28

So, it will take 28 minutes for both pools to have the same amount of water.

To calculate how much water will be in each pool at that time, we can multiply the rate by the number of minutes and add the initial amount of water for either pool:

For the first pool: 922 + (33.75 * 28) = 1653 liters

For the second pool: 1300 + (20.25 * 28) = 1653 liters

Therefore, after 28 minutes, each pool will contain 1653 liters of water.

what is x
3x = 0.5x2

Answers

Assuming that x2=x^2, we can multiply both sides by 2 (separating x^2) to get 6x=x^2. Next, we can divide both sides by x to get 6=x (we do this to separate x)

Jordan is cutting a 2 meter by 1 1/4 meter piece of rectangular paper into two pieces along its diagonal. what is the area of each of the pieces?

Answers

area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

Answer: area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

You need to buy 5 notebooks for your classes at school. Each notebook costs $2.79. What is the total costs of 5 notebooks Before tax?

Answers

multiply 2.79 x 5

2.79*5 = 13.95 before tax

The slope of a line running through points (2, 3) and (1, 7) is:

4.
-4.
2.
-2.

Answers

You are going to use the equation y2-y1/x2-x1, and you will get negtive 4

If a circle has a diameter of 30 meters, which expression gives its area in square meters?

A.15^2 x π
B. 30 x π
C. 30^2 x π
D. 15 x π

Answers

Area of a circle is given by [tex] \pi r^{2} [/tex] where [tex]r[/tex] is the radius

Radius of a circle is half of the diameter

We have the diameter 30 meters, so the radius is 30÷2=15 meters

Area of the circle = [tex] \pi (15)^{2} [/tex]

Note: The option given doesn't show the [tex] \pi [/tex] symbol but it seems like the correct answer is option A

Answer:

A.15^2 x π (APEX)

Step-by-step explanation:

Simplify 1/x-10 divided by 9x/x^2-9x-10

Answers

In fractional form, I think this is written as

[tex] \frac{1}{x-10} / \frac{9x}{ x^{2} -9x-10} [/tex]

When dividing, the first term is the dividend, the second term is the divisor and the answer is the quotient. When you divide fractions, you multiply the dividend with the reciprocal of the divisor. In this case

[tex] \frac{1}{x-10} * \frac{x^{2} -9x-10}{9x } [/tex]

The answer is 

[tex] \frac{ x^{2} -9x-10}{9 x^{2} -90x} [/tex]

Furthermore, we can simplify the terms through factoring, The numerator could be factored into (x+1)(x-10). The denominator could be factored to 9x(x-10). Since the term (x-10) is common, you can cancel them to get to the final answer which is

(x+1)/9x

Answer:(x+1)/9x

Step-by-step explanation: Hope this helps

If tan theta = -4/3 in quadrant II, what is cos theta?

A. -4/5

B. 3/5

C. 4/5

D. -3/5

Answers

[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ tan(\theta )=-\cfrac{4}{3}\cfrac{\leftarrow opposite}{\leftarrow adjacent}[/tex]

notice, the tangent has a negative sign, for that to happen, either the numerator or denominator must be negative, who may that be? well, we know the angle is in the II quadrant, on the II quadrant, the cosine or x-coordinate (adjacent side) is negative, so, is the adjacent.

that means, the opposite side is 4 and the adjacent one is -3

well, let's find the hypotenuse

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+4^2}\implies c=\sqrt{25}\implies \boxed{c=5}\\\\ -------------------------------\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad \qquad cos(\theta )=\cfrac{-3}{5}[/tex]

bear in mind that, the square root will give use +/- roots, however, in the case of the hypotenuse, is just the radius unit, thus is never negative.

Answer:


The answer is:

D. -3/5

What are the roots of the equation y=x^2 -5x-24

Answers

Factor
(x-8)(x+3)

Check:
-8+3=-5
-8*3=-24

Use ZPP
x-8=0
x=8

x+3=0
x=-3

Final answer: x=-3, x=8

Simplify the expression

Answers

The answer is D, I'm 95% sure, double check just in case
[tex]4 \sqrt{6}+5 \sqrt{6}=(4+5) \sqrt{6}=9 \sqrt{6} [/tex]

D.



The formula F=9/5(K−273.15)+32
converts a temperature from kelvin K to degrees Fahrenheit F

a. Solve the formula for K

Answers

Just subtract 32, then divide by 9/5 (or multiply by the reciprical) then add 273.15.
K=5/9(F-32)+273.15

The formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]

The given expression:

[tex]F = \frac{9}{5} (K - 273.15) + 32[/tex]

To find:

the formula for K

The formula for K is obtained by making K the subject of the formula as shown below;

[tex]F = \frac{9}{5} (K - 273.15) + 32\\\\subtract \ 32 \ from \ both \ sides \ of \ the \ equation\\\\F - 32 = \frac{9}{5} (K - 273.15)\\\\multiply \ both\ sides \ by \ 5\\\\5(F - 32) = 9(K - 273.15)\\\\divide \ both\ sides \ by \ 9\\\\\frac{5}{9} (F - 32) = K - 273.15\\\\add \ 273.15 \ to \ both\ sides \ of \ the \ equation\\\\\frac{5}{9} (F - 32) + 273.15 = K\\\\[/tex]

Thus, the formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]

Learn more here: https://brainly.com/question/15469690

He measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. what is the measure of the smallest angle?

Answers

In a triangle, the three interior angles always add to 180°

4x + 5x + 6x = 180
15x = 180
x = 180/15
x = 12

the measure of the smallest angle = 4x = 4*12 = 48°

If i want to be a real boy whats the equation?

Answers

15²=225
225-(7.5²•3.14)=48.375 or 48.38 :)

Answer: 15²=225

225-(7.5²•3.14)=48.375 or to the nearest form 48.38.

Step-by-step explanation: In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".

At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?

Answers

Let a and c be the number of adult and children tickets sold respectively.

a=2c

6.2c+9.8a=593.4, using a from above in this equation gives you:

6.2c+9.8(2c)=593.4  perform indicated multiplication on left side

6.2c+19.6c=593.4  combine like terms on left side

25.8c=593.4  divide both sides by 25.8

c=23

So 23 child tickers were sold that day.

Which is the equation of the trend line that can be generated by using the data from year 1 and 5?

Answers

answer is
y = 6.75x + 81.25

you can double check by plug in x values (year) into the equation to find out y values (# of participants)

For those looking for the letter the answer is C

Your welcome :)

Find x and the measures of the indicated parts.

BC and AC

Answers

x is 3 bc is 6 ac is 12
you can make a proportion:
5÷10=6÷(x+3+9)
and then find ac=12 then find the values of x and bc

Write [tex](2a)^3[/tex] without exponents.

Answers

hello ;
(2a)^3 =(2)^3 (a)^3 = 8(a)^3
(2a)³ = 2³a³ = 8a³ = 8aaa

What is the point-slope equation of a line with slope -4 that contains the point (-2, 7)?

A. y + 7 = -4(x + 2)
B. y + 7 = -4(x - 2)
C. y - 7 = -4(x - 2)
D. y - 7 = -4(x + 2)

Answers

point slope form is
y - y1 = m(x - x1)

m = -4
(-2, 7)

y - 7 = -4(x + 2)

answer is D

Melinda has 1 seashell, and Jun has 9 seashells. If Melinda and Jun put their seashells together and then divide them up equally, how many will each one of them have? 3 5 8 10

Answers

5 seashells , because 9 + 1 = 10 and if you were to give them an equally amount of seashells it would be 5 if you split 10 in half . SO the answer would be 5 . 

Answer:

B.) 5

Step-by-step explanation:

Just did this :3

HELP ASAP PLEASE QUESTION IS

Answers

i think its 244 ? i dont remember this stuff once you hit geometry you forget alot
8*16=128
9*12=108
128+108=236
236 is the answer

Lou has 3 over 4 of an hour to do his math homework, play video games and help with dinner. If he splits his time equally between the three activities, how much time will he spend on each?

_____ of an hour


Answers

3/4 divided by 3 

3/4 *1/3 = 3/12 = 1/4


Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim t → −2 t4 − 3 2t2 − 3t + 3

Answers

Final answer:

To evaluate the limit of the given function, substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get 0.7647.

Explanation:

To evaluate the limit of the given function, we can substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get:

lim t → -2 t^4 - 3 / 2t^2 - 3t + 3 = (-2)^4 - 3 / 2(-2)^2 - 3(-2) + 3 = 16 - 3 / 8 + 6 + 3 = 13 / 17 = 0.7647

Therefore, the limit is approximately 0.7647.

The coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1).
Find the midpoint of FJ
A) (0,4)
B) (1, -2)
C) (-4, 0)
D) (5, 2)
This is a question from my math chapter 20: Figures in the Coordinate Plane

Answers

i think that is C i had that one but i forget

hope that help

BMK

Answer:

B. [tex](1,-2)[/tex]  

Step-by-step explanation:  

We have been given that coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1). We are asked to find the coordinates of mid-point of segment FJ.

We will use mid-point formula to solve our given problem.

[tex]\text{Mid-point}=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]

Upon substituting the coordinates of points F and J in mid-point formula we will get,

[tex]\text{Mid-point}=\frac{-5+7}{2},\frac{-3+-1}{2}[/tex]

[tex]\text{Mid-point}=\frac{2}{2},\frac{-4}{2}[/tex]

[tex]\text{Mid-point}=1,-2[/tex]

Therefore, the coordinates of mid-point of segment FJ are [tex](1,-2)[/tex] and option B is the correct choice.

If 3 consecutive integers sum to 63, the largest of the 3 = ?

Answers

x+(x+1)+(x+2)=63
3x+3=63
3x=60
x=20
Consecutive integers are: 20, 21, 22
Answer: 22

This problem states that the sum of 3 consecutive integers is 63 and it asks us to find the largest integer.

Three consecutive integers can be represented as followed.

X → first integer

X + 1 → second integer

X + 2 → third integer

Since the sum of our three consecutive integers is 24, we can write an equation.

X + X + 1 + X + 2 = 63

We can simplify our equation on the left and it will read...

3x + 3 = 63       -3    -33x = 60 ÷3   ÷3             ← divide both sides by 3X = 20Largest integer = X + 220 + 2 = 22Largest integer = 22

What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches?

Answers

what is the question ?????

What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches? what are we taking the diffference from

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