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3 years ago

Factor completely 3x^4 - 3x ^3 - 18x ^2. Which of the following is one of the factors?

Mathematics

1 answer:

Otrada [13]3 years ago

7 0

Answer:

$3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).$

Step-by-step explanation:

The expression $3x^4 - 3x ^3 - 18x ^2$ consists of three terms:

$3x^4;$
$-3x^3;$
$-18x^2.$

These three terms have common factor $3x^2.$ Thus,

$3x^4 - 3x ^3 - 18x ^2=3x^2(x^2-x-6).$

Consider the expression $x^2-x-6.$ You can rewrite it as

$x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3).$

The whole expression takes look

$3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).$

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What is the median of 68, 69, 71, 71, 71, 73, 74, 75, 75, 78

Yanka [14]

Answer:

Step-by-step explanation:

cross out 4 from left to right, right to left, you get 71 and 73, the mean of those two numbers is 72

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3 years ago

Let the area of a rectangle in square metres is x^2+13x+42 how much longer is the length than the width of the rectangle

worty [1.4K]

Answer:

Step-by-step explanation:

Area of rectangle

So we have to factorise the expression

x²+13x+42

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x(x+6)+7(x+6)

(x+7)(x+6)

x+7-(x+6)

x+7-x-6

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3 years ago

Carter ran 7/8 mile in a race. Taylor ran 1/4 mile. How much further for carter run than Taylor?

Artist 52 [7]

Answer:

1 17/20 is the answer

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3 years ago

Read 2 more answers

22. An employee joined a company in 2017 with a starting salary of $50,000. Every year this employee receives a raise of $1000 p

Setler79 [48]

Answer:

(a) The recurrence relation for the salary is

$S_{n+1}=1.05*S_n+1000\\\\S_0=50000$

(b) The salary 25 years after 2017 will be $217044.85.

Step-by-step explanation:

We can define the next year salary $S_{n+1}$ as

$S_{n+1}=S_n+1000+0.05*S_n=1.05*S_n+1000$

wit S0=$50000

If we extend this to 2 years from 2017 (n+2), we have

$S_{n+2}=1.05*S_{n+1}+1000=1.05*(1.05*S_n+1000)+1000\\S_{n+2} =1.05^2*S_n+1.05*1000+1000\\S_{n+2}=1.05^2*S_n+1000*(1.05^1+1)$

Extending to 3 years (n+3)

$S_{n+3}=1.05*S_{n+2}+1000=1.05(1.05^2*S_n+1000*(1.05^1+1))+1000\\\\S_{n+3}=1.05^3S_n+1.05*1000*(1.05^1+1)+1000\\\\S_{n+3}=1.05^3*S_n+1000*(1.05^2+1.05^1+1)$

Extending to 4 years (n+4)

$S_{n+4}=1.05*S_{n+3}+1000=1.05*(1.05^3*S_n+1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1.05*1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1000*(1.05^3+1.05^2+1.05^1+1.05^0)$

We can now express a general equation for S_n (salary at n years from 2017)

$S_n=1.05^nS_0+1000*\sum_{0}^{n-1}1.05^n$

The salary at 25 years from 2017 (n=25) will be

$S_{25}=1.05^{25}S_0+1000*\sum_{0}^{24}1.05^i\\\\S_{25}=3.386*50000+1000*47.72=217044.85$

8 0

4 years ago

This is ratio math.A passenger car will go 420 miles on 17.5 gallons in city driving. What is the rate in miles per gallon? The

I am Lyosha [343]

We are given two variables, distance and volume of gas required to reach the distance.

We are then asked to find the rate of consumption in miles per gallon.

The approach is simply to divide distance by the volume to get the rate per unit gallon.

$\begin{gathered} \frac{420}{17.5}\cdot\frac{\text{miles}}{\text{gallons}} \\ 24\text{ miles per gallon.} \end{gathered}$

This means that for each gallon consumed, 24 miles are covered.

24 mpg

5 0

2 years ago