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Marina86 [1]
3 years ago
12

Factor x^4 + x y^3 + x^3 + y^3 completely. Show your work.

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0
\bf x^4+xy^3+x^3+y^3\impliedby \textit{now let's do some grouping}
\\\\\\
(x^4+xy^3)~~+~~(x^3+y^3)\implies x(x^3+y^3)~~+~~(x^3+y^3)
\\\\\\
\stackrel{\stackrel{common}{factor}}{(x^3+y^3)}(x+1)\\\\
-------------------------------\\\\
\textit{now recall that }\qquad \qquad \textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
a^3-b^3 = (a-b)(a^2+ab+b^2)\\\\
-------------------------------\\\\
(x+y)(x^2-xy+y^2)(x+1)
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Two mechanics worked on a car. The first mechanic worked for 15
nevsk [136]

Answer: For the sum of 130

First: $90

Second: $40

Step-by-step explanation:

We write equations for each part of this situation.

<u>The Total Charge</u>

Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.

<u>The Sum of the Rates</u>

Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.

We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.

For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.

15a + 5 (130-a)=1550

15a+650-5a=1550

10a+650-650=1550-650

10a=900

a=$90 was charged by the first mechanic.

We substitute to find the second mechanic's rate.

90+b=130

90-90+b=130-90

b= $40 was charged by the second mechanic

5 0
3 years ago
Simplify 42 ⋅ 48 thanks
Andreyy89
42•48=2,016. Hope this helped!
4 0
3 years ago
Norma Jean makes $25 per hour. She works 35 hours per week. She gets a commission of 15% on her total sales. How much should Nor
TEA [102]

Answer:

$24166.67

Step-by-step explanation:

$25 per hour and works 35 hours per week

Norma Jean makes 35 * 25  (<em>without sales) = </em>$875

<em> </em>Total commission made by Norma<em> </em>= 4500-875 = $3625

<em>let total number of sales by Norma be x</em>

15% is the same as 15/100

<em>so </em>(15/100) * x =3625 <em> multiplying both sides by 100</em>

15x = 362500<em> making x subject of formula</em>

x = 362500/15

x = 24 166.67

Norma should sell total items worth $24166.67

 

6 0
3 years ago
Read 2 more answers
If k(t)=3/4t-3 what is the value of k(-12)?
Valentin [98]

Answer:

-3.0625

Step-by-step explanation:

just plug in -12

3/4t-3

3/2(-12)-13

then solve to get -3.0625 or -3.06

and this is how you solve any problem like this.

8 0
3 years ago
Please help!!!!!!!!!!
aksik [14]
The answer is 9
You divide by 1215 by 15 and the answer is 81
Then you find the square root of 81 and the answer is 9
5 0
3 years ago
Read 2 more answers
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