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3 years ago

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

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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Fill in the table using this function rule. y = 10x + 1

aleksandr82 [10.1K]

Y=10x+1
x=-1→y=10(-1)+1=-10+1→y=-9
x=0→y=10(0)+1=0+1→y=1
x=1→y=10(1)+1=10+1→y=11
x=5→y=10(5)+1=50+1→y=51

x y
-1 -9
0 1
1 11
5 51

8 0

3 years ago

Read 2 more answers

A consumer testing service tested whether the average baking time of whole wheat bread in gas ovens was less than the average ba

vichka [17]

Answer:

Part 1) The explanatory variable is the type of oven

It is a categorical variable

Part 2) The response variable is the baking time

It is a quantitative variable

part 3) two-sample z-test for proportions should be used for the test

Step-by-step explanation:

An explanatory variable is an independent variable that is not affected by all other variables. In this experiment, the type of oven is the input variable and it is not affected by any other variable

A categorical variable is one that has two or more categories without any intrinsic ordering of the categories. The type of oven is either gas or electric, so it is categorical.

A response variable is a dependent variable whose variation depends on other variables. The baking time in this experiment depends on the type of oven used

A quantitative variable is one that take on numerical values.

A two proportion z-test allows you to compare two proportions to see if they are the same. The null hypothesis (H0) for the test is that the proportions are the same. The alternate hypothesis (H1) is that the proportions are not the same.

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3 years ago

MUST HELP!!!! (+50 POINTS +BRANILEST +5 STARS +THANKS ON PROFILE)

Flura [38]

Answer:

Personification is your answer.

Hope it helps!!!

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3 years ago

What are the rules for multiplying negative integers

Sergeeva-Olga [200]

Answer:

Negative time a negative equals a positive!

Step-by-step explanation:

When you multiply two negative numbers or two positive numbers then the product is always positive. The same also goes for dividing negative integers.

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2 years ago

Read 2 more answers

I will name you brainliest!

liq [111]

Answer:

Step-by-step explanation:

a specific shade of red nail polish requires 7 parts of red to 2 parts of yellow. A mixture contains 35 quarts of red and 8 quarts of yellow.

How can you fix the mixture to make the correct shade of red?

:

The red:yellow ratio is 7:2, we can write the mixture as 7%2F9 or 77.8% red

:

The existing mixture of 35:8 is a 43 quart mixture and can be written as: 35%2F43 or 81.4% red

:

we need to add yellow to reduce the per cent of red

:

Let y = amt of yellow required to do this

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7%2F9*(y+43) = 35

Multiply both sides by 9

7(y+43) = 9 * 35

7y + 301 = 315

7y = 315 - 301

7y = 14

y = 14/7

y = 2 quarts of yellow to be added, for total mixture of 45 quarts

;

:

Check this, it still contains 35 quarts of red but the percentage has changed

35%2F45 = 77.8% red which is what we want, a ratio of 7:2

here you go i hope it helps

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3 years ago