Which of the following is x⁴ + y⁴ identically equal to?

1 answer:

8 0

$x^4+y^4 \\ \\x^4= (x^2)^2, y^4 = (y^2)^2 \\ \\x^4- y^4= (x^2)^2 - (y^2)^2 = (x^2 + y^2)(x^2 - y^2 )\\ \\now \ you \ can \ factor \ the \ second \ again \\ \\(hopefully \ you \ see \ that \ it's \ a \ difference \ of \ squares): \\ \\x^4 - y^4= (x^2 + y^2)(x + y)(x - y) \\ \\Answer : \ (A) \ (x^2 + y^2)(x + y)(x - y) \\ \\ \\ a^2-b^2 =(a-b)(a+b)$

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Stella graphed y = 100 - 25/3 * x to represent the percentage of battery life remaining on her phone after x hours. What is a re

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Answer:

from 0 to 12 hours, that is $0\leq x\leq 12$

Step-by-step explanation:

Notice that the x represents the number of phone hours used, therefore it has to be a number larger or equal zero, but NOT a negative number.

So on one end we have that the number of phone hours used (x) must be larger or equal zero: $x\geq 0$

On the other hand, when the battery goes to zero, there are no more phone hours to use. We can find what is that other limit by making the battery percent (y variable) equal to zero, and solve the equation for x, thus giving us the upper limit of usable phone hours:

$y=0=100-\frac{25}{3} x\\\frac{25}{3} x=100\\25 x = 100*3 = 300\\x = \frac{300}{25} = 12$