Perform the indicated operation. (y4 - 1) ÷ (y + 1)

2 answers:

7 0

$The\ domain:\\D:y\neq-1\\\\(y^4-1)\div(y+1)=\dfrac{(y^2)^2-1^2}{y+1}=\dfrac{(y^2-1)(y^2+1)}{y+1}\\\\=\dfrac{(y-1)(y+1)(y^2+1)}{y+1}=(y+1)(y^2+1)=y^3+y^2+y+1\\\\Used:\\(a^n)^m=a^{nm}\\\\a^2-b^2=(a-b)(a+b)$

Dmitry_Shevchenko [17]4 years ago

3 0

Answer: y^3 - y^2 + y - 1

Step-by-step explanation: Factor the numerator and denominator and cancel the common factors. This should leave you with y^3-y^2+y-1.

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A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is

GaryK [48]

Answer:

Trail Mix costs $2.50 per pound, and Jelly Beans cost $1.50 per pound.

Step-by-step explanation:

Using x for trail mix and y for jelly beans, we have a system of equations being

$\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.$

We can solve this system using substitution

5x+3y=17

Divide by 5 to have a coefficient of 1 before x

$x+\frac{3}{5} y=\frac{17}{5}$

Subtract $\frac{3}{5} y$ from each side to single out one variable to one side

$x=\frac{17}{5} -\frac{3}{5} y$

Now, we can plug in our value for x into the given equation

$2(\frac{17}{5} -\frac{3}{5} y)+12y=23$

Open the parentheses

$\frac{34}{5} -1\frac{1}{5} y+12y=23$

Merge Y values

$6.8+10.8y=23$

Separate numerical values from variables

$10.8y=16.2$

Divide by 10.8 in order to have a coefficient of 1

$y=1.5$

Now that we have one of the values, we know that a pound of jelly beans costs $1.50. We can now plug in 1.5 for y into one of our equations to find x.

$5x+3(1.5)=17$