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3 years ago

When simplifying x^3 · x^2, the exponents are added together. True False

1 answer:

8 0

When multiplying exponentials, there is a rule that states if the bases are the same, we add the exponents together.

In this problem, the two bases that are being multiplied are the same, x.

Therefore, we will add the exponents: x^3 • x^2 = x^5.

The correct answer is true. The exponents are added together when simplifying this expression.

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Solve your answers using inequalities using a number line strategy or a factor table strategy. Express your answers using set no

PtichkaEL [24]

$S=\lbrace x\parallel x1\rbrace$

Explanation

$(x+3)^2(x+1)(x-1)>0$

Step 1

solve for each factor:

set each factor equal to zero

$\begin{gathered} (x+3)^2=0 \\ x=-3 \end{gathered}$ $\begin{gathered} x+1=0 \\ x=-1 \end{gathered}$ $\begin{gathered} x-1=0 \\ x=1 \end{gathered}$

so, we have 3 critical numbers

-3,-1 and 1

Step 2

now, let's make a table to evaluate each interval , (select a number from the interval)

$\begin{gathered} a)(x+3)^2 \\ \text{for x=-5} \\ (x+3)^2=(-5+3)^2=4 \\ so\text{ }\Rightarrow positive \\ \text{for x= -2} \\ (x+3)^2=5^2=25\Rightarrow positive \\ \text{for x= 0} \\ (0+3)^2=9\Rightarrow positive \\ for\text{ x= 2} \\ (2+3)^2=(2+3)^2=25\Rightarrow positive \end{gathered}$

b) (x+1)

$\begin{gathered} x+1 \\ \text{for x=-4} \\ -4+1=-3\Rightarrow negative \\ \text{for x=-2} \\ -2+1=-1\Rightarrow negative \\ \text{for x=0} \\ 0+1=1\Rightarrow positive \\ \text{for x= 2} \\ 2+1=3\Rightarrow positive \end{gathered}$

c)(x-1)

$\begin{gathered} x-1 \\ \text{for x=-4} \\ -4-1=-\Rightarrow negative \\ \text{for x=-2} \\ -2-1=-3\Rightarrow negative \\ \text{for x=0} \\ 0-1=-1\Rightarrow\text{negative} \\ \text{for x= 2} \\ 2-1=1\Rightarrow positive \end{gathered}$

Step 3

now, make th multiplication of the signs ( check the table in step 2)

so, we got

(-infi, -1) U (1, inf)

as we need that the product of the factors is greater than zero ( positive) , the solution is( set notation)

$S=\lbrace x\parallel x1\rbrace$

I hope this helps you

5 0

1 year ago

tony misplaced 7 stamps from his collection. He knows that each stamp of his worth $0.15 and that the total value of them is now

Vesna [10]

First we multiply 7 and 0.15 to see how many he lost. We get 1.50 so now we know he lost 1.50 of his collection. we add 5.55 and 1.50 and get 7.05 we divide 7.05 by 0.15 47.

Tony had 47 stamps

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3 years ago

Mining is considered the _ job in the United States

gavmur [86]

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7 0

3 years ago

Read 2 more answers

+<br> If f(x)= x+3/2, what is the equation for f-1(x)

bixtya [17]

Answer:

f-(x) = -(x)+3/2