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3 years ago

12

Using the exponent rules, when multiplying

1 answer:

34kurt3 years ago

8 0

We can rule out a and d since they go hand in hand, and we’re talking about multiplying.
c.) add

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Let f(x)=x^2+5x−8. What is the average rate of change from x = 2 to x = 6?

Lena [83]

F(2)=4+10-8=6; f(6)=36+30-8=58. Average rate of change is (58-6)/(6-2)=52/4=13

7 0

4 years ago

Simplify each exponential expression to the form x^n where n is positive.

vaieri [72.5K]

The expression is:

$\sqrt{\frac{x^{3}x^{8}}{x^{6}}}$

We will use following steps to simplify it:

Step 1:

Use product property of exponents:

$x^{a}*x^{b}=x^{a+b}$

$x^{3}*x^{8}=x^{8+3}$

$x^{3}*x^{8}=x^{11}$

That gives us the expression:

$\sqrt{\frac{x^{11}}{x^{6}}}$

Step 2:

Use division property of exponents:

$\frac{x^{a}}{x^{b}}=x^{a-b}$

$\frac{x^{11}}{x^{6}}=x^{11-6}$

$\frac{x^{11}}{x^{6}}=x^{5}$

This simplifies the expression:

$\sqrt{x^{5}}$

Step 3:

Writing the square root as power 1/2:

$\sqrt{x^{5}}=x^{5*\frac{1}{2} }$

$\sqrt{x^{5}}=x^{\frac{5}{2} }$

Answer:

The final simplified form in x^n form is :

$x^{\frac{5}{2} }$

4 0

4 years ago

Sandra has a cylindrical mold for making candles with a radius of 3.4 cm and a height of 6 cm. If Sandra uses a rectangular bloc

Wittaler [7]

Answer:

$14\ candles$

Step-by-step explanation:

step 1

Find the volume of the cylindrical mold

The volume is equal to

$V=\pi r^{2} h$

we have

$r=3.4\ cm$

$h=6\ cm$

assume

$\pi=3.14$

substitute

$V=(3.14)(3.4)^{2}(6)$

$V=217.79\ cm^{3}$

step 2

Find the volume of the wax

The volume is equal to

$V=(15)(12)(18)$

$V=3,240\ cm^{3}$

step 3

Divide the volume of the wax by the volume of the cylindrical mold, to calculate the number of candles

$3,240/217.79=14.9\ candles$

Round down

$14\ candles$

5 0

3 years ago

If x^3+ax^2-18x+b = (x+5)(x-4)(x+2) what is a and b

blondinia [14]

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$(x + 5)(x - 4)(x + 2) =$

$(x + 5) ({x}^{2} - 2x - 8) =$

${x}^{3} - 2 {x}^{2} - 8x + 5 {x}^{2} - 10x - 40 = \\$

${x}^{3} + 3 {x}^{2} - 18x - 40$

_________________________________

Compare :

${x}^{3} + 3 {x}^{2} - 18x - 40$

${x}^{3} + a {x}^{2} - 18x + b$

Thus :

$a = 3$

and

$b = - 40$

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6 0

3 years ago

2 Charles is saving $5 each week from his allowance. He already saved $15 from the money he earned from mowing his neighbor's la

Luba_88 [7]

Answer:

15 + 5w ≥ 75

Step-by-step explanation:

Let the number of weeks be represented as w.

We are told from the question that:

Charles is saving $5 each week from his allowance. He already saved $15 from the money he earned from mowing his neighbor's lawn.

The word "at least" in mathematics means equal to or greater than and it is represented by the sign ≥

Therefore, our inequality equation is written as:

15 + 5w ≥ 75

7 0

3 years ago