If a space heater draws 10 amps from a 120-volt household circuit, and electricity costs 100 per

ANTONII [103]

Megan:
x to the one third power = $x ^{1/3}$
x to the one twelfth power = $x ^{1/12}$

The quantity of x to the one third power, over x to the one twelfth power is:
 $\frac{x ^{1/3}}{x ^{1/12}}$

Since $\frac{ x^{a} }{ x^{b} } = x ^{a-b}$
then $\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12}$

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

$\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12} = x^{1/4}$

Julie:
x times x to the second times x to the fifth = x * x² * x⁵

The thirty second root of the quantity of x times x to the second times x to the fifth is
 $\sqrt[32]{x* x^{2} * x^{5} }$

Since $x^{a}* x^{b}= x^{a+b}$
Then $\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }$

Since $\sqrt[n]{x^{m}} = x^{m/n} }$
Then $\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}$

Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.

3 0

3 years ago

HELP FAST ALL OF MY POINTS TO BE GIVEN TO YOU

gogolik [260]

Answer:

C > 9

Step-by-step explanation:

3 0

3 years ago

Coach Beard has 24 softballs to use this fall. She orders 2 more buckets of softballs that have 20 in each bucket. How many soft

jek_recluse [69]

Answer:

64 softballs

Step-by-step explanation:

Coach Beard currently already has 24 softballs.

When she orders 2 more buckets with 20 in each, that's another 20 + 20 = 40 softballs added to the original 24. So, let's add these two numbers:

24 + 40 = 64

The answer is 64 softballs.

~ an aesthetics lover

3 0

4 years ago

Read 2 more answers

7^3 times 7^-7 times 7

dusya [7]

Hello there! :)

Answer: $\frac{1}{343}$

*The answer must have a fraction.*

Step-by-step explanation:

Lesson: Zero and Negative Exponents.

Distributive property: a(b+c)=ab+ac

First, you apply exponent rule.

$a^b*a^c=a^b^+^c$

$7^-^3$

$\frac{1}{7^3}=7^3=7*7*7=343$

Final answer: $\frac{1}{343}$

Hope this helps!

Thanks!

-Charlie

Have a great day!

:)

:D

4 0

3 years ago

Which number line shows the correct locations of ALL the given values?

bija089 [108]

A is the only number line that correctly shows the locations of all given values.

Answer=A

***EDIT***

Okay, so if you look at the number line, you notice that the distance between one line and the next is equal to 1/4. When we move to the left, we decrease in value. When we move to the right, we increase in value.

So, knowing that, lets look at A and see if all of the numbers are correctly placed.

1/2 should be two lines to the right of 0 (since distance between one line and the next is equal to 1/4, and 1/4+1/4=2/4 or 1/2)

-4 is a relatively easy value to find, since its line is labeled.

-2 3/4 should be three lines to the right of -2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of -2 u get -2 3/4)
(-2-3/4=-2 3/4)

1 1/4 should be three lines behind 2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of 2 you get 1 1/4)
(2-3/4=1 1/4)

6 0

3 years ago