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3 years ago

Simplify each expression (2a^4)^-3, a ≠ 0

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

8 0

Answer:

1/(8a^12)

Step-by-step explanation:

(2a^4)^-3

Rewriting

2^-3 * a^4^-3

We know x^y^z = x^(y*z)

2^-3 * a^(4*-3)

2^-3 * a^-12

We know x^-y = 1/a^y

1/2^3 * 1/a^12

1/8 * 1/a^12

1/(8a^12)

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Itzik 45 seconds to fill an 18 down container how long will it take to fill a 40 gallon container

Akimi4 [234]

When answering this question, I'm assuming "18 down" means 18 gallons
To find the answer, we can divide:
40/18 = 5
( This basically means that there are 5 containers in the 40 gallon container)
knowing this:
45*5 = 225
(Basically solves the time to fill 5 containers)
It will take 225 seconds

4 0

4 years ago

Read 2 more answers

How many grams are 2.7x10-^4 grams

andrew-mc [135]

Answer:

0,00027 grams!

Step-by-step explanation:

This is a scientific notation problem.

When a number is followed by a $10^{-1}$ , it means that said number has one zero at the beginning.

In this case, the number is followed by $10^{-4}$ , so that means that 2.7 has four zeros at the beginning. So, 2.7x $10^{-4}$ grams is equal to 0,00027 grams! (always the comma goes after the first zero).

6 0

4 years ago

1-58. Mr. Wright was making a table to figure out how much it costs to send a certain numt

Drupady [299]

A table of values can be used to represent variables that are directly proportional.

The complete table of proportions is:

$\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]$

Given that

$\left[\begin{array}{ccccccccc}Letters&10&2&[\ ]&7&1&500&[\ ] \\Cost&0.45&0.90&6.75&[\ ]&[\ ]&[\ ] & 18.90\end{array}\right]$

Let:

$L \to$ Letters

$C \to$ Cost

Using proportional reasoning, we have:

$C = kL$

Where

$k \to$ ratio of proportion

For the first values of C and L, we have:

$C = kL$

$0.45 = k \times 10$

Divide both sides by 10

$k = 0.045$

So, the equation of proportion is:

$C = 0.045L$

When C = 6.75, we have:

$C = 0.045L$

$6.75 = 0.045L$

Solve for L

$L = \frac{6.75}{0.045}$

$L = 150$

When L = 7, we have:

$C = 0.045L$

$C = 0.045 \times 7$

$C = 0.315$

When L = 1, we have:

$C = 0.045L$

$C = 0.045 \times 1$

$C = 0.045$

When L = 500, we have:

$C =0.045L\\$

$C =0.045 \times 500$

$C =22.5$

When C = 18.90, we have:

$C = 0.045L$

$18.90 = 0.045L$

Solve for L

$L=\frac{18.90}{0.045}$

$L=420$

Hence, the complete table is:

$\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]$

Read more about proportions at:

brainly.com/question/21126582

8 0

3 years ago

Solve x^2 – 8x + 41 = 0 for x.

icang [17]

$\displaystyle x^2 - 8x + 41 = 0 \\\\ \Delta=b^2-4ac \\ \Delta=(-8)^2-4\cdot1\cdot41 \\ \Delta=64-164 \\ \Delta=-100 \\ \\ X_{1,2}= \frac{-b\pm i \sqrt{-\Delta} }{2a} = \frac{8 \pm 10i}{2} \\ \\ X1=4-5i \\ \\ X2=4+5i$