show that a^12 can be written as a perfect square and a perfect cube

Answers

Answer 1

Answer:

Step-by-step explanation:

Doing this the long way, write a^12 as a product of "a"s

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

Now group them into groups of 4

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

There are 3 groups of 4 so you can write it as [(a^4)]^3 which is a cube

Now do the same thing with groups of 6s

a^12 = a * a * a * a * a * a * a * a * a * a * a * a

a^12 = (a^6)^2

So the two answers are

Perfect cube:  [(a^4)]^3

Perfect square: (a^6)^2


Related Questions

Perimeter of Triangle Please. Thank you ASAP

Answers

Step-by-step explanation:

The perimeter of a parallelogram is twice the sum of the length of a longer and a shorter side.

The length can be evaluated by the distance formula between two points (x_1,y_1), (x_2, y_2)

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For the longer side,

[tex]d=\sqrt{(7-(-4))^2+(3-2)^2}=\sqrt{122}[/tex]

or the shorter side,

[tex]d=\sqrt{(7-6)^2+(3-(-2))^2}=\sqrt{26}[/tex]

Therefore, the perimeter is given by,

[tex]2(\sqrt{122}+\sqrt{26})\approx254.2[/tex]

Please help! You don’t have to explain how you got the answer! Tysm.

Answers

1.) .777777778
2.) .8
3.) .6
4.) .285714286
5.) .15

The largest theater has 42 rows.There are 14 seats in the first row.Each row has 4 seats more than the previous row.how many total are there in this theater?

Answers

Answer:

41 x 18 = 738 + 14 = 752

Step-by-step explanation:

Its says that there 42 rows .First row has 14 seats and the rest of 41 rows has with + 4 more so every row has 18 seats ,and asks how many seats are in total in the theater . To show that you understood the question you have to multiply 41x18 which gives 738 and then add + 14 from the first row so you can find out how many seats are in total .Hope that helps .

HELPP!!
describe the pattern. then write the next 3 numbers
729,243,81,27

Answers

Answer: it's being devided by 3  heres is an equation [tex]\frac{729}{3^{n-1} }[/tex]  the next 3 numbers are 9,3,1

-8.2 +9.1
Yes I’m just making sure I got this question right but tell me what the answer is pls!

Answers

Answer:

0.9 is your answer.

Jenny's aquarium holds 25 quarts of water. She buys a new one that holds 32 quarts.
How much additional water can the new aquarium hold?

Answers

Answer:

7 quarts

Step-by-step explanation:

you subtract the amount that the first aquarium can hold from the second amount

Law of indices a×10⁰×a​

Answers

Step-by-step explanation:

a×10⁰×a

Since, m⁰=1 therefore

a×1×a

a × 10⁰ × a = a × 1 × a = a × a =

Three consecutive even integers have a sum of 36. Find the integers.

Answers

first integer=x

second integer=x+1

third integer= x+2 (x + 1 + 1)

x + (x + 1) + (x + 2) = 36

g(x)=3x-8
g(1)
help!

Answers

The question is asking to evaluate the function when the input value is 1 meaning we substitute one for every case of x. 3(1)-8 is equal to -5. Meaning g(1)=-5

Yea also all of this

Answers

Answer:

yea I cant really do this over a screen

Answer:

16) photo

Step-by-step explanation:

- parallel lines never meet (a, b, c have no points in common)

- perpendicular lines meet other lines at one point, forming two angles of 90 °

Select the correct answer.
A vegetable farmer fills of a wooden crate with 1 of a pound of tomatoes. How many pounds of tomatoes can fit into one crate?
A. 2 pounds
B. of a pound
c 11 pounds
D. 14 of a pound

Answers

I think the answer is A, i’m not sure about that

find the 50th term of 0,3,6,9

Answers

Answer:

150

Step-by-step explanation:

3×0=0

3×1=3

3×2=6

3×3=9

....

3×50=150

Somebody help me?
I’ve been stuck on the same question for days now

Answers

Answer:

7

Step-by-step explanation:

You've said that both triangle are equal.

This means, both are in proportion

Let the unknown side be x

4 : 5 : x = 36 : 45 : 63

Divide LHS by 9

4 : 5 : x = 4 : 5 : 7

Since you may see x and 7 are same. So, the missing side is 7.

Answer:

Step-by-step explanation:

[tex]\frac{AB}{PQ} = \frac{BC}{QR}[/tex]                      #1 Find same sides  

So, [tex]\frac{4}{36} =\frac{BC}{63}[/tex]                 #2 fill it in.

36BC= 252                 #3 Cross multiply.

[tex]\frac{36BC}{36}[/tex]= [tex]\frac{252}{36}[/tex]                      #4 Divide by 36

BC= 7                           #5 Here's your answer!

If you want to check, plug the sides in.

[tex]\frac{4}{36} =\frac{5}{45} =\frac{7}{36}[/tex]

[tex]\frac{1}{9} =\frac{1}{9} =\frac{1}{9}[/tex]

The siplified fractions should all equal the same number. If they do, the triangles are similar.

Hope this helps!

Plz mark me the Brainliest!

Good Luck!

Damon works 32 hours per week and earns $10.75 per hour.

a. Estimate his weekly earnings. Explain how you determined

your estimate.

b. Find the exact amount he earns per week.

c. Is your answer reasonable based on your estimate? Explain.

u will be awarded brainlest if u answer this correctly.

Answers

A 340
B 10.75 times 32 is 344$
C they are both close

Write the slope-intercept form of the given line. Include your work in your final answer.

Answers

Step 1: Find the slope:
To find the slope, find two points on the graph and count the “rise over run” between the points.
Two points here are (0,-1) and (2,1). To get from (0,-1) to the other point, you need to go “up 2” and then “right 2”. This means your slope is 2/2 or 1.

Step 2: Find the y-intercept:
We can see the y-intercept is (0,-1) on the graph. We’ll use the “-1” from that point for our equation.

Step 3: Put it all together:
The slope-intercept form is y=mx+b, where m is the slope and b is from the y-intercept.
Putting Step 1 and Step 2 into play, we have:
y = x - 1

Note: since m=1, we don’t need to write y = 1x -1. That 1 on the 1x is unnecessary.

Find the location of K

Answers

Answer:

-2

Step-by-step explanation:

what is 384757 + 293

Answers

The answer is 385050 because the one on top of this one is right

What have you discovered regarding data representation methods? What's the difference between qualitative and quantitative data?

For data and probability

Answers

Step-by-step explanation:

Qualitative data are discrete, for instance, "Yes/No" type questions. They are usually presented in bar charts or pie charts to show the portion of different populations with certain characteristics in a single experiement (e.g. Not allergic to ginger VS allergic to ginger).

Qualitative data are usually continuous, and can show a trend or distribution numerically. They are usually presented by, for instance, line charts (e.g. Distribution of resident age in block E)

10 divide 6.0 please

Answers

Answer:

1.6667

Step-by-step explanation:

It took awhile to get this

help !!!! what is the m and b ?????

Answers

Answer:

m is the slope and b is the y intercept

Step-by-step explanation:

Which of the following points lies on the line 2x+y=6? 1. (1.4) 2.(0,6) 3. (2,0) A. I only B. 2 only C. 3 only D. 1 and 2 only E. 2 and 3 only​

Answers

Your answer is D. 1 and 2 only

A copy machine makes 44 copies per minute. How long does it take to make 187 copies

Answers

It will take 4 minutes and 15 seconds, to make 187
187 / 44 = 4.25
60 seconds per minute / .25 (4) = 15 seconds
So, 4 minutes and 15 seconds (4.25 minutes) is how long it will take to make 187 copies

definition of a quadratic function

Answers

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Step-by-step explanation:

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero

Step-by-step explanation:

What is the square root of 9000?

Answers

Approximately 94.8683

is -15 an integer and rational number?​

Answers

Answer:

I guess it would help you

i hope this helps i’m not to sure if it is a integer or a rational number

Lol help me :0

Company Employees attended a year end banquet. 43of the quests ordered chicken, while 12 more of them ordered steak and 9 fewer ordered seafood. How many quests attended the banquet?

I did 43+12-9 which = 46
But tbh I think i might be completely wrong. This is for Algebra 2 so why would a teacher give me this easy of a question. I'm also just thinking not to smart LOL please help

Answers

Answer:

58

Step-by-step explanation:

only 3 people ordered seafood so u add 43 12 and 3

SORRY IF I AM WRONG

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 6 and the denominator is decreased by 5, the new rational number obtained is 3/2. Find the original rational number.

Answers

Answer:

6/13

Step-by-step explanation:

6    +   6    =    12            3

----                    ----    =    ---

13     -   5    =     8            2

Answer:

Original Rational number is = 6/13

Step-by-step explanation:

Let Numerator be : x

Denominator be : x + 7

Now,

Numerator is increased by 6Denominator is decreased by 5the new rational number obtained is 3/2

Numerator = x + 6

Denominator = ( x + 7) - 5

According to the question,

[tex] \displaystyle \: \sf \dashrightarrow \: \frac{x + 6}{(x + 7) \: - 5} = \: \frac{3}{2} [/tex]

[tex]\displaystyle \: \sf \dashrightarrow \: 2(x + 6) \: = 3 \{ \: (x + 7 ) - 5\} \: [/tex]

[tex]\displaystyle \: \sf \dashrightarrow \: 2x \: + 12 \: = \: 3(x + 2)[/tex]

[tex]\displaystyle \: \sf \dashrightarrow2x + 12 \: = 3x + 6[/tex]

[tex]\displaystyle \: \sf \dashrightarrow \: 2x - 3x \: = \: 6 - 12[/tex]

[tex] \: \: \: \displaystyle \: \sf \dashrightarrow \: - x \: = - 6 \\ \\ \: \: \: \: \: \: \displaystyle \: \bf \dashrightarrow \: x \: = 6[/tex]

Numerator = 6

Denominator = x + 7

= 6 + 7

= 13

Thus ,

[tex]\: \bf { \red{ \underline{\dashrightarrow \: obtained \: rational \: number \: = \: \frac{6}{13} }}}[/tex]

[tex] \pink{\rule{160pt}{5pt}}[/tex]

how many seconds are in 5 hours abs 30 minutes

Answers

Answer:

19800 seconds

Step-by-step explanation:

9
. 10
11
12
Yesterday, Jessica had 95 baseball cards. Today, she got d more. Using d, write an expression for the total number of baseball cards she has now.
ローロ

Answers

Answer:

95+d

Step-by-step explanation:

This is confusing and makes no sense

Answers

Answer:

A is the answer

rrrrrrrr

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