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creativ13 [48]
3 years ago
9

What is the factorization of 729^15+1000​

Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0

\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} 729=27^2\\ \qquad (3^3)^2\\ 1000=10^3 \end{cases}\implies 729^{15}+1000\implies ((3^3)^2)^{15}+10^3 \\\\\\ ((3^2)^{15})^3+10^3\implies (3^{30})^3+10^3\implies (3^{30}+10)~~[(3^{30})^2-(3^{30})(10)+10^2] \\\\\\ (3^{30})^3+10^3\implies (3^{30}+10)~~~~[(3^{60})-(3^{30})(10)+10^2]

now, we could expand them, but there's no need, since it's just factoring.

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Rosemarie drove from Philadelphia, Pennsylvania, to Pittsburgh, Pennsylvania. The distance between Philadelphia and Pittsburgh i
Nat2105 [25]

Answer:

The speed was 61\frac{miles}{hour}

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

s------> the speed in miles per hour

d ----> the distance in miles

t ----> is the time in hours

we know that

s=\frac{d}{t}

we have

d=305\ miles

t=5\ hours

substitute

s=\frac{305}{5}

s=61\frac{miles}{hour}

7 0
3 years ago
Solve the simultaneous equations:<br><br> 5x + 3y = 9<br> 7x - 2y = 25<br><br> x=__<br> y=__
kondor19780726 [428]

Answer:

x= 3, y= -2

Step-by-step explanation:

5x+3y= 9

x= 25÷7 + 2÷7 y

5(25÷7 +2÷7 y)

5( 25÷7 +2÷7 y ) + 3y= 9

y= -2

x= 25÷7 + 2÷7 x (-2)

x= 3

5 0
3 years ago
Omar is born weighing 8 pounds,3 ounces.The doctor says he should gain a about 5 ounces each week for the next 4 weeks.How much
hoa [83]
Start weight- 8.03
week 1 - 8.8
week 2 - 8.13
week 3 - 9.03
week 4 - 9.08

So, the Omar should weigh 9 pounds 8 ounces by the end of 4 weeks.

I hope this helped!
6 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLIEST TO RIGHT ANSWER!!
daser333 [38]

Answer:

Step-by-step explanation:

2 - Corresponding angles theorem

6 - Alternate exterior angles theorem

8 - Transitive Property

3 0
3 years ago
Read 2 more answers
HELP I AM IN A TEST AND SOMEONE DELETED MY OTHER QUESTION BEFORE! AND I STILL NEED HELP PLZ I WILL GIVE BRAINLIEST AND THANKS AN
saw5 [17]

Answer:

2.

30-7x4 = 2

3.

80

Step-by-step explanation:

2.

First, do 7x4, which equals 28. Then subtract that from 30, and you get 2.

3.

Do the parentheses first, 21-6=15. Then 15 divided by 0.2 = 75. 75+5=80.

Sorry I couldn't help on any of the other ones, I don't have much time.

5 0
2 years ago
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