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3 years ago

First to answer gets something good ;)

Mathematics

1 answer:

lesya [120]3 years ago

7 0

Answer:

should be the second one 75 + 20x <55 +44x

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What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a sum of cubes.

Sum of cubes

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

8 0

2 years ago

Mr Coope drives 472 miles in 8 hours. At this rate, how many miles would he drive in 6

KatRina [158]

8hrs = 480mins
6hrs = 360 mins
472/480 = 0.983...
0.983... x 360 = 354
D) 354

6 0

2 years ago

If a bus driver get paid $20,000 a year and he works 35 weeks a year how many weeks will it take for him to earn $2000

alexgriva [62]

Answer:

3.5?

Step-by-step explanation:

2,000 is 10% of 20,000

3.5 is 10% of 35

7 0

3 years ago

Read 2 more answers

Find the equation that is equivalent to the quadratic equation shown. Explain why

zysi [14]

C - (x-3)^2=36

If we expand (x-3)^2=36:

(x-3)(x-3)=36
x^2-3x-3x+9=36
x^2-6x+9=36

Then subtract 36

x^2-6x-27=0

7 0

3 years ago

Pls, can someone answer this, Explain, using words and numbers, how to subtract 7x - ( 6x + 13). Remember to include the solutio

Hitman42 [59]

So first you distribute the negative to the 6x and 13 which will flip the sign of both of them to -6x and -13 so take away the parentheses and the equation is now 7x-6x-13. You combine the x’s and you get 1x-13 or x-13

3 0

2 years ago