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2 years ago

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Gcdbvfgvfnc vc vfnfbnfnbvgn

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jonny [76]2 years ago

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no way dude really? thats so cool

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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 <em>sum and difference of cubes</em>, 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 <u><em>perfect cube numbers</em></u> (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 <em>sum and difference of cubes </em>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 <em>sum of cubes.</em>

<em>Sum of cubes</em>

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

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

Simplify the expression. State any excluded values.<br><br> x^ 2 - 36/42x - 7x^ 2

REY [17]

Consider the expression $x^2-\dfrac{36}{42}x-7x^2.$

This expression contains two terms with $x^2,$ group them:

$x^2-7x^2=x^2(1-7)=-6x^2.$

Now simplify term $\dfrac{36}{42}x=\dfrac{6}{7}x.$

Now $x^2-\dfrac{36}{42}x-7x^2=-6x^2-\dfrac{6}{7}x=6\left(-x^2-\dfrac{1}{7}x\right)=-6x\left(x-\dfrac{1}{7}\right).$

This expression is defined for all x.

3 0

2 years ago

A box contains 9 identical glass spheres that are used to make snow globes.

DIA [1.3K]

Uhmmm B I pretty sure

5 0

2 years ago

Choose the correct simplification of 8x2(4x 2x2 − 1). (5 points) group of answer choices 32x4 − 16x3 8x2 32x4 16x3 − 8x2 16x4 −

nekit [7.7K]

The second option is the correct answer

$16x^{4}+40x^{3} -24x^{2}$

The expression given to us is:

$8x^{2} (5x+2x^{2}-3 )$

Herein, we can simplify it by opening up the bracket and multiplying each term inside the bracket by the term which is outside the bracket.

Thus, we get:

$8x^{2} (5x+2x^{2}-3 )=8*5x^{2+1} +8*2x^{2+2}-8*3x^{2}$

$40x^{3} +16x^{4}-24x^{2}$

Rearranging the above expression in descending order of power we get:

$16x^{4}+40x^{3} -24x^{2}$

From the given options we can see this is the second option. Hence the second option is the correct answer.

Learn more about equation here brainly.com/question/14180340

#SPJ4

8 0

1 year ago

A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $5 per foot and fencing for th

Vesnalui [34]

The answer is "141.17647058823529411764705882353", hope this helps! Please Mark me the brainliest! ☺

4 0

2 years ago