What is the answer to: 18

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

Haben knows that the angle of elevation from the top of a rock formation to a stake in the ground 50 feet from its base is 42°.

Murrr4er [49]

Answer:

The height of the rock formation is $45.02\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

$tan(42\°)=h/50$

solve for h

$h=50*tan(42\°)=45.02\ ft$

4 0

3 years ago

Read 2 more answers

Click and drag like terms onto each other to simplify fully -2x+1+7x-3y

erma4kov [3.2K]

After it is fully simplified, it will be 5x+1-3y

7 0

2 years ago

8-2|4-5y|=4 | | stands for absolute value

Contact [7]

Answer:

y = (2/5) OR y = (6/5)

Step-by-step explanation:

The first step is isolating the expression within the absolute value bars. The first thing we can do is subtract both sides by 8. If we do that, we get -2|4-5y| = -4. Now, to completely isolate the absolute value, we would have to divide by -2. This yields |4 - 5y| = 2. Finally, we can remove the absolute value bars. However, to do this, we need to first understand what an absolute value bar does to an equation. Lets say that |x| = 2. Absolute value describes the DISTANCE of some quantity from 0 (on the number line). Therefore, x (which is inside the absolute value bars) can be either positive or negative 2 (they are BOTH two units away from 0). Similarly, in this case, (4 - 5y) can either be 2 or -2 (because the absolute value of both is 2). Now we have two possible solutions to solve for:

4 - 5y = 2 OR 4 - 5y = -2

5y = 2 OR 5y = 6

y = (2/5) OR y = (6/5)

If we plug both of these answers back into the equation we can see that they both check out.

4 0

1 year ago

from 1970 to 1980 the consumer price index increased from 38.8 to 82.4. If a container of onion dip cost $0.48 in 1970 and the p

Vikki [24]

We need to find the percent increase from 38.8 to 82.4, so

x * 38.8 = 82.4
x = 82.4/38.8
x = 2.1237

Multiply by 100 to convert to percentage (move decimal 2 places to the right)

2.1237 = 212.37%

Now we can apply this percentage increase to the onion dip...

0.48 x 212.37% =
0.48 x 2.1237 = 1.019

Round to the nearest cent $1.02 is the amount of increase. Now add it to the original price to get today's price...

$1.02 + .48 = $1.50

5 0

3 years ago

Read 2 more answers

What is the answer to: 18 - 5z + 6z > 3 + 6