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Roman55 [17]
3 years ago
8

What is the factorization of 729x^15 + 1000?

Mathematics
1 answer:
Tcecarenko [31]3 years ago
8 0

Answer:

729x¹⁵ + 1000

This is a case of a sum of cubes.

729 is the cube of 9

1000 is the cube of 10

x¹⁵ is the cube of x⁵

A sum of perfect cubes can be factored into 

(a + b) (a² - ab + b²)

(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)

(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION

9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)

729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000

729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000

729x¹⁵ + 1000

Step-by-step explanation:

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Rosetta has 1/8 bag of cat food left. She divides the remaining of the cat food into 12 equal sized portions. What fraction of a
Nookie1986 [14]

Answer:

1/96

Step-by-step explanation:

6 0
3 years ago
Can someone solve this for me with their explanation please?
Lana71 [14]

First you want to subtract 36

so it looks like this \sqrt[4] {(4x+164)^3}=64

Then you want to cancel out the square root 4 by raising that to the 4th power (you must do this to both sides)

{(4x+164)^3}=64^4 which is equal to {(4x+164)^3}=16777216

Then you take the cube root to both sides [tex]\sqrt[3]{(4x+164)^3}=\sqrt[3]{16777216}[tex]

Then you end up with the equation 4x+164=256

Then subtract 164 to both sides

4x=92

then divide 92 by 4

Then you get x=23




7 0
3 years ago
The line goes through the ordered pair (10, 6) It has a y-intercept of -2.
VLD [36.1K]

Answer: the x-intercept would be (2,-2)

Step-by-step explanation:

6 0
3 years ago
Help please ..............
Cloud [144]

Answer:

x = 437.3 ft

Step-by-step explanation:

The angle at the top of the triangle = 90° - 29° = 61°

Using the sine ratio in the right triangle

sin61° = \frac{opposite}{hypotenuse} = \frac{x}{500}

Multiply both sides by 500

500 × sin61° = x, hence

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8 0
3 years ago
Read 2 more answers
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan
Mekhanik [1.2K]

<em><u>An inequality that shows the distance Johnathan could of ran any day this week is:</u></em>

x\leq 3.5

<em><u>Solution:</u></em>

Let "x" be the distance Johnathan can run any day of this week

Given that,

Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles

Therefore,

Number of days ran = 5

The most he ran in 1 day = 3.5 miles

Thus, the maximum distance he ran in a week is given as:

distance = 5 \times 3.5 = 17.5

The maximum distance he ran in a week is 17.5 miles

If we let x be the distance he can run any day of this week then, we get a inequality as:

x\leq 3.5

If we let y be the total distance he can travel in a week then, we may express it as,

y\leq 17.5

8 0
3 years ago
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