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gizmo_the_mogwai [7]
3 years ago
5

Help! im in class right now and dont have much time!

Mathematics
2 answers:
Hatshy [7]3 years ago
6 0

Answer:

\frac{1}{m^{8} }

Step-by-step explanation:

m^{-8} p^{0}

m^{-8} 1       ∴Zero power of any number is equal to 1

\frac{1}{m^{8} }            

Harman [31]3 years ago
4 0

Answer:

D. \frac{1}{m^8}

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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
3 years ago
A sphere has a radius of 5.3 ft. What is the volume of the sphere to the nearest tenth? use 3.14 for pi. Question 3 options:
Alenkinab [10]
Your answer would be c
623.3 ft^3
5 0
3 years ago
Find the cost of kg of apples and the cost of an orange using simultaneous equations method:
PtichkaEL [24]
Cost of kg of apples = £1.08
cost of an orange = £0.12
hi, the solution is in the pic below. sorry for the messy working!

6 0
3 years ago
Please help :) it would be appreciated! thanks!
Paha777 [63]
I think it’s Function
7 0
3 years ago
Read 2 more answers
What is the height of an equilateral triangle if the sides are 10
4vir4ik [10]

Answer:

The height of the equilateral triangle is 5\sqrt{3}\ units

Step-by-step explanation:

we know that

An equilateral triangle has three congruent sides, and three congruent angles that each measure 60 degrees

To find out the height of an equilateral triangle, apply the Pythagoras Theorem in the right triangle ABD

Remember that the height of an equilateral triangle bisects the base.

see the attached figure to better understand the problem

AB^2=AD^2+BD^2

substitute the given values

10^2=5^2+BD^2

Solve for BD

100=25+BD^2

BD^2=100-25

BD^2=75

BD=\sqrt{75}\ units

simplify

BD=5\sqrt{3}\ units`

therefore

The height of the equilateral triangle is 5\sqrt{3}\ units

7 0
3 years ago
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