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Stells [14]
3 years ago
13

Factor this polynomial completely. x^2-81

Mathematics
2 answers:
expeople1 [14]3 years ago
7 0

The answer to your question is (x+9)(x-9)

Step-by-step explanation:

Rewrite 81 as 92

x2−92

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)

where a=x and b=9

(x+9)(x−9)

Hope this helped you out:)

ikadub [295]3 years ago
4 0

Answer:

a=x and b=9

(x+9)(x−9)

Explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)

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The period of the function is that distance where the function becomes equal again.
 We have then:
 Part 1:
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 T = 3
 Part 2:
 The period of the function is:
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 Answer:
 
The period of functions 1 and 2 respectively are:
 
T = 3
 
T = 4
6 0
3 years ago
The dimensions for a rectangular prism are x + 2 for the length, x + 3 for the width, and x for the height. What is the volume o
Jlenok [28]
V = lwh

V = (x + 2)(x + 3)(x)

V = (x)(x^2 + 3x + 2x + 6)

V = (x^3 + 3x^2 + 2x^2 + 6x)

V = x^3 + 5x^2 + 6x

All you do is foil the dimensions together and then combine like terms. Hope this helps!
7 0
3 years ago
4 x 10^6 is how many times large then 1 x 10^4
Molodets [167]

Answer:

<h2>400</h2>

Step-by-step explanation:

4\times10^6\text{ is how many times large than}\ 1 \times 10^4?\\\\\dfrac{4\times10^6}{1\times10^4}=\dfrac{4}{1}\times\dfrac{10^6}{10^4}=4\times10^{6-4}=4\times10^2=4\times100=400

4 0
3 years ago
What is a measurement<br>​
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Step-by-step explanation:

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Read 2 more answers
A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,
tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0
3 years ago
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