MATHEMATICS HIGH SCHOOL

Calculate 10P7.A. 720
B. 70
C. 3
D. 604,800

Answers

Answer 1
Answer: P(10, 7) = 10!/(10 - 7)!
P(10, 7) = 10!/3!
P(10, 7) = (10✖️9✖️8✖️7✖️6✖️5✖️4✖️3✖️2✖️1)/(3✖️2✖️1)
P(10, 7) = 10✖️9✖️8✖️7✖️6✖️5✖️4
P(10, 7) = 90✖️56✖️30✖️4
P(10, 7) = 5,040✖️120
P(10, 7) = 604,800

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Which expression is equivalent to (7x - 5 ) - ( 3x - 2)?

Answers

(7x - 5 ) - ( 3x - 2) 

7x-5-3x+2 

(7x-3x)-5+2          \ Gather \ like \ terms  

4x-5+2 

4x-3
Distribute the minus sign into the second parenthesis to get 7x-5-3x+2.
Then combine like terms to get 4x-3

Prove that: (a2 - b2)3 + (b2-c2)3+ (c2-a2)3 = 3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a).

Answers

L=(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=(*)\n\n(a^2-b^2)^3=a^6-3a^4b^2+3a^2b^4-b^6\n\n(b^2-c^2)^3=b^6-3b^4c^2+3b^3c^4-c^6\n\n(c^2-a^2)^3=c^6-3c^4a^2+3c^2a^4-a^6\n\n(*)=a^6-3a^4b^2+3a^2b^4-b^6+b^6-3b^4c^2+3b^2c^4-c^6+c^6-\dots\n\dots-3c^4a^2+3c^2a^4-a^6\n\n=-3a^4b^2+3a^2b^4-3b^4c^2+3b^2c^4-3c^4a^2+3c^2a^4\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)

R=3(a+b)(a-b)(b+c)(b-c)(c+a)(c-a)\n\n=3(a^2-b^2)(b^2-c^2)(c^2-a^2)\n\n=3(a^2b^2-a^2c^2-b^4+b^2c^2)(c^2-a^2)\n\n=3(a^2b^2c^2-a^4b^2-a^2c^4+a^4c^2-b^4c^2+a^2b^4+b^2c^4-a^2b^2c^2)\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)\n\nL=R

(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(b +c)(c + a)(a - b)(b - c)(c - a)
(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)
(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2)

(a^2 - b^2)^3 = (a^2 - b2)(a^2 - b^2)(a^2-b^2) = a^6 - 3a^4b^2 + 3a^2b^4 - b^6
(b^2 - c^2)^3 = (b^2 - c^2)(b^2 - c^2)(b^2 - c^2) = b^6 - 3^4c^2 + 3b^2c^4 - c^6)
(c^2 - a^2)^3 = (c^2 - a^2)(c^2 - a^2)(c^2 - a^2) = c^6 - 3a^2c^4 + 3a^4c^2 - a^6

a^6 - 3a^4b^2 + 3a^2b^4 - b^6 + b^6 - 3b^4c^2 + 3b^2c^4 - c^6 + c^6 - 3a^2c^4 + 3a^4c^2 - a^6
-3a^4b^2 + 3a^2b^4 - 3b^4c^2 + 3b^2c^4 - 3a^2c^4 + 3a^4c^2
3(-a^4b^2 + a^2b^4 - b^4c^2 + b2^c^4 - a^2c^4 + a^4c^2)

3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2)

3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2

Find the smallest solution to the equation 2/3x^2=24

Answers

24/(2/3)=16
sqrt(16)=4

x=4

What is equal to the expression square root of 40/2

Answers

First you would simplify what's in the square root, to get root 20. If you want the exact number, and not the approximation, you would take out whatever squares are in that number (20=2*2*5) so your answer is 2root5.


However, if you want the approximation, simply plug it into your calculator and get 4.18154055.

How do you solve 2/3=m/42

Answers

(2)/(3) = (m)/(42) \n \n (2)/(3) * 42 = m \ / \ multiply \ each \ side \ by \ 42 \n \n (84)/(3) = m \ / \ simplify \n \n 28 = m \ / \ simplify \n \n m = 28 \ / \ change \ sides \n \n

The final result is m = 28.
2/3 = m/42

m/42 = 2/3
*42       *42

2/3 * 42/1 = 84/3 = 28

m = 28

Answer: m = 28

A 26‘long painting is how many yards long?

Answers

Hello! 

If a painting is 26 feet long, it's 8 and 2/3 yards long.

This is because there is 3 feet in a yard. You would do 26 divided by 3. You would get 8 yards and have 2 feet left. Obviously 2 feet is smaller than a yard, so it'd be 2/3 of a yard. Therefore the answer is 8 and 2/3 yards.

Hope this helped! :)
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