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Math questions pre algebra?

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My Math teacher gave us some math problems and told us to google it so see what other people came up with.... here goes....

Find the Domain
1. g(x)= 1/3x-3

2. f(x)= (the square root sign) -x-2

Solve...
1. x^3=x

2. x^2=-5x=24

Simplify
1. x^2+2x-3/x-5

2. x^3-27/x-3

3. (2x^-5y^-1)-3/(-5x^-3y^-4)-2

4. (x^-2y^3/-2x^-5y^7)^-3
asked Mar 30, 2013 in PRE-ALGEBRA by andrew Scholar

17 Answers

0 votes

1.

g(x) = 1 / 3x - 3

We can find the domain then

3x - 3 = 0

Add 3 to each side

3x - 3 + 3 = 3 + 0

3x = 3

Divide 3 to each side

3x / 3 = 3 / 3

x  = 1

There the domain is x = 1.

answered Apr 1, 2013 by diane Scholar

Domain of image is all real numbers.

Domain of image is image

0 votes

 f(x) = the square root sign -x  - 2

f(x) =sqrt(-1(x + 2))

Substitute i^2 = -1 in the f(x)

f(x) = sqrt(i^2 ( x + 1)

f(x) = isqrt (x + 1)

We can find the Domain sqrt(x + 1) = 0

Take square each side

x + 1 = 0

Subtract from 1 to each side

x + 1 -  1 = 0 - 1

x + 0 = -1

x = -1

The domain is x = -1.

answered Apr 1, 2013 by diane Scholar

Domain of image is image

0 votes

 Solve x3 = x

Subtract x to each side

x3 - x = 0 - x

x3 - x = 0

Take out common term x in x3 - x = 0

x(x2 - 1) = 0

x(x2 - 12) = 0

Recall : a2 - b2 = (a - b)(a + b)

Substitute a = x  and b = 1 in the x2 - 12

x(x - 1)(x + 1) = 0

It have 3 roots

x = 0 or x - 1 = 0 or x + 1 = 0

x - 1 = 0

Add 1 to each side

x - 1 + 1 = 0 + 1

x - 0 = 1

x = 1

x + 1 = 0

Subtract 1 from each side

x + 1 - 1 = 0 - 1

x + 0 = -1

x = -1

The solution of the equation : -1 , 0 , 1.

 

 

answered Apr 1, 2013 by diane Scholar
0 votes

 Solve x3 = x

Subtract x to each side

x3 - x = 0 - x

x3 - x = 0

Take out common term x in x3 - x = 0

x(x2 - 1) = 0

x(x2 - 12) = 0

Recall : a2 - b2 = (a - b)(a + b)

Substitute a = x  and b = 1 in the x2 - 12

x(x - 1)(x + 1) = 0

It have 3 roots

x = 0 or x - 1 = 0 or x + 1 = 0

x - 1 = 0

Add 1 to each side

x - 1 + 1 = 0 + 1

x - 0 = 1

x = 1

x + 1 = 0

Subtract 1 from each side

x + 1 - 1 = 0 - 1

x + 0 = -1

x = -1

The solution of the equation : -1 , 0 , 1.

answered Apr 1, 2013 by diane Scholar
0 votes

x2 -5x = 24

Subtract 24 to each side

x2 + 5x  -24= 24 - 24

x2 + 8x - 3x  -24 = 0

Take out common term x  and -3 in the above equation

x(x + 8) -3(x +8) = 0

Take out common term x + 8 in the above equation

(x + 8)(x - 3) = 0

x + 8 = 0 or x - 3 = 0

If x + 8 = 0

Subtract 8 from each side

x + 8 - 8 = -8

x + 0 = -8

x = -8

If x - 3 = 0

Add 3 to each side

x -3 + 3 = 0 + 3

x - 0 = 3

x = 3.

The solution of the equation : -8 , 3.

answered Apr 2, 2013 by diane Scholar

Solutions of the equation x2 -5x = 24 are x = -3 , 8.

0 votes
Simplify 1. x^2 + 2x - 3 / x - 5 (x^2 + 3x - x - 3) / x - 5 Take out common term x and -1 in the above expression x(x + 3) -1(x + 3) / x - 5 Take out common term x + 3 x + 3[x - 1] / x - 5 (x + 3)(x - 1) / x - 5.
answered Apr 2, 2013 by diane Scholar
0 votes

 Simplify

2.

x3  - 27 / x - 3

=x3 - 33 / x - 3

Recall : (a3 - b3) = ( a - b)(a2 + ab + b2)

Substitute x = a  and b = 3 in the above formula

(x - 3)(x2 + 3x + 32) / (x - 3)

= (x2 + 3x + 9).

 

 

answered Apr 2, 2013 by diane Scholar
0 votes

4.

(x-2y3 / -2x-5y7)-3

Apply the power rule (a / b)-3 = a-3 / b-3

(x-2y3)-3 / (-2x-5y7)-3

Apply the power rule (ab)-3 = a-3 b-3

x6y-9 / -2x15y-21

Apply the power rule

y-9+21 / -2x15-6

y12 / -2x9

-1/2(y12 / x9)

-1/2(y12 x-9).

answered Apr 4, 2013 by diane Scholar
0 votes

3.

(2x-5y-1) -3 / (-5x-3y-4) - 2

Apply the power rule

((2 / x5y) - 3) / (-5 / x3y4) - 2

(2 - 3x5y / x5y) / (-5 - 2x3y4 / x3y4)

Simplify

(x3y4 / x5y)(2 - 3x5y / -(5 + 2x3y4))

Apply the power rule

(y4-1 / x5-3)(2 - 3x5y / -(5 + 2x3y4))

-(y3 / x2)(2 - 3x5y / 5 + 2x3y4)

[-y3(2 - 3x5y) / x^2(5 + 2x3y4)] .

 

answered Apr 4, 2013 by diane Scholar
0 votes

Siimplify

4) Given ( x ^-2 y ^ 3 / -2x  ^-5 y ^ 7 ) ^ -3

Apply the power rule (a / b) ^ -3 = a ^ -3 / b ^ -3

( x ^ -2 y ^ 3 ) ^ -3 / ( -2 x ^ -5 y ^ 7 ) ^ -3

Apply the power rule ( ab )^ -3 = a ^ -3 * b ^ -3

x ^ 6 y ^ -9 / ( ( -2 ) ^ -3 x ^ 15 y ^ -21 )

Apply the power rule

x ^ 6 y ^ -9 / ( -1/8) x ^ 15 y ^ -21

- 8 y ^ - 9 + 21 / x ^ 15 - 6

- 8 y ^ 12 / x ^ 9

- 8 y ^ 12 x ^ -9

answered May 10, 2013 by jeevitha Novice

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