Math

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Solve the system of equations
3x-y=11
-5x+y=12

2.
Perform the indicated operation and simplify (5/(x-2)+(4(x^2-2x)

3.simpify and write with only positive exponents (7x^3y^-2)/(x^-4y^9)^-3

4.
find the solution of the inequality
2x-11 is less than or equal to -4(5x-3)

5. the length of a recangle is 5 feet less than twice the width. the area is 25 square feet. using w as the variable. write an equation that can be used to calculate the width.
(2w^2-5)

  • Math -

    Any help would be appreciated. This is for my study guide in order to do well on my test. Someone please help.

  • Math -

    #1
    From the first, y=3x-11
    Plug that into the second:
    -5x+3x-11 = 12
    -2x = 23
    x = -23/2
    y = -91/2

    Or, you can just add the equations to eliminate the y terms:
    -5x = 23
    ...

    #2 Your parentheses are unbalanced. If you mean
    5/(x-2) + 4/(x^2-2x)
    5/(x-2) + 4/(x(x-2))
    5x/(x(x-2)) + 4/(x(x-2))
    (5x+4)/(x(x-2))
    (5x+4)/(x^2-2x)

    #3
    (7x^3y^-2)/(x^-4y^9)^-3

    (x^-4y^9)^-3 = x^12 y^-27
    Since you're dividing by that, you have

    (7x^3y^-2)*(x^-12 y^27)
    7x^-9 y^25
    7y^25/x^9

  • Math -

    #4.
    2x-11 <= -4(5x-3)
    2x-11 <= -20x + 12
    22x <= 23
    x <= 23/22

    #5.
    length is 2w-5
    area is 25, so

    w(2w-5) = 25
    2w^2-5w = 25
    2w^2 - 5w - 25 = 0
    (2w+5)(w-5) = 0
    w=5 (-5/2 is not a usable width)
    the rectangle is a square 5x5

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