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Math Help - [SOLVED] simplify

  1. #1
    animal
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    [SOLVED] simplify

    I have these problems,need help with ans.:
    1. -6(2x-9)-4x+5 (simplify)
    2. x-6/y-5 (simply)
    3. (x/6) to the 3rd. (simplify)
    4. y-7x/6x+xy given x=1 & y=3 (evaluate)
    5. 8x+7 given x=3 (evaluate)
    6. -(8z-7w+2y) (simplify)
    7. 6 sq. root sign over 7 + 3 sq. root sign over 7 (simplify)
    8. 19/sq. root sign over 19 (simplify)
    9. 5 to the 4th dot 5 to the 8th (simplify)
    10. 7 0 power (simplify)
    11. determine whether 15>16 (true or false)
    12. sq. root sign 100/9 (simplify)
    13. 2+6(x-2) to the 3rd. given x=4 (evaluate)
    14. (x neg. 5th power)neg. 3rd (simplify)
    15. express &evaluate the distance between the number 84 and neg. 34 using absolute value?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by animal View Post
    1. -6(2x-9)-4x+5 (simplify)
    2. x-6/y-5 (simply)
    -6(2x-9)-4x+5 = (-6)*(2x) + (-6)*(-9) - 4x + 5

    = -12x + 45 - 4x + 5

    = -16x + 50

    There is no way to simplify the second problem.

    -Dan
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  3. #3
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    Quote Originally Posted by animal View Post
    I have these problems,need help with ans.:
    1. -6(2x-9)-4x+5 (simplify)
    2. x-6/y-5 (simply)
    3. (x/6) to the 3rd. (simplify)
    4. y-7x/6x+xy given x=1 & y=3 (evaluate)
    5. 8x+7 given x=3 (evaluate)
    1.) -6*(2x - 9) - 4x + 5

    -12x + 54 - 4x + 5

    -16x + 59

    2.) x - 6/y - 5 is already simplified; perhaps you mean (x - 6)/(y - 5) which is also simplified..unless you want to expand it to x/(y - 5) - 6/(y - 5) ..

    3.) (x/6)^3

    x^3/216

    4.) Evaluate y - 7x/6x + xy : (1,3)

    Well, I'm not sure if you mean what you have written, or (y - 7x)/(6x + xy).. or.. who knows.

    Any way, what you have:

    3 - 7(1)/6(1) + (1)(3) = 3 - 7/6 + 3 = 6 - 7/6 = 29/6

    Or, if you meant what I have:

    (3 - 7(1))/(6(1) + (1)(3)) = -4/9

    5. Evaluate 8x + 7 : x = 3

    8(3) + 7 = 24 + 7 = 31
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  4. #4
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    Quote Originally Posted by topsquark View Post
    -6(2x-9)-4x+5 = (-6)*(2x) + (-6)*(-9) - 4x + 5

    = -12x + 45 - 4x + 5
    9*6, not 9*5
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by animal View Post
    3. (x/6) to the 3rd. (simplify)
    9. 5 to the 4th dot 5 to the 8th (simplify)
    10. 7 0 power (simplify)
    12. sq. root sign 100/9 (simplify)
    14. (x neg. 5th power)neg. 3rd (simplify)
    You need to know the following rules:
    (In the following, m and n are integers, and a and b are real numbers not equal to 0.)
    a^n = a*a*...*a (n times)
    a^0 = 1
    a^n * a^m = a^(n + m)
    (a^n)^m = a^(n*m)
    a^(-n) = 1/(a^n)
    sqrt(a) = a^(1/2)
    a^n * b^n = (ab)^n

    So.
    3. (x/6) to the 3rd = (x/6)^3 = (x^3)/(6^3) = (x^3)/216

    9. 5 to the 4th dot 5 to the 8th = 5^4 * 5^8 = 5^(4 + 8) = 5^12

    10. 7 0 power
    I presume this is 7^0 = 1?

    12. sq. root sign 100/9 = sqrt(100/9) = sqrt(100)/sqrt(9) = 10/3
    (Or:
    sqrt(100/9) = (100/9)^(1/2) = [100^(1/2)]/[9^(1/2)] = [(10^2)^(1/2)]/[(3^2)^(1/2)]
    = 10/3)

    14. (x neg. 5th power)neg. 3rd = (x^5)^(-3) x^(5*(-3)) = x^(-15) = 1/(x^15)

    -Dan
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AfterShock View Post
    9*6, not 9*5
    Blarg. And I was just saying how early in the morning it is on another post...

    -Dan
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by animal View Post
    )
    11. determine whether 15>16 (true or false)
    PLEASE tell me you're joking.

    Quote Originally Posted by animal View Post
    )
    15. express &evaluate the distance between the number 84 and neg. 34 using absolute value?
    d = |84 - (-34)| = |84 + 34| = 118

    or

    d = |(-34) - 84| = |-118| = 118

    -Dan
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  8. #8
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    Quote Originally Posted by animal View Post
    6. -(8z-7w+2y) (simplify)
    7. 6 sq. root sign over 7 + 3 sq. root sign over 7 (simplify)
    8. 19/sq. root sign over 19 (simplify)
    9. 5 to the 4th dot 5 to the 8th (simplify)
    10. 7 0 power (simplify)
    6.) Simplify -(8z - 7w + 2y)

    Distribute the negative:

    -8z + 7w - 2y, and this is simplified.

    7.) Simplify 6*sqrt(7) + 3*sqrt(7) <-- that?

    If so, then 9*sqrt(7).

    8.) Simplify 19/sqrt(19)

    Multiply by sqrt(19)/sqrt(19) (which is multiplying by 1), and then

    19*sqrt(19)/19 = sqrt(19)

    9.) Simplify 5^4 "dot" 5^8. By "dot" I doubt you mean dot product, and instead multiplication. Thus, add exponents since bases are the same:

    5^12

    10.) 7 0 power (simplify) <-- Um, 7^(0) ?

    If so, any non-neg. integer raised to the 0th power is always 1.

    Therefore, 7^0 = 1
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  9. #9
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    Quote Originally Posted by animal View Post
    12. sq. root sign 100/9 (simplify)
    13. 2+6(x-2) to the 3rd. given x=4 (evaluate)
    14. (x neg. 5th power)neg. 3rd (simplify)
    11, 15 done already.

    Well, a comment on 11:

    "Determine whether 15 > 16"

    Do you know what > means? What comes first...15...or 16? I'll let you figure that out.

    12.) sqrt(100)/9 <-- that? Or, sqrt(100/9);

    If it's the penultimate, then 10/9; if it's the latter, then 10/3.

    13.) Evaluate 2 + 6(x - 2)^3 : x = 4

    2 + 6(4 - 2)^3 = 2 + 6(2)^3 = 2 + 6*8 = 2 + 48 = 50.

    14.) Simplify x^(-5)*"neg. 3rd"

    What is neg. 3rd?

    [x^(-5)]^(-3) ? If so:

    x^(-5) = 1/(x^5); and then,

    (1/(x^5))^(-3) = 1/(x^(-15)) = x^15
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