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Math Help - Algebra quadratic formula word problem

  1. #1
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    Algebra quadratic formula word problem

    I have two problems I am new here and I want to see how this site works...
    so...
    #1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.

    2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
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  2. #2
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    Quote Originally Posted by lightstevoo View Post
    I have two problems I am new here and I want to see how this site works...
    so...
    #1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.

    2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
    Try to obtain equations from your problems.
    For the first one:
    Let a be the first number, and b be the second number,
    thier sum = 5 \implies a+b=5 .... (1)
    thier product = 5 \implies ab=5 .... (2)
    Now, If we subtract a from the both sides in equation (1), we will get:
     b = 5 - a .... (3)
    By substituting (3) in (2), we get:
     a(5-a)=5
    5a-a^2=5

    Now, Solve the last quadratic equation for a.
    Once you have the values of a, substitute them in (3) to obtain the value of b.
    Do not remember to reject the negative values; because the question said that : the two numbers are positive.

    I will leave the second for you.
    Try to obtain some equations from it.
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  3. #3
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    Hi there lightstevoo, welcome to MHF!

    Quote Originally Posted by lightstevoo View Post
    I have two problems I am new here and I want to see how this site works...
    so...
    On this forum we try to 'help' you solve the problem not just solve it for you.


    Quote Originally Posted by lightstevoo View Post
    #1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.
    Lets say your numbers are x and y. From the problem

    x+y = 5

    and

     x\times y = 5

    The first statement can be writtien as

    x = 5-y

    Lets use that to put into the secons statement which becomes

     (5-y)\times y = 5

    Now you need to exapnd this and solve

     5y-y^2 = 5

    Have a go from here

    Quote Originally Posted by lightstevoo View Post

    2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
    This is similar to the first

    Lets call the x the length and y the width. As one side (lets call it the width of your triangle) of your rectangle is the barn then only 3 sides need to be fenced.

    So you have

    x+x+y= 100

    and

    x\times y = 1200

    The first statement can be writtien as

    2x+y= 100 then y= 100-2x

    Can you take it from here?

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  4. #4
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    Q1.

    (x-a)(x-b)=x^2-(a+b)x+ab=x^2-5x+5

    a\ and\ b\ are\ \frac{5+\sqrt{25-20}}{2}\ and\ \frac{5-\sqrt{25-20}}{2}

    Q2.

    The barn side dimensions are

    x,\ 50-\frac{x}{2}

    Use the area to solve for x.
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  5. #5
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    thank you

    i got the answer thanks to you guys

    so ㅡㅡㅡ ㅡ ㅡ ㅡ
    l l
    x l l x
    l l
    l l
    ㅡ ㅡ ㅡ ㅡ ㅡ ㅡ
    100-2x


    (100-2x)x= 1200
    x^2-50x+600
    and then you do the quadratic formula.
    then you get the answers
    20, and 30
    then you plug it in
    FINAL ANSWERS
    30,40
    20, 60

    thank you!
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  6. #6
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    yes and i got it thank you!
    emm
    the answer is
    5 plus or minus radiacal 5 /2
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  7. #7
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    I hope my pen dimensions were not confusing, lightstevoo.

    My x was the side against the barn.
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  8. #8
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    Quote Originally Posted by lightstevoo View Post
    yes and i got it thank you!
    emm
    the answer is
    5 plus or minus radiacal 5 /2
    Don't forget to click Thanks on the posts that help you!
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