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Dede

  • 2 years ago

The volume of a rectangular box is given by the formula v=LWH. The volume of the box is 495Cu. units. find the width and length. ( L=x+2, width=x, ht=5

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  1. Schrodinger
    • 2 years ago
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    Okay, let's put this into the form of an equation. Since l*w*h = 495, we can say:\[495=(x+2)(x)(5).\] By that, \[495=(5x ^{2}+10x)\] Now, just solve for x. Let's divide by 5 on both sides to eliminate the coefficient on the x^2. 495/5=99. \[99=x ^{2}+2x\] From here we factor to solve for x. Let's put it in the form of a quadratic, so: \[x ^{2}+2x-99=0.\] Do you know how to factor?

  2. Dede
    • 2 years ago
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    Not strong for this type

  3. Schrodinger
    • 2 years ago
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    Okay, so we'll factor this like any other quadratics. Quadratics are typically in this form:\[ax ^{2}+bx+c=0.\] That being said, one common method to factor a quadratic is to factor the value of the third term into two values that will equal the coefficient of the b term if they're added together. Can you solve this, Dede?

  4. Dede
    • 2 years ago
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    I'll try

  5. Dede
    • 2 years ago
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    Can u walk me through this?

  6. Schrodinger
    • 2 years ago
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    Sure. We need to factor 99 and find two factors that add to equal 2. Now tell me, what two factors add to equal 2?

  7. Dede
    • 2 years ago
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    1s

  8. Dede
    • 2 years ago
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    11 and 9

  9. Schrodinger
    • 2 years ago
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    Oops, what factors would equal -99?

  10. Dede
    • 2 years ago
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    -9 and 11

  11. Schrodinger
    • 2 years ago
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    Yup! From here, we can put these in the from of two sets of parentheses, like this: \[(x-9)(x+11)\]and set that equal to zero. Then, you solve each separate set of parentheses like such: \[(x-9)=0 ...x=9\] \[(x+11)=0...x=-11\] Now, we can only take one value of x, the positive value, do you understand why?

  12. Dede
    • 2 years ago
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    Yes cos it can't be a negative #

  13. Schrodinger
    • 2 years ago
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    Yep. So then you plug it into the original question and solve for the length and width: \[l=x+2...l=(9)+2\] \[w=x\]

  14. Dede
    • 2 years ago
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    width(x) equal to 9 and length x+2 =11

  15. Schrodinger
    • 2 years ago
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    Yep! Congratulations! Hope this helped. :)

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