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anonymous

  • 4 years ago

Lenght of rectangle is 7 cm less than 4 times its width. Area is 36, find dimensions. Is this set up right? : 4x-7=36

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  1. asnaseer
    • 4 years ago
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    not quite - the question says that the length is 7cm less than 4 times its width, so if we call the length y and the width x, then you can write: y = 4x - 7 It also says the area is 36, so we know the area of a rectangle is length times width, therefore: xy = 36 Now you have two equations with two unknowns so you should be able to solve this to find x and y.

  2. anonymous
    • 4 years ago
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    What do you mean by that? How can i set it up to solve?

  3. asnaseer
    • 4 years ago
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    substitute the expression for y from the first equation into the second equation. that will give you a quadratic equation in x to solve.

  4. anonymous
    • 4 years ago
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    ok be right back.. :)

  5. anonymous
    • 4 years ago
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    is answer 165?

  6. asnaseer
    • 4 years ago
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    the question was asking for the dimensions of the rectangle - so you need an answer for x and y.

  7. anonymous
    • 4 years ago
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    ok im back

  8. asnaseer
    • 4 years ago
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    so how did you get 165?

  9. anonymous
    • 4 years ago
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    i put it into the top equation the area

  10. anonymous
    • 4 years ago
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    The length of a rectanlge is 7 cm less than 4 times its width. Its area is 36, find dimensions

  11. anonymous
    • 4 years ago
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    I put it down here to make it easier for you

  12. asnaseer
    • 4 years ago
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    we have two equations:\[y=4x-7\tag{a}\]and:\[xy=36\tag{b}\]if we substitute the expression for y from equation (a) into equation (b) we get:\[x(4x-7)=36\]\[4x^2-7x=36\]\[4x^2-7x-36=0\]this is a quadratic equation which you should be able to factor (or use the quadratic equation formula) to find the two possible answers for x.

  13. anonymous
    • 4 years ago
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    do i use bottom equation to solve now :D and two ( ) are my answer? :D

  14. asnaseer
    • 4 years ago
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    you need to solve:\[4x^2-7x-36=0\]this will give you two possible answers for x. one will be a positive value and the other will be a negative value. since a rectangle cannot have a negative length you can reject the negative solution. you will therefore be left with one answer for x. plug this value of x back into equation (a) above to find the corresponding value for y. that will then give you the dimensions of the rectangle.

  15. anonymous
    • 4 years ago
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    4 and -9/4? :/

  16. asnaseer
    • 4 years ago
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    correct values for x: now you can reject the negative value as I stated above.

  17. anonymous
    • 4 years ago
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    so i take out negative so its only 9/4

  18. anonymous
    • 4 years ago
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    is the answer 4 and 9?

  19. asnaseer
    • 4 years ago
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    no. the quadratic equation gave you two possible solutions for x. one of these was x=4 and the other was x=-9/4. since a rectangle cannot have a negative length, you can reject the solution x=-9/4. you are therefore left with x=4 as the only valid solution for the width of the rectangle. plug this value of x into equation (a) above to get the correct valid value for the length y of the rectangle.

  20. anonymous
    • 4 years ago
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    I think i understand now but can you give me the answer? :( I wont ask again, its just this stupid program im using keeps knocking me off and giving me new questions, the server is freaking out and if i leave it sitting for awhile trying to figure it out it makes me start over, which is unfair

  21. asnaseer
    • 4 years ago
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    the last step is very easy - you should be able to calculate it yourself.

  22. anonymous
    • 4 years ago
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    what do i substitute 4 into again?

  23. asnaseer
    • 4 years ago
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    equation (a) above

  24. asnaseer
    • 4 years ago
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    substitute x=4 into: y = 4x - 7

  25. anonymous
    • 4 years ago
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    so its y=4(4)-7? gets y

  26. asnaseer
    • 4 years ago
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    yes

  27. anonymous
    • 4 years ago
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    answer is 9?

  28. anonymous
    • 4 years ago
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    4 then 9?

  29. asnaseer
    • 4 years ago
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    yes, so length of rectangle is 9 and width is 4

  30. anonymous
    • 4 years ago
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    thank you :)

  31. asnaseer
    • 4 years ago
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    yw

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