You decide to build a rectangular garden in your backyard. You’ve designated an area of 180m^2 for your

You decide to build a rectangular garden in your backyard. You've designated an area of 180m^2 for your garden. Due to the configuration of your backyard, the width of the garden must be 8 meters less than the length.

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  1. [tex]Length = 18m[/tex]

    [tex]Width = 10m[/tex]

    Step-by-step explanation:

    Given

    [tex]Area = 180m^2[/tex]

    [tex]Width = Length - 8[/tex]

    Required

    Determine the Length and the Width

    Represent Width with W and Length with L;

    So, we have:

    [tex]Area = L * W[/tex]

    [tex]Area = L * (L - 8)[/tex]

    [tex]180 = L * (L - 8)[/tex]

    [tex]180 = L^2 - 8L[/tex]

    [tex]L^2 - 8L - 180 = 0[/tex]

    Expand

    [tex]L^2 - 18L + 10L- 180 = 0[/tex]

    [tex]L(L - 18) + 10(L- 18) = 0[/tex]

    [tex](L + 10)(L- 18) = 0[/tex]

    Split

    [tex]L + 10 =0[/tex] or [tex]L - 18 = 0[/tex]

    [tex]L = -10[/tex] or [tex]L = 18[/tex]

    But length cant be negative:

    So,

    [tex]L = 18[/tex]

    Recall that:

    [tex]Width = Length - 8[/tex]

    [tex]W = 18 - 8[/tex]

    [tex]W = 10[/tex]

    Hence:

    [tex]Length = 18m[/tex]

    [tex]Width = 10m[/tex]

  2. The answer would be d i think but i’m for sure it is not a and c
    [tex]The vertex of this parabola is at (-2,1) .which of the following could be its equation a. x=4(y+1)^2[/tex]

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