Kathy is fencing in her yard that has an area of 800 square feet. her yard is in the shape of a rectangle where the length is 60 less than 5 times the width. find the length and width

The dimensions of the yard are W=20ft and L=40ft.

Step-by-step explanation:

Let be:

W: width of the yard.

L:length.

Now, we can write the equation of that relates length and width:

(Equation #1)

The area of the yard can be expressed as (using equation #1 into #2):

(Equation #2)

Since the Area of the yard is , then equation #2 turns into:

Now, we rearrange this equation:  

We can divide the equation by 5 :

We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since and . The equation factorised looks like this:

Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:

Therefore, the dimensions of the yard are W=20ft and L=40ft.

51-50

step-by-step explanation:

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)