Mike wants to put 150 square feet of artificial turf in his front yard. This is the maximum area of artificial turf allowed by his homeowners association. He wants to have a rectangular area
of turf with length one foot less than 3 times the width. Find the length and width. Round to
the nearest tenth of a foot.

Step-by-step explanation:

Area of the rectangular area = Length * width

A = LW 1

If he wants to have a rectangular area  of turf with length one foot less than 3 times the width, then

L = 3W - 1 2

Substitute 2 into 1

A = (2W-1)W

A = 2W^2 - W

Since area = 150sq.ft

150 = 2W^2 - W

2W^2 - W - 150 = 0

Factorize

2W^2 - W - 150 = 0

W = 1±√1+4(300)/2(2)

W =  1±√1201/2(2)

W = 1±34.655/4

W = 35.655/4

W = 8.91375

W = 8.9 (to nearest tenth)

Get the length

L = A/W

L = 150/8.9

L = 16.85

L = 16.6ft

Hence the length is 16.6ft and the width is 8.9ft

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!