20) If the area of a rectangular playground is p^2 -6p - 7 square feet, what is the perimeter of the
playground?

Explanation:

Write an equation to solve the problem.

Area of rectangle = L(w)

Assuming that the width measures x meters, the length measures x + 5 meters.

500 = x(x + 5)

500 =

x

2

+ 5x

0 =

x

2

+ 5x - 500

As you may already know, a trinomial of the form

a

x

2

+ bx + c, a = 1, you must find 2 numbers that multiply to c and that add to b. Two numbers that multiply to -500 and add to +5 are +25 and -20

0 = (x + 25)(x - 20)

x = -25 and 20

Since a negative length is impossible, the width mesures 20 meters and the length measures 25 meters.

Practice exercises:

A rectangle has a perimeter of 90 meters. Find the maximum area.

The area of a right triangle is 120

m

2

. The base measures half the sum of the height and one. Find the perimeter.

Find the area and perimeter of a right triangle the has a height that is 2 more than the double of the width and that has a hypotenuse that measures

√

68

meters.

Good luck!

Step-by-step explanation:

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!