Paul walks 25 feet away from his house and places a mirror on the ground. he backs 5 feet away from the mirror so that he can see the tip of the roof. paul's eyes are 6 feet above the ground. paul and the house are both perpendicular to the ground. the angles between the top of the house, the mirror, and the ground and between paul's eyes, the mirror, and the ground are congruent as shown in the image below:
image depicts a mirror on the ground between a person and a house. the mirror is 5 feet away from the person and 25 feet away from the house.
what is the height of the house? show your work and explain your reasoning in complete sentences.

you have 2 similar triangles., the triangle formed from the mirror and paul and the triangle formed by the mirror and the house.

all the angles from one triangle are congruent to all the angles from the other triangle, which make the sides proportional.

the ratio of the sides for paul is 6/5

the ratio of the sides for the house is   x/25, where x is the height of the house.

now set the equations to equal each other and solve for x:

6/5 = x/25

cross multiply : (6*25) = (5*x)

simplify:

150 = 5x

divide both sides   by 5 to solve for x:

x = 150 / 5

x = 30 feet.

the house is 30 feet high.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a