Let 1st integer be x and next consecutive be x+1
1/2•x + 1/5•(x+1) = 10
x/2 + x/5 + 1/5 = 10
-1/5 -1/5
x/2 + x/5 = 49/5
(x/2)•5/5 + (x/5)•2/2 = 49/5
5x/10 + 2x/10 = 49/5
7x/10 = 49/5
•10 •10
7x = 98
÷7 ÷7
x = 14 --> 1st integer
x+1 = 14+1 = 15 --> next consecutive integer
Answer:
16 feet
Step-by-step explanation:
As said in the problem statement, the angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent.
We also know that Sarah and the house are perpendicular to the ground.
So if we draw a triangle from the top of the house, to the mirror, to the bottom of the house, and another triangle from Sarah's eyes, to the mirror, to Sarah's feet, we get two triangles that have the same angles. Therefore, the triangles are similar, and we can write a proportion:
4 / 5 = h / 20
h = 16
The house is 16 feet tall.
According to google, the red marks mean those two lines are the same length. If that's the case, we know that x is the angle in both corners of the lower triangle. We also know that because the angle of a straight line is 180, that the top angle of the bottom triangle is 140, because it's divided into two parts, one of which is 40. That leaves 140 for the rest. Now we know that there are 180 degrees in a triangle so x=(180-140)/2 = x=20degrees.
The right angle in the left corner is 90 degrees. It is divided in two parts, the lower one of which we just found to be 20. So the other part must by 70deg.
So for the upper angle y, we have 180-70-40= y=70degrees
