9) x= -7
10) x= 10
11) x= 5
12) x= 6
13) x= 4
14) x= -9
15) x= 3
16) x= 9
sorry it took so long! hope this helps!! :)
Answer: Using the proportion beteween the sides of the similar triangles, the distance between the endpoints of the beams P and Q is 3.2 inches.
Option a. 3.2 inches
Solution
PR=3.7 inches; CR=5.6 inches; AC=4.9 inches
As the two triangles QRP and ARC are similar, their sides must be proportionals, then:
PQ/AC=PR/CR=QR/AR
Replacing the given values in the proportion above:
PQ/(4.9 inches)=(3.7 inches)/(5.6 inches)=QR/AR
PQ/(4.9 inches)=3.7/5.6
Solving for PQ: Multiplying both sides of the equation by 4.9 inches:
(4.9 inches)[PQ/(4.9 inches)]=(4.9 inches)(3.7/5.6)
PQ=(4.9)(3.7)/5.6 inches
PQ=18.13/5.6 inches
PQ=3.2375 inches
Rounding to one decimal place:
PQ=3.2 inches
The sum of the 3 angles of a triangle is 180 °
the sum of the arc of a circle is 360°
⇒ the inscribed angle = the angle measure of the arc it intercepts/2
This can be easily figured out. Check to see what points are on the bottom and that is your answer.
B
Perimeter: P=24 ft
Lenght: L
Width: W
The length is 2 ft longer than the width:
(1) L= W+2 ft
Perimeter: P=2(W+L)
P=24 ft
2(W+L)=24 ft
Dividing both sides of the equation by 2:
2(W+L)/2 =(24 ft)/2
(2) W+L=12 ft
We have a system of 2 equations and 2 unkowns:
(1) L=W+2
(2) W+L=12
Using the method of substitution: Replacing L by W+2 in the second equation:
(2) W+L=12
W+(W+2)=12
W+W+2=12
2W+2=12
Solving foe W
2W+2-2=12-2
2W=10
Dividing both sides of the equation by 2:
2W/2=10/2
W=5
Replacing W by 5 in the first equation:
(1) L=W+2
L=5+2
L=7
Answers:
What is the width? 5 ft
What is the length? 7 ft
