A)
To be similar triangles have to have equal angles
triangle ZDB'
1)angle Z=90 degrees
triangle B'CQ
1) angle C 90 degrees
angle A'B'Q=90
DB'Z+A'B'Q+CB'Q=180, straight angle
DB'Z+90+CB'Q=180
DB'Z+CB'Q=90
triangle ZDB'
DZB'+DB'Z=180-90=90
DB'Z+CB'Q=90
DZB'+DB'Z=90
DB'Z+CB'Q=DZB'+DB'Z
2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )
3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.
so this triangles are similar by tree angles
b)
B'C:B'D=3:4
B'D:DZ=3:2
CQ-?
DC=AB=21
DC=B'C+B'D (3+4= 7 parts)
21/7=3
B'C=3*3=9
B'D=3*4=12
B'D:DZ=3:2
12:DZ=3:2
DZ=12*2/3=8
B'D:DZ=CQ:B'C
3:2=CQ:9
CQ=3*9/2=27/2
c)
BC=BQ+QC=B'Q+QC
BQ' can be found by pythagorean theorem
Answer:
60.22in^2.
Step-by-step explanation:
First, find the area of the rectangle. 14.1x7=98.7.
Then, we need to find the area of the circle and subtract it from the area of the rectangle.
The area of the circle is pi*r^2. so, pi*3.5^2 is about 38.48. (The radius is half of the diameter, so the radius would be 3.5).
Since there are two halves of the circle, we can just subtract 38.48 from 98.7 so get the area of the shaded region. So, the area of the yellow area is 60.22in^2.
Answer:
B
Step-by-step explanation:
A proportional relationship is represented by linear function with its linear parameter "b" equal to zero. Since b is equal to zero, the line passes through the origin and the function/relation is proportional.
To verify that we divide the y coordinate over the x coordinate we obtain a constant called k, which is the slope.
For instance:
According to this function we can easily check a proportional relationship among its points:
49.5/ 5.5
= 9 minutes to run one mile
