Answer:
For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.
Step-by-step explanation:
Answer:
80.64
Step-by-step explanation:
12.6*6.4=80.64
Step-by-step explanation: Notice that the two equations in this problem have the same slope of -1/4 but different y-intercepts.
When lines have the same slopes, they are parallel.
Parallel lines never meet/intersect so there is no solution.
3:5=m:60
m= 36
1. B)36
22in30 min
22+22=44
44in 1hr
44x3=132 in 3hr
2. D)132
Answer:
-336/527
Step-by-step explanation:
Trig identities are involved.
tan(2x) = 2tan(x)/(1 -tan(x)²)
Using tan = sin/cos, we can write this in terms of sine and cosine as ...
tan(2x) = (2sin(x)/cos(x))/(1 -sin(x)²/cos(x)²) = 2sin(x)cos(x)/(cos(x)² -sin(x)²)
= 2sin(x)cos(x)/(1 -2sin(x)²)
Now, the cosine can be found from ...
cos(x) = √(1 -sin(x)²)
for sin(θ) = 24/25, cos(θ) = √(1 -(24/25)²) = 7/25 . . . . 1st quadrant angle
Filling in the values in the above identity, we have ...
tan(2θ) = 2(24/25)(7/25)/(1 -2(24/25)²) = 336/-527
tan(2θ) = -336/527
_____
You can use a calculator or estimate that the angle for sin(θ) = 24/25 will be greater than 67.5°, so double the angle will be greater than 135°. (θ ≈ 74°) This means ...
- 2θ > 135°, so the magnitude of tan(2θ) will be less than 1
- 2θ is in the 2nd quadrant, so the sign of tan(2θ) will be negative
These observations will help you choose the correct answer without any further math.
