Yes - they have to be similar. Since they are using the same line as the hypotenuse, the ratio of the other two sides are in the same ratio (ie, the slope of the line), the 3 inner angles will be the same. Thus, the triangles will be similar.
The answer would be:
C. 144in2
hope that helped
32
The absolute value takes the distance from zero, it doesn’t matter weather it is positive or negatively
Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
Answer:
SOLUTION STEPS
6
8
5
+−6
3
1
Multiply 6 and 8 to get 48.
8
48+5
−
3
6×3+1
Add 48 and 5 to get 53.
8
53
−
3
6×3+1
Multiply 6 and 3 to get 18.
8
53
−
3
18+1
Add 18 and 1 to get 19.
8
53
−
3
19
Least common multiple of 8 and 3 is 24. Convert
8
53
and
3
19
to fractions with denominator 24.
24
159
−
24
152
Since
24
159
and
24
152
have the same denominator, subtract them by subtracting their numerators.
24
159−152
Subtract 152 from 159 to get 7.
24
7
Step-by-step explanation:
