Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
Answer:
50
Step-by-step explanation:
180 seconds is 3 minutes. If you divide 156 by 3, you will get 52. If you are looking for 2 minutes, you have to multiply 52 by 2. The answer is 104 revolutions in 2 minutes.
Answer:
vertex: (2,-18)
Step-by-step explanation:
y = ax² + bx + c
(-1,0) : a - b + c = 0 ...(1)
(5,0) : 25a +5b +c = 0 ...(2)
(0,-10): 0a + 0b + c = -10 c=-10
(1) x5: 5a - 5b + 5c = 0 ...(3)
(2)+(3): 30a + 6c = 0 30a = -6c = 60 a = 2
(1): 2 - b -10 = 0 b = -8
Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18
equation: y = a(x-h)²+k (h,k): vertex
vertex: (2,-18)
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