Answer:
520
Step-by-step explanation:
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Answer:
A
Step-by-step explanation:
It just makes the most sense
Step-by-step explanation:
<h3>
Answer: 250</h3>
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Explanation:
x = speed of the plane in mph
x-180 = speed of the car, since its 180 mph slower than the plane
For the plane, we can form the equation
distance = rate*time
d = r*t
500 = xt
t = 500/x
For the car, we can say,
d = rt
140 = (x-180)t
140 = (x-180)*(500/x)
140x = 500(x-180)
140x = 500x - 90,000
140x - 500x = -90,000
-360x = -90,000
x = (-90,000)/(-360)
x = 250
The speed of the plane is 250 mph
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Extra info:
The car's speed is x-180 = 250-180 = 70 mph
It takes the plane t = d/r = 500/250 = 2 hours and it takes the car t = d/r = 140/70 = 2 hours. Both vehicles travel for 2 hours, which helps to confirm the answer.
Answer:
The measure of ∠GKH is 27°
Step-by-step explanation:
- In the isosceles triangle, the base angles are equal in measures
- The measure of an exterior angle at a vertex of a triangle equals the sum of the measures of two opposite interior angles
In Δ HJK
∵ HJ = JK
→ That means the triangle is isosceles
∴ Δ HJK is an isosceles triangle
∵ ∠JHK and ∠JKH are base angles
→ By using the first rule above
∴ m∠JHK = m∠JKH
∵ m∠HJK = 70°
∵ m∠JHK + m∠JKH + m∠HJK = 180° ⇒ interior angles of a triangle
∴ m∠JHK + m∠JKH + 70 =180
→ Subtract 70 from both sides
∴ m∠JHK + m∠JKH = 110
→ Divide their sum by 2 to find the measure of each one
∴ m∠JHK = m∠JKH = 110 ÷ 2 = 55°
∵ ∠JHK is an exterior angle of ΔGHK at vertex H
∵ ∠HGK and ∠GKH are the opposite interior angles to ∠JHK
→ By using the 2nd rule above
∴ m∠JHK = m∠HGK + m∠GKH
∵ m∠JHK = 55°
∵ m∠HGK = 28°
∴ 55 = 28 + m∠GKH
→ Subtract 28 from both sides
∴ 27° = m∠GKH
∴ The measure of ∠GKH is 27°
