Answer:
m∠RPQ = 8°
Step-by-step explanation:
m∠QRS = 4x - 15
m∠RPQ = x + 1
m∠PQR = x - 2
m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS
m∠QRS = m∠RPQ + m∠PQR {Exterior angle property of triangle}
4x - 15 = x +1 + x - 2
4x - 15 = x + x + 1-2 {Combine like terms}
4x - 15 = 2x - 1 {Subtract 2x from both sides}
4x - 2x - 15 = - 1
2x - 15 = - 1 {Add 15 to both sides}
2x = -1 + 15
2x = 14 {Divide both sides by 2}
x = 14/2
x = 7
m∠RPQ = x + 1 = 7 + 1 = 8°
Average speed for the entire trip, both ways, is
(Total distance) divided by (total time) .
We don't know the distance from his house to the gift store,
and we don't know how long it took him to get back.
We'll need to calculate these.
-- On the trip TO the store, it took him 50 minutes, at 6 mph.
-- 50 minutes is 5/6 of an hour.
-- Traveling at 6 mph for 5/6 of an hour, he covered 5 miles.
-- The gift store is 5 miles from his house.
-- The total trip both ways was 10 miles.
-- On the way BACK home from the store, he moved at 12 mph.
-- Going 5 miles at 12 mph, it takes (5/12 hour) = 25 minutes.
Now we have everything we need.
Distance:
Going: 5 miles
Returning: 5 miles
Total 10 miles
Time:
Going: 50 minutes
Returning: 25 minutes
Total: 75 minutes = 1.25 hours
Average speed for the whole trip =
(total distance) / (total time)
= (10 miles) / (1.25 hours)
= (10 / 1.25) miles/hours
= 8 miles per hour
The momentum formula is
p = m*v
where,
p = momentum (not sure why p is chosen but many physics books tend to pick this letter)
m = mass in kilograms
v = velocity in meters per second
So let's calculate the momentum for the 4500 kg vehicle
p = m*v
p = 4500*85
p = 382500 kg m/s
And let's do the same for the 3700 kg vehicle
p = m*v
p = 3700*85
p = 314500 kg m/s
Answer:
7
Step-by-step explanation:
1. Use sine law to solve
3/sin35 = x/sin55
3sin55/sin35 = 7
Answer:
1) No
2) No
3)Yes
4)No
Step-by-step explanation:
Distributive property: a(b + c) =a*b + a*c
1) 4(5c + 3) = (4*5c) + 4*3
= 20c + 12
NO
2) 2(8f - 5) = (2*8f) - (2*5)
= 16f - 10
NO
3) 3(4g + 7) = (3*4g) + (3*7)
= 12g + 21
YES
4) 6(4j - 6) =(6 * 4j) - (6*6)
= 24j - 36
NO
