k = 12
cancel out the r on both sides
then divide -144 by -12.
you get 12.
Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.
Answer:
Dale live 315 miles from the mountains
Step-by-step explanation:
Let y be the speed of Dale to the mountains
Time taken by Dale to the mountains=7 hrs
Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1
Time taken by Dale back home = 5hours
Since it speed increased by 18 miles per hour back home it speed = y+18
So distance traveled home =speed × time = (y+18)5 ...... eqn 2
Since distance cover is same in both the eqn 1 and eqn 2.
Eqn 1 = eqn 2
7y = (y+18)5
7y = 5y + 90
7y - 5y = 90 (collection like terms)
2y = 90
Y = 45
Substitute for y in eqn 1 to get distance away from mountain
= 7y eqn 1
= 7×45
= 315 miles.
∴ Dale leave 315 miles from the mountains
Answer:
∠F ≈ 53°
General Formulas and Concepts:
<u>Trigonometry</u>
- sin∅ = opposite over hypotenuse
- sin inverse evaluates "backward" to find the measure angle
Step-by-step explanation:
<u>Step 1: Define</u>
Looking at ∠F
opposite leg of ∠F = ED = 8
hypotenuse = FE = 10
<u>Step 2: Find m∠F</u>
- Substitute: sin∠F = 8/10
- Simplify: sin∠F = 4/5
- Take sin inverse: ∠F = sin⁻¹(4/5)
- Evaluate: ∠F = 53.1301°
- Round: ∠F ≈ 53°
If 24 students went on a field trip, and 24 students represented eight tenths of the class, then

.
First, multiply by 10 on both sides.
240 = 8x
Divide by 8 on both sides.
x = 30.
The class has 30 students in all.
This is, however, only the equation way to solve.
Answer:
65.75
Step-by-step explanation:
All you do is divide.