I am studying for my final and I have several problems that I need help understanding. Here goes.
s = 1/2gt^2 solve for g
Tom earns $6,000 less than 2 times as much as Rachel. If their 2 incomes come to $60,000 how much does each make?
A train leaves town A for town B traveling at 40 mph. At the same time a second train leaves town B for town A at 50 mph. If the two towns are 720 miles apart how long will it take for the 2 trains to meet?
3/2x - 9 = 1/2x + 7 solve for x
Last one
v = kt/p solve for k
How do these get worked out? Please help.
Here goes.
s = 1/2gt^2 solve for g
**** multiply both sides by 2, divide both sides by t^2
Tom earns $6,000 less than 2 times as much as Rachel. If their 2 incomes come to $60,000 how much does each make?
2R-6000=T
R+T=60000
A train leaves town A for town B traveling at 40 mph. At the same time a second train leaves town B for town A at 50 mph. If the two towns are 720 miles apart how long will it take for the 2 trains to meet?
the distance both travel (added) is 720miles.
720=40T+50T solve for T
3/2x - 9 = 1/2x + 7 solve for x
subtract 1/2 x from each side, add 9 to each side.
Last one
v = kt/p solve for k multiply both sides by p/k
Sure! I'll explain how to solve each of these problems step by step. Let's start with the first one:
1. To solve for g in the equation s = (1/2)gt^2, you want to isolate g on one side of the equation.
- Begin by multiplying both sides of the equation by 2 to get rid of the fraction:
2s = gt^2
- Next, divide both sides of the equation by t^2 to isolate g:
g = 2s / t^2
So, g is equal to 2s divided by t^2.
Moving on to the second problem:
2. Let's determine the incomes of Tom and Rachel. We'll set up an equation using the given information.
- Let's assume Rachel's income is x dollars.
- According to the problem, Tom earns $6,000 less than twice Rachel's income, so Tom's income can be represented as 2x - 6000.
- The sum of their incomes is $60,000, so we set up the equation:
x + (2x - 6000) = 60000
- Combine like terms on the left side of the equation:
3x - 6000 = 60000
- Add 6000 to both sides to isolate the term with x:
3x = 66000
- Divide both sides by 3 to solve for x:
x = 66000 / 3
- Simplify:
x = 22000
- Now substitute the value of x back into the expressions for Tom and Rachel's incomes:
Tom's income = 2x - 6000 = 2(22000) - 6000 = 44000 - 6000 = 38000
Rachel's income = x = 22000
So, Tom makes $38,000 and Rachel makes $22,000.
Now let's move on to the next question:
3. This problem involves two moving objects. Since they are moving towards each other, their speeds are added together to find their combined speed. We can use the formula:
- Time = Distance / Speed
- The two trains are traveling towards each other, so their combined speed is the sum of their individual speeds:
Combined speed = 40 mph + 50 mph = 90 mph
- The total distance between the two towns is 720 miles, so we can plug these values into the formula to find the time:
Time = Distance / Speed = 720 miles / 90 mph = 8 hours
Therefore, it will take the two trains 8 hours to meet.
Now let's move on to the fourth problem:
4. To solve the equation (3/2)x - 9 = (1/2)x + 7 for x, we want to isolate the term with x on one side of the equation.
- Begin by subtracting (1/2)x from both sides:
(3/2)x - (1/2)x - 9 = 7
- Combine like terms on the left side of the equation:
x - 9 = 7
- Now, add 9 to both sides to isolate x:
x - 9 + 9 = 7 + 9
- Simplify:
x = 16
So, x is equal to 16.
Finally, let's look at the last problem:
5. To solve for k in the equation v = kt/p, you want to isolate k on one side of the equation.
- Start by multiplying both sides of the equation by p:
pv = kt
- Next, divide both sides of the equation by t to isolate k:
k = pv / t
Thus, k is equal to pv divided by t.
I hope these explanations help! Let me know if you have any further questions.