*not multiple choice*

u^-3 = 1/125

y - 1 = 4y - 2/3 * not sure how to do
this

what is the y intercept of the line?
y= -3x - 5 * my answer is 5

when 40 is added to the number miles she ran last week..the result is the same as adding 10 to 4 times the number she ran last week. * not sure how to do this, because I have to find the miles she ran last week.

what is the slope of the line 4y - 6x + 12 = 0 in simplest form? * not sure how to do this

Answer this Question

1.

u^-3 = 1/125
1/u^3 = 1/125
u^3 = 125
u = 5

2.
y-1 = 4y - 2/3
each term times 3
3y - 3 = 12y - 2
-9y = 1
y = -1/9

3. your are right

4.
number of miles last week --- x

x+40 = 4x + 10
-3x = -30
x = 10
She ran 10 miles last week

5. change it into the form y = mx + b
(takes 2 steps)

4y - 6x + 12 = 0
4y = 6x - 12
y = (6/4) - 12/4
y = (3/2)x - 3

To solve the equations and answer the questions, I'll explain the step-by-step process for each one:

1. Solve u^-3 = 1/125:
To solve this equation, we can rewrite it as u^-3 = (1/5)^3 since 1/125 can be simplified to 1/5^3. We know that when the base and the exponent have the same value, it is equivalent to saying that u = the base. Therefore, u = 1/5.

2. Solve y - 1 = 4y - 2/3:
To solve this equation, we need to isolate the variable y. First, distribute the -2/3 to get y - 1 = 4y - 2/3. Then, rearrange the equation by moving all the terms containing y to one side: y - 4y = -2/3 + 1. Simplify the equation: -3y = -2/3 + 3/3, which can be written as -3y = 1/3. Finally, divide both sides by -3 to solve for y: y = (1/3) / -3, which simplifies to y = -1/9.

3. Find the y-intercept of the line y = -3x - 5:
The y-intercept is the value of y when x is equal to zero. Therefore, substitute x = 0 into the equation and solve for y: y = -3(0) - 5, which simplifies to y = -5. Hence, the y-intercept is -5.

4. Solve the equation "when 40 is added to the number miles she ran last week, the result is the same as adding 10 to 4 times the number she ran last week":
Let's assume the number of miles she ran last week is represented by 'm'. The equation can be written as m + 40 = 4m + 10. To solve this equation, subtract m from both sides to get 40 = 3m + 10. Next, subtract 10 from both sides to get 30 = 3m. Finally, divide both sides by 3 to solve for m, which gives us m = 10. Therefore, she ran 10 miles last week.

5. Find the slope of the line 4y - 6x + 12 = 0:
To find the slope, we need to rearrange the equation into the slope-intercept form (y = mx + b), where 'm' represents the slope. Firstly, isolate the 'y' term: 4y = 6x - 12. Then, divide both sides by 4 to get y = (6/4)x - 3, which simplifies to y = (3/2)x - 3. Now, we can identify that the slope 'm' is equal to 3/2. Hence, the slope of the line is 3/2.

Please let me know if there's anything else I can assist you with!