CPhill

Translate into an algebraic equation and solve.  Find three consecutive odd integers such that the difference between four times the first integer and twice the largest integer is two. 

Let the integers be 2n+ 1, 2n + 3 and 2n +5

So

4(2n + 1) - 2(2n + 5)  = 2    simplify

8n + 4  - 4n -10  = 2

4n - 6  = 2    add 6 to both sides

4n = 8     divide both sides by 4

n = 2

So....the first integer is 2(2)+ 1 = 5    and the last integer  is 2(2) + 5 = 9

Take the goat across first

Come back and take the cabbage across.......take the goat back

Leave the goat and take the wolf over

Come back and take the goat over

That's the way math works sometimes......If you don't see it....you don't see it......then.......when you do see it....you wonder why you didn't see it in the first place  !!!!  LOL!!!

(4^(3/4))^(2/3)/(4^-(5/3))^(3/2)

Step by step

The numerator is  (4^(3/4))^(2/3)  = 4^(1/2)  = 2     ...so....

2 / (4^-(5/3))^(3/2) = 2 / 4^(-5/2)   = 2 * 4^(5/2)  = 2 * [4^(1/2)] ^5  = 2 *[2]^5  = 2 * 32  = 64

(The calculator is definitely a victim of "rounding," here......!!!)

Correct, Angelica   .....x > 54....and your graph is correct....

Well ....if she spent 2/3rds of her allowance, she must have 1/3 left...

So just multiply (1/3) x 24 to get your answer...

What's giving you trouble??  calculating the slope??.....or simplifying the equation??......something else??

Let N be the number of workouts

So we want to find when....

3N + 98  = 10N    subtract 3N from both sides

98 = 7N    divide by 7 on both sides

14 = N

So...they will pay the same after 14 workouts.....

Correct-a -mundo !!!!!!

We'll use y = mx + b

First, we need to find the slope, (m)........this is defined as ......the change in y /  change in x

Look at  (4, 5) and (-8, -4)

Note that, from the first point to the second, y changes by -9

And x changes by  -12

So.....the slope is    -9 / -12  = -3 / -4   = 3/4  = "m"

Now using either one of the points - i'll use the first one -we can substitute for y, m and x in y = mx + b to find "b"....so we have

5= (3/4)(4) + b  simplify

5= 3 + b    subtract 3 from both sides

b = 2

So our equation is

y = (3/4)x + 2

Check to see that the second point "works" in this equation.....just fill in for "x" and "y'

Does that help??