Question

Hello!

Answer 1

This is simple algebra :)

First, we can write the question as an algebraic equation.

Given that Doug spent 40 more hours than Laura, we can represent Laura as (x) and Doug as (x+40).

"Doug and Laura spent a combined 250 hours." So we can write this as

(x) + (x+40) = 250

Now simplify:

2x + 40 = 250

Solve x by subtracting 40 from both sides of the equation:

2x = 210

Therefore:

x = 210/2

= 105

So Laura (x) spent 105 hours!

Answer 2

Answer:

Step-by-step explanation:

Left Frame

f(x) = x^2 - 6x + 8

f(x) = (x - 2)(x - 4)

The question is a fancy way of asking you to represent the quadratic formula in factored form.

Second from left Frame

This is a problem just to see if you really do know what f(g(3)) equals.

You are not asked to figure out what the function is exactly -- just what it does.

Start with g(3) = 2. What you do is just put that in the brackets for g(3) in the combined function f(g(3)) = f(2) because g(3) =2.

f(2) = 3. That's given. So the final answer is f(2) = 3

Center Frame

x^2 + y^2 + 4x- 2y = - 1  

You have to complete the square twice.

( x^2 + 4x + (4/2)^2 ) = (x + 2)^2

(y^2 - 2y + (-2/2)^2 ) = (y - 1)^2

So The next thing you have to realize is that you have added 4 on from the top completed Square and 1 from the bottom completed square.

Ultimately it will look like this.

(x + 2)^2 + (y - 1)^2 = - 1 + 4 + 1 = 4

That 4 on the right = r^2

To find r, you need to take the square root of 4

sqrt 4 = 2

radius = 2

Second from the Right

What this question is saying is that when x = 3, y = 6. Since in loose terms y and f(x) mean the same thing, what you get is

3(3)^2 -b*3 + 12 = 6

27 - 3b + 12 = 6

39 - 3b = 6              Subtract 39 from both sides.

-3b = 6 - 39             Combine

-3b = -33                  Divide by - 3

-3b/-3 = -33/-3         Combine

b = 11

Right Frame

Let Doug = D

Let Laura = L

The two equations are

D + L = 250

D = L + 40                Put the second equation into the first.

L+40 + L = 250        Combine on the left

2L + 40 = 250          Subtract 40

2L = 250 - 40           Combine

2L = 210                    Divide by 2

L = 210/2                   Combine

L = 105

So if L = 105 Doug will be 40 more

D= 105 + 40

D =  145