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
This means that 1/12 of all the students surveyed wanted more seafood and 1/3 wanted more fruits and veggies. The least common multiple of 3 and 12 (or the LCD of the two fractions) would be 12.