catmg

f(x) = 4

The first case, -x + 3, which would be x = -1. 

This works since -1 =< 0. 

The second case, 2x - 5, x = 4.5. 

This works since 4.5 > 0. 

f(x) = -1

The first case -x + 3, x = 2. 

However this does not work since 2 is not less than or equal to 0. 

The second case 2x - 5, x = 2. 

This works since 2 > 0. 

f(f(2)) = 4

f(x) = 4.5

The first case -x + 3, x = -1.5.

This works since -1.5 =< 0

The second case 2x - 5, x = 9.5/2. 

Thiw works since 9.5/2 > 0. 

f(f(-1.5)) = 4

f(f(4.75)) = 4

So we have 3 cases.

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Hello, good luck on your study plan. :))

A tip, find a friend to study with, you're less likely to get distracted if you know that someone is doing it with you. 

As for your question, the best way is to plug in -b/(2a) into x. 

For example, if I have the parabola x^2 + 8x + 16, you already know the x coordinate is -4. (-b/(2a))

Knowing the x, we can plug that in to find the y. 

(-4)^2 + 8(-4) + 16 = 0

So our y coordinate is 0. 

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1/a^2 + 1/b^2 = (a^2 + b^2)/(a^2b^2)

Using vietas, ab = 4/5, a + b = 11/5. 

Can you do it from here?

Remember, a^2 + b^2 = (a+b)^2 - 2ab

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x^2 + 8x + 4 will have the same roots as 2(x^2 + 8x + 4).

2(x^2 + 8x + 4) = 2x^2 + 16x + 8

2 + 8 = 10

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w = weight of 1 cup

b = weight of empty bottle

2w + b = 360

5w + b = 600

Can you solve it from here?

Hint: start by subtracting the 2 equations. 

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3, 5, 9 is not a valid triangle since 3 + 5 < 9

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(2/3)/2 = 1/3

She only needs 1/3 cups of flour. 

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The table isn't showing up, but the theoretical probability of spinning a 5 is 1/10*100 = 10.  

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I'm sorry, but is this a problem on the map test?

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Nice. :))

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