proyaop

Hmmm, I will teach you how to do ratios.

If you see there are a specific ratio, and there is a certain quantity, divide the original ratio by the quantity.

The ratio of daisies to roses is 8:18. 4 daises would be half the ratio quantity, so the #of roses is half the ratio quantity of roses. 18/2 = 9.

Thus there are 9 roses.

The meaning of 'of' in math is the multiplication sign. Thus 60% of x is 22 would be: 0.6 * x = 22. Divide both sides by 0.6, you have 110/3 = x.

11% of 110/3 = 0.11*110/3. 12.1 / 3 = 121/30. 

11% of x = 121/30

:)

The ratio of cars to trucks is 14:10. Divide both sides of the ratio by 2, then the ratio would be 7 cars to 5 trucks (7:5). Since there are 5 trucks, the corresponding amount of cars would be 7.

Thus, there are 7 cars.

:)

f(f(x)) = 5 = f(x')

If x' >= -4, then 5 = x'^2 - 4; x' = 3.

If x' < -4, then 5 = 3x' + 1; x' = 4/3.

Case 1: f(x) = 3

If x >= -4, then 3 = x^2 - 4; x = sqrt(7).

If x < -4, then 3 = 3x + 1; x = 2/3.

Case 2: f(x) = 4/3

If x >= -4, then 4/3 = x^2 - 4; x = 4sqrt(3)/3.

If x < -4, then 4/3 = 3x + 1; x = 1/9.

Thus there are 4 values of x that work, and the values are above.

There is a much quicker way to do it than calculating it; try looking at how many options there are for the range of x (in this case there are 2: x >= -4, x < -4) then multiply by the #of 'f's (in this case 2: f(f(x))). 2 x 2 = 4. :)

Since there is no statement on who normally lies or not --- I will treat this as an IRL situation.

So E and B are saying it was the other person because E is defending himself, and B is the accusor because he said it BEFORE E. A first said that D broke it, and D was also defending himself. C didn't break it because noone accused him, and he said so himself so the probability of him breaking it was the least. 

If D was telling the truth, then he would've not only defended himself, but also put the blame on someone else. I think B is less suspicious than D, and is just blind or saw it wrong. 

Child D broke it (i think) 

Sorry guest, but you have it mixed up --- complementary is sum to 90 --- SUPPLEMENTARY is the term you are proposing to use.

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Substituting the values in, we have:

2x + 7 + 18 = 90

2x + 25 = 90

2x = 65

x = 32.5

Angle F = 72 degrees

Angle G = 18 degrees

:)

To find the value of 'x', we use 30-60-90 triangle ratios.

The hypotenuse of the triangle with base 1 is 2.

Thus the shortest length of the similar triangle with hypotenuse 'x', is 2. Multiplying by 2, we get:

x = 4