Kromy

has multiple answers (2^3 * 3 works, but 2 * 3 * 5 also works). 

40 = 5 * 2^3 

6 = 2 * 3

75 = 5 ^2 * 3

12 = 2^2 * 3

We have three 5s, and definitely more than three 2s. Thus we have 3 terminal zeros. (remember, 5 * 2 = 10). 

Rewrite the quadratic as \( x^2 -8x + (8 + c)\). This quadratic forms a "U-shape." Thus, we want the vertex to have a y coordinate of 1. The vertex occurs at  \(x =\frac{-b}{2a}\) for the quadratic ax^2 + bx + c. Plugging in our values, we have \(\frac{8}{2} = 4\). This is the x-coordinate to the vertex of the parabola. Plugging in this number and setting the equation equal to 1, we have 16 - 32 + 8 + C = 1. Therefore, C = 9 generates a vertex of (4,1). Any higher C would generate a vertex with a y coordinate greater than 1. Thus the largest real number C would be 9. 

2028 is a leap year, so February has 29 days. 2.5 minutes for 100 onions means 5 minutes for 200 and 1 hour for 2400. There are 24 hours in a day, so each day he dices 57600 onions. So in the month of february in 2028, he will dice 29 * 57600 = 1670400 onions. That's a lot of onions!

bro just draw the triangle and use pythagorean theorem 

Read my previous answer to your previous question. You need BC to find BZ. Again, use Angle Bisector Theorem. 

Hint: Google Angle Bisector Theorem. Now try to apply it on BY. What do you get? Should be a straight-forward solution. 

An additional Hint: You need to apply Angle Bisector Theorem not once, but twice.