CubeyThePenguin

head start = 28 feet

overall speed of the two = 4.5 ft/sec - 0.5 ft/sec = 4 ft/sec

It takes 28/4 = 7 seconds for the hare to catch up.

sum of roots = -b/a = 11/5

product of roots = c/a = 4/5

\(\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab} = \frac{\frac{11}{5}}{\frac{4}{5}} = \boxed{\frac{11}{4}}\)

You can split a 13-14-15 triangle into a 9-12-15 triangle and a 5-12-13 triangle, so the area is \(\frac{9 \cdot 12}{2} + \frac{5 \cdot 12}{2} = 84\).

angles in a triangle add up to 180 degrees

(4x - 16) + (6x - 1) + (4x - 13) = 180

14x - 30 = 180

14x = 210

x = 15

48 degrees

(9, -3) and (-5, -7)

midpoint: \((\frac{9-5}{2}, \frac{-3-7}{2}) = (2, -5)\)

slope: \(\frac{-7+3}{-5-9} = \frac{2}{7}\)

perpendicular bisector has a perpendicular slope and passes through the midpoint:

\(y+5 = \frac{2}{7}(x-2)\)

width = W

length = 5W - 6

perimeter = 2(W) + 2(5W - 6) = 96

2W + 10W - 12 = 96

12W = 108

W = 9

L = 5W - 6 = 39

Let the number of Skittles of each color be a, b, c, d, and e. We have 12 skittles in total:

a + b + c + d + e = 12

Note that we also need at least one of each color, so we can substitute a' = a + 1, b' = b + 1, and so on, to ensure that each color has at least one Skittle.

a' + b' + c' + d' + e' = 7

This is an example of stars and bars, and the ways to choose is (7+5-1) choose (7-1) = 462.

write in vertex form first: y = a(x + 1)^2 + 7

The coefficient "a" is there because knowing the vertex isn't enough to determine the equation. We can plug in the point (0, 10):

10 = a + 7

a = 3

So, the equation is y = 3(x+1)^2 + 7.

sum of roots = -b/a = -10/2 = -5

product of roots = c/a = 5/2

(2a - 3)(4b - 6) = 8ab - 12a - 12b + 18

= 8(5/2) - 12(-5) + 18

= 98

sum of roots = -b/a = m/2 = -6

product of roots = c/a = n/2 = 10

m + n = -12 + 20 = 8