Without solving the equation, determine the nature of the roots of x^2 - 2x - 8 = 0.

Consider the following equation -167 + 37 = 49 - 21p select the equation that has the same solution as the given equation. o a. p - 5 + ip = 7 - p ob. +55 + 12p = 5p + 16 c. 2 + 1.25p = -3.75p + 10 d. -14 + 6p = -9 - 6p reset next

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5: 2: 3. how many cups of pear juice should she use to make 20 cups of punch?