Prove that the roots of the equation X^2 - 2px + p^2 - q^2 = 0 where p and q are constants, are real.

Maggie is making a necklace using 14 inch string and identical beads. Maggie has placed 12 beads next to each other starting at the left end of the string as shown in the figure. The 12 beads fill 3 inches of the string.

Katie is working on a math worksheet with 50 problem. She has completed 20 problems in 25 minutes. If she continues at the same place, what will her total time be for her to complete the worksheet?

How many lines of reflective symmetry does an equilateral triangle have

Solve for x. -2 (5x+4) - 3x+3=-18

Use the diagram below to first identify the angle pair and then use the angle relationship to find the value of x. 10207 X+159 Part A: Identify the angle pair. Part B: Find the vale of x.

A tree is 8 feet tall when planted. after one year, its height has increased by one-sixth of its original height. at the end of the second year, its height is 37.5% greater than its original height.

The area of a rectangle is 45 square inches. One dimension is 5 inches. What is the perimeter?

Graph: f (x) = 3sin (pi/3) (x+3) + 2 find: per: amp: Hor: Vert: D: R:

If the data below were represented with a stem-and-leaf plot, a stem of 3 would have how many leaves?

The length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.