Suppose that ln 3 = p and ln 7=q. Use properties of logarithms to write the logarithm in terms of p and q.

ln 21

Triangle ABC has vertices A (4, 5), B (0, 5), and C (3, - 1). The triangle is translated 3 units to the left and 1 unit up. What are the coordinates of B' after the translation? a. (1, 6) b. (-3, 6) c. (0, 0) d. (3, 1)

There are six professors teaching the introductory discrete mathematics class at someuniversity. The same final exam is given by all five professors. The exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible).

Is - 2.22 a rational or real or integers

Write each number in expanded form one

Sam decides to build a square garden. If the area of the garden is 25x2 + 30x + 9 square feet, what is the length of one side of the garden?

Which shows three ordered pairs that are all solutions of the equation y = x + 8? A. (0, 8), (1, 7), and (2, 9) B. (1, 8), (2, 16), and (3, 24) C. (1, 9), (3, 11), and (5, 13) D. (8, 0), (9, 1), and (10, 2)

The distance between 4 and 11 is

A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting. Write an expression for the combined area of the painting and frame

How many 1-inch cubes do you need to fill a cube that has an edge length of 1 foot?

The Hundred Years' War changed France dramatically. A great sense of national pride emerged among the French people, and they developed a strong loyalty to the King. The King gained the power to raise taxes.