At a store, toothbrushes cost x dollars and bars of soap cost y dollars. One customer bought 4 toothbrushes and 2 bars of soap for $22. Another customer bought 12 toothbrushes and 10 bars of soap for $76. Both amounts do not include tax. Write and solve a system of equations for x and y.

Examine the two-step equation. − 7 4 + x 4 = 2 which property of operations allows you to add the same constant term to both sides? amultiplication property of equality bdivision property of equality caddition property of equality dsubtraction property of equality

Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4 by substituting x = 1 and x = 2.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.