The largest 2-digit number is 99. how many 2-digit numbers must be in a set in order to apply the pigeonhole principle to conclude that there are two distinct subsets of the numbers whose elements sum to the same value? you may need a calculator for this.

Atriangle has side lengths of 15 inches and 30 inches. it also has angles that measure 45º and 20º. which of the following identifies the possible third angle of the triangle? a. 15 in., 65º b. 45 in., 65º c. 17 in., 115º d. 14 in., 115º

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

The rectangle shown has a perimeter of 108 cm and the given area. its length is 6 more than five times its width. write and solve a system of equations to find the dimensions of the rectangle.