Algebraic properties of trees (Acta Universitatis Carolinae by Ladislav Nebeský

By Ladislav Nebeský

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8. In the metric system, 1 centimeter ϭ 10 millimeters. 9. If the length of a rectangle is l inches and its width is w inches, then the perimeter, in feet, can be represented by 24(l ϩ w). 10. The value, in dollars, of x five-dollar bills and y ten-dollar bills can be represented by 5x ϩ 10y. 4 Simplify the algebraic expressions in Problems 1 – 14 by combining similar terms. (Objective 1) 1. 3. 5. 7. Ϫ7x ϩ 11x 5a2 Ϫ 6a2 4n Ϫ 9n Ϫ n 4x Ϫ 9x ϩ 2y 2. 4. 6. 8. 5x Ϫ 8x ϩ x 12b3 Ϫ 17b3 6n ϩ 13n Ϫ 15n 7x Ϫ 9y Ϫ 10x Ϫ 13y 9.

Then simplify the numerical expression to answer the question. (Objective 8) 96. A scuba diver was 32 feet below sea level when he noticed that his partner had his extra knife. He ascended 13 feet to meet his partner, get the knife, and then dove down 50 feet. How far below sea level is the diver? 97. Jeff played 18 holes of golf on Saturday. On each of 6 holes he was 1 under par, on each of 4 holes he was 2 over par, on 1 hole he was 3 over par, on each of 2 holes he shot par, and on each of 5 holes he was 1 over par.

The product (or quotient) of two positive numbers or two negative numbers is the product (or quotient) of their absolute values. 2. The product (or quotient) of one positive and one negative number is the opposite of the product (or quotient) of their absolute values. Evaluate exponential expressions. 3/Objective 3) Exponents are used to indicate repeated multiplications. The expression bn can be read “b to the nth power”. We refer to b as the base and n as the exponent. Solution The integers are Ϫ4 and 0.

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