A treatise on elementary algebra by by James Hamblin Smith

By by James Hamblin Smith

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2x2 ϩ x Ϫ 5 12. 3n2 ϩ n Ϫ 7 13. Ϫ1x ϩ 52 14. Ϫ1n Ϫ 32 Translate each phrase into an algebraic expression. 15. seven fewer than a number 16. a number decreased by six 17. the sum of a number and four 18. a number increased by nine Create a mathematical model using descriptive variables. 29. The length of the rectangle is three meters less than twice the width. 30. The height of the triangle is six centimeters less than three times the base. 31. The speed of the car was fifteen miles per hour more than the speed of the bus.

1 62 result 1k 0 ϭ 12 c.

Find a formula for volume in terms of x. b. Find the volume if x ϭ 2. Solution ᮣ a. V ϭ S 3 S substitute 2x 2 for S ϭ 12x2 2 3 ϭ 8x6 2x2 2x2 2x2 b. For V ϭ 8x , V ϭ 8122 6 substitute 2 for x # ϭ 8 64 or 512 122 6 ϭ 64 The volume of the cube would be 512 units3. 2 Exponents, Scientific Notation, and a Review of Polynomials 13 The Quotient Property of Exponents x ϭ 1 for x 0, we note a x x5 x # x # x # x # x ϭ x3, pattern that helps to simplify a quotient of exponential terms. For 2 ϭ # x x x the exponent of the final result appears to be the difference between the exponent in the numerator and the exponent in the denominator.

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