TAILIEUCHUNG - Number operation review 9

Tham khảo tài liệu 'number operation review 9', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ALGEBRA REVIEW x y What is the equation represented in the graph above a. y x2 3 b. y x2 3 c. y x 3 2 d. y x 3 2 e. y x 1 3 Answer b. This graph is identical to a graph of y x2 except it is moved down 3 so that the parabola intersects the y-axis at 3 instead of 0. Each y value is 3 less than the corresponding y value in y x2 so its equation is therefore y x2 3. 84 ALGEBRA REVIEW Rational Equations and Inequalities Rational numbers are numbers that can be written as fractions and decimals and repeating decimals . Similarly rational equations are equations in fraction form. Rational inequalities are also in fraction form and use the symbols and instead of . Example x 5 x2 5x 14 Given J x2 3x - 10 L 30 find the value of x. Factor the top and bottom x 5 x_ 7 x- 2 _ 30 x 5 x -2 30 You can cancel out the x 5 and the x 2 terms from the top and bottom to yield x 7 30 Now solve for x x 7 30 x 7 - 7 30 - 7 x 23 Practice Question Tf x 8 x2 11x - 26 _ 17 L t flop vninp nfw If x2 6x 16 17 What is the value of x a. -16 b. -13 c. 8 d. 2 e. 4 Answer e. To solve for x first factor the top and bottom of the fractions x 8 x2 11x 26 -1-7 x2 6x - 16 - 17 x 8 x 13 x 2 17 x 8 x -2 _ 17 You can cancel out the x 8 and the x 2 terms from the top and bottom x 13 17 Solve for x x 13 - 13 17 - 13 x 4 85 ------------------------------------ ALGEBRA REVIEW ---------------------------------------- Radical Equations Some algebraic equations on the SAT include the square root of the unknown. To solve these equations first isolate the radical. Then square both sides of the equation to remove the radical sign. Example 5Vc 15 35 To isolate the variable subtract 15 from both sides 5Vc 15 - 15 35 - 15 5Vc 20 Next divide both sides by 5 5yc _ 20 5 __ 5 Vc 4 Last square both sides Vc 2 42 c 16 Practice Question If 6Vdl 10 32 what is the value of d a. 7 b. 14 c. 36 d. 49 e. 64 Answer d. To solve for d isolate the variable 6Vd - 10 32 6Vd - 10 10 32 10 6Vd 42 cVd 42 6 6 Vd 7 Vd 2 72 d 49 .

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