Concept explainers
For Exercises 35–42, use
. (See Example 4)
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College Algebra (Collegiate Math)
- For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_forwardim 2. 2.arrow_forwardIn Exercises 101–103, perform the indicated operations. 1 1 1 101. x" – 1 x" + 1 x2" – 1 (1-X- -X ) (1 – (1 – 102. (1 - x + 1) x + 2 x + 3 103. (x – y)-1 + (x – y)-2arrow_forward
- dt 123 .2.c B 8t + +C +C 20arrow_forwardFor Exercises 81–100, make an appropriate substitution and solve the equation. (See Examples 10–11) 81. (2x + 5)? – 7(2x + 5) - 30 = 0 82. (Зх — 7)? - 6(3х — 7)-16 3D 0 83. (x + 2x)? – 18(r + 2x) = -45 84. (x + 3x)? - 86. (у? — 3)? — 9(y? — 3) — 52 %3D 0 14(x + 3x) = -40 85. (x + 2)2 + (x + 2) – 42 = 0 10 2 10 - 61 m - - 27 = 0 x + + 35 = 0 87. 88. - 121 x + т - m m 89. 2 + 2 + = 12 90. + 3 + 6 + 3 = -8 91. 5c2/5 11c/5 + 2 = 0 92. З3 d'/3 – 4 = 0 93. y'/2 – y/4 6 = 0 94. n'/2 + 6n/4 – 16 = 0 95. 9y 10y + 1 = 0 96. 100х-4 29x-2 + 1 = 0 | 97. 4t – 25 Vi = 0 98. 9m – 16Vm = 0 100. 392 + 16q -1 99. 30k-2 – 23k- + 2 = 0 + 5 = 0arrow_forwardA. y = -2(x – 4)² + 1 B. y = 2(x – 4)² + 1 C. y = 2(x + 4)² – 1 D. y = -2(x + 4)² – 1 7. 2 3 4 A. y = (x + 4)2 + 2 B. y =÷(x – 4)² + 2 C. y =(x + 4)2 - 2 D. y = ÷(x – 4)² – 2 8. %3Darrow_forward
- For questions 10 – 11, use the table to answer the questions. It is set up to multiply two polynomials. (show your work)arrow_forwardIn Exercises 14–16, divide as indicated. 14. (12x*y³ + 16x?y³ – 10x²y²) ÷ (4x?y) 15. (9x – 3x2 – 3x + 4) ÷ (3x + 2) 16. (3x4 + 2x3 – 8x + 6) ÷ (x² – 1)arrow_forwardExercises 81–84 involve the perimeter and area of various geometric figures. Refer to Table 1.6 on page 60 if you've forgotten any of the formulas. In Exercises 81-82, find the perimeter and area of each rectangle. Express answers in simplified radical form. 81. V125 feet 2V20 feet 82. 4V20 feet V80 feet 83. Find the perimeter of the triangle in simplified radical form. V80 m V45 m V125 m 84. Find the area of the trapezoid in simplified radical form. V2 feet Võ feet Vỹ feetarrow_forward
- The question is in the imagearrow_forwardIf A = {2,3}, B = {1,3}, C = {1, 2}, determine (A x B x C) n(C × A × B).arrow_forwardIn Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.arrow_forward
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