Intermediate Algebra - 2e, 2017a

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x +2is simplified because there are no common factors of x + 2 and x +3. x +3 2x is not simplified because x is a common factor of 2x and 3x. 3x b ≠0,c ≠0, then a b = a · c b · c and a · c b · c = a b . b ≠0,c ≠0 x +5 x 2+5 2 ! x 2 +5x +6 x 2 +8x +12
x 2 − x − 2 x 2 − 3x + 2 . x 2 − 3x − 10 x 2 + x − 2 . 3a2 −12ab +12b 2 6a 2 −24b 2 3a 2 −12ab +12b 2 6a 2 −24b 2 3 ⎛ ⎝a 2 −4ab +4b 2⎞ ⎠ 6 ⎛ ⎝a 2 −4b 2⎞ ⎠ 3(a −2b)(a −2b) 6(a +2b)(a −2b) a −2b and 3. 3(a −2b)(a −2b) 3 ·2(a +2b)(a −2b) a −2b 2(a +2b) 2x2 − 12xyx + 18y 2 3x 2 − 27y 2 5x2 − 30xyx + 25y 2 2x 2 − 50y 2 −a −a =−1·a.
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Intermediate Algebra 2e SENIOR CONT
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OPENSTAX OpenStax provides free, pe
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n n.
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2·2·2·2·3
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a + b a b a b a − b a b a
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a n n th a n “a n th a 2
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5+2 3 +3 ⎡ ⎣6−3(4−2) ⎤
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7 4 5x 3x n 2 9n 2
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twelve more than y twelve added to
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3x 2 +12x +11+14x 2 +8x +5 5b 2 +9
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2 −2 2 −2, −
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−9__ − |−9| −9__−9 −9
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−5 + (−3),
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a 3−1 b −3 − (−1) c −3−
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7−(−4−3) −9. 7−(−4 −
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a −100 ÷ (−4) b 7·6 c 4(−8)
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8(−9) ÷ (−2) 3 8(−9) ÷ (
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15 −6 −
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a 15 − 8 b −15 − (−8) c −
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a b
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− 315 770 . − 69 120 .
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− 27 7 ÷ ⎛ ⎝ − 35 ⎞ 36
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7 12 + 11 15 . 13 15 + 17 20 .
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5x 6 · 310 5x ·3 6·10 5 x ·3 2
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1 + 42 ⎛1 ⎛ ⎞ 2 . ⎝4 ⎠
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− 108 63 − 104 48 120 252 18
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− 1 8 + 7 12 − 7 15 − y 4
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a b c 18.379. a b
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−23.5 − 41.38 23.5 ______ +41
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a b c
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a 0.374 b − 5 8 a b 5 8
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n n 2 n 8 2
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−25? −25? () 2 = −25?
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4, −3. 3 4 3 4
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71% 150% 39.3% 7.8% 1.56 0.
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8+9 9+8, 8+9=9+8.
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⎛2 ⎝ + 7 ⎞ 9 12⎠ + 5 . 12
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7 15 · 823 · 15 7 7 15 · 15 7
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100 ⎛ ⎝0.3 + 0.25q ⎞ ⎠.
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4(x −8) − (x +3) 4x −32−x
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43m + (−12n) + (−16m) + (−9n)
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0
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a ≠ b a < b a ≤ b a > b a ≥ b
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−1 −1a =−a −1
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m m = n 2 , m = n, n ≥0. m
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x =4, a x 3 b 5 x c 2x 2 −5x +3
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a − 3y 10 − 5 6 b − 3y 10 ·
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756. 5n +8+2n −1 x =−2
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5 − 2(n + 1). 5 6 1 4 .
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2(m − 4) + 3 = −1. 5(a − 3
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6 ⎛ ⎝p − 3 ⎞ ⎠ − 7 = 5
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12n 4 + 9(
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1 12 x + 5 6 = 3 4 . 1 4 x + 1
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y =9. 1 5 (n + 3) = 1 (n + 2).
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x =9 0.25n + 0.05(n + 5) = 2.95
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18(5j − 1) + 29 = 47 24(3d − 4
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s =
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−12 −3? −3−9 = ? −12 −
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n 1 st odd integer n +2 2 nd consec
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a b c a
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change = new amount − original am
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a b a b
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Let r = rate of interest. I = Prt 1
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−36. −3.
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a b
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h = 3V πr 2. A = 1 bh 2 A
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h = A = 1 2 bh 126 = 1 2 ·
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a 2 + b 2 = c 2 a 2 +12 2 = 13 2 a
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P = 2L +2W 96 = ? 2·34+2·14 96 =
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w +40= P = 2L +2W 360 = ? 2(
Page 155:
C = πd C = πd π. V =
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a b c
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p = 8p +3= $3.02? 7(
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40 − f = 26 · 3
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D = rt,
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+ 15.
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Now solve this equation 70t +60t =
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Walk 3 mph (0.5 hour) = 1.5 miles B
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a b c
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a x ≥−3b x < 2.5 c x ≤− 3 5
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ax + b < c, ax + b ≤ c, ax + b >
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c 5 3 . 5 3 a p − 3 4
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6x < 10x + 19.
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1 4 x − 12 1 x > 1 6 x + 7
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Let t = the number of text messages
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Let h = the number of hours. 525
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6h −4(h −1) ≤7h −11 4k −
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2 (x + 10). 5 −(x − 4).
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3x − 4 < 5 4x + 9 ≥ 1.
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−4≤3x −7
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x ≤ 21 2 x ≥ −12 (−
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x −2 x ≥−4 x ≤−1 x >
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2−7x ≥−5 4(x −3) +7>3. a
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If |x| =5 then x =−5 or x =5
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2|x −7| +5=9 2|x −7| =4 |x −
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|u| ≤ a, −a ≤ u ≤ a.
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−5 |u| ≥ a, u ≤−a u
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|actual-ideal| ≤ tolerance |x −
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|2x −5| +2=3 |4x −3|
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change = new amount − original am
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a < x < b a < x x < b. a < x < b
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−135.
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x 2 −2 < x 15p −30 9h −7(h
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| 1 2 x +5 | +4=1 |6x −5| = |2x
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4 1 2
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(x, y)
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(−3, −4) c x =2, y
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Ax + By = C y =2x −3 a
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y = 3x − 1. a b (3, −1) (
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1 2 y = 1 2 x +3 (x, y) (0,
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x = a. (a, 0). y = b. (0, b)
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y =4 y =4x y
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(3, 0) (0, 6) (4, 0) −3 (0,
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y =0 x =0 y =0
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x - 2y = 4.
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5x − 2y = 10. 3x − 4y = 12.
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y = −x.
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y = 1 2 x −3; (0, −3); (2,
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y =−x y = 3 2 x y =−2 3 x
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m = rise run . m = rise run
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m = rise run m = 2 0
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(−2, −3) (−7, 4). (−2,
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m = rise run
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a y = 2 5 x − 1 b x + 4y = 8
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a y =5b 4x −5y =20c x =−3d y =
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T = 1 n + 40 4 a b
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m = 2 , 5
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a 2x + 5y = 5 y = − 2 5 x − 4
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y =−5x −4 y. x −5y =5 −5y
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(2, 5); m =− 1 3 (1, 4) m =−
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y = 3 4 x −3; 3x −4y =−2 3x +
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y = mx + b. 2 5 (0, 4). −
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m = y − y 1 x − x 1 x − x 1
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(−2, −4) (1, −3). (−4,
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y =2x −3. m ∥ =2. m ∥
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(−2, 1)?
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(3, −2). −2.
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y (0, 5) (0, −6) −3 y (
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(2, 6) (5, 3) (4, 3) (8, 1) (
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x > 2 4x + 3 > 23 8 < x
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(−8, 12) (−8, 12) y > x +4.
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y > x +4 y = x +4 y > x +4.
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y =−2x + 3. y = 1 2 x − 4.
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3x − y = 6.
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(0, 0) (0, 0) x −2y
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x = a y = b vertical line horizonta
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a b c
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y =− 1 3 x −2.
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a b
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{1, 4, 9, 16, 25} {(1, 1), (2, 8
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a b c a
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c {321-549-3327, 427-658-2314, 32
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y = f (x), x is the independent var
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g(x +2), x +2 c g(x) + g(2),
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a b {(1, 4), (2, 8), (3, 12), (4
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a b c a 2x + y
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a 2 3 b 3 2 . a |7| b |−3|.
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y =2x −3 y =2x
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f (x) =−2x −4. f (x) =−2x
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f (x) = x 2 . f (x) = x 2 .
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f (x) = x f (x) = x
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[−3, 3].
Page 352 and 353:
x = 3 2 π, −1. f ⎛ ⎝ 3 2
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a a b b a a b b
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a f (0). b f ⎛ ⎝ 1 2 π⎞
Page 358 and 359:
Ax + By = C Ax + By > C A
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m = rise run . m = rise run
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f (x) y = f (x),
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x − y =−1 x +2y =6 2x +3y =12
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(2, −2); m = 5 (−3, 4); m =−
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(2, 10) (−2, −2) (7, 1) (5,
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a b c
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a b f (x) =5x +1
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a (2, 5) b (−1, −3) c (0, 2) d
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h(y) =3|y −1| −3, h(−4).
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3x − y = 12. 2x − 3y =
Page 383 and 384:
⎧x − 3y = −3 ⎨ . ⎩ x + y
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⎧ y = − 1x + 2 ⎨ 4 . ⎩ x +
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a ⎧ =3x −1 ⎨y ⎩6x −2y =12
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⎧2x + y =7 ⎨ ⎩x −2y =6 .
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⎛ ⎝ 5 4 , − 1 ⎞ 2⎠ .
Page 393 and 394:
⎧ ⎨ ⎩ 4x −3y =9 7x +2y =−
Page 395 and 396:
(3, 6). ⎧1 x − 3 1 2 ⎨ y =
Page 397 and 398:
a ⎧ ⎨ ⎩ 3x +8y =40 7x −4y
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⎧ ⎨ y =−1 2 x +5 ⎩x +2y =1
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n = m = m = 9 2
Page 404:
e = c =
Page 407 and 408:
x = y =
Page 409 and 410:
L = W =
Page 411 and 412:
k = j − 1 2 ⎧ ⎨ k = j − 1
Page 413 and 414:
s = c =
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347 + 18 = 365 365 · 3 = 1,095
Page 418 and 419:
4.5
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a ·12=12a, c ·7=7c. a = c =
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n =36 $0.10 = $6.30 $0.05 = $1
Page 424 and 425:
x = y = −0
Page 426 and 427:
s + b = 40,000, 0.08s + 0.03b =
Page 428 and 429:
a b c d a
Page 430 and 431:
$3.80.
Page 432 and 433:
a b c
Page 434:
ax + by + cz = d, (x, y, z
Page 437:
a (1, −3, 2) b (4, −1, −5)
Page 440 and 441:
x =−4 y =1. x =−4 (−4,
Page 442 and 443:
y +2z = 3 y = −2z +3 x +2y −
Page 444 and 445:
⎧ ⎨ ⎩ 2x −6y + z =3 3x −4
Page 446 and 447:
3(x + 2) + 4 = 4(2x − 1) + 9.
Page 448 and 449:
⎡1 −1 2 3 ⎤ ⎢2 1 −2 1⎥
Page 450 and 451:
⎡ ⎣ 1 −1 2⎤ 4 −8 | 0⎦ .
Page 452 and 453:
⎧ ⎨ ⎩ 3x +8y +2z =−5 2x +5y
Page 454 and 455:
⎧x + y +3z =0 ⎨x +3y +5z =0.
Page 456 and 457:
⎧ x + y − z = 0 ⎨2x + 4y −
Page 458 and 459:
⎧2x + y =2 ⎧3x + y =2 ⎨ ⎨
Page 460 and 461:
2×2 3×3 5(−2) − (−
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a | 4 −2 3 1 0 −3 −2 −4 2|
Page 464 and 465:
|3 −2 4 0 −1 −2 2 3 −1|,
Page 466 and 467:
D x D y , ⎧2x + y
Page 468 and 469:
⎧ ⎨ ⎩ 3x −5y +4z =5 5x +2y
Page 470 and 471:
⎧ ⎨ ⎩ x +3y =4 −2x −6y =3
Page 472 and 473:
⎡ ⎣ 6 −2 ⎤ 3 −1⎦ ⎡
Page 474 and 475:
2a < 5a + 12. ⎛ ⎝ ⎛ 3, 1
Page 477 and 478:
⎧ y < 3x + 2 ⎨ ⎩ y > −x −
Page 479 and 480:
⎧ ⎨ ⎩ x −2y −4 x −2y
Page 481 and 482:
⎧3x − 2y ≥ 12 ⎨ ⎩y ≥ 3
Page 483 and 484:
x = the number of small photos. y =
Page 485 and 486:
h = the number of hamburgers. c = t
Page 487 and 488:
⎧3x + y >5 ⎧4x − y −8 ⎨
Page 489 and 490:
a b c d
Page 491 and 492:
Choose the Most Convenient Method t
Page 493 and 494:
|+ − + +| − + − + − ⎧ a 1
Page 495 and 496:
( 3 4
Page 497 and 498:
⎧3x − y =−1 ⎧4x +3y =−2
Page 499 and 500:
⎧ ⎨ y ≤−3 4 x +1 ⎩x ≥
Page 501 and 502:
3x 2 + 3x + 1 + 8x 2 + 5x + 5.
Page 503 and 504:
a 7y 2 −5y +3 b −2a 4 b 2 c 3x
Page 505 and 506:
a 8y 2 + 3z 2 − 3y 2 b m 2 n 2
Page 507 and 508:
⎛ ⎝a 3 − a 2 b ⎞ ⎠ −
Page 509 and 510:
h(t) = −16t 2 + 175
Page 511 and 512:
a 47x 5 −17x 2 y 3 + y 2 b 5c 3 +
Page 513 and 514:
⎛ ⎝7x 2 −2xy +6y 2⎞ ⎠ +
Page 515 and 516:
(−2)(−2)(−2). 8x 24y .
Page 517 and 518:
d a b 9 · b 8 b 4 2x · 4 x c
Page 519 and 520:
am a m. m > n n < m m = n?
Page 521 and 522:
10 −3 a −n = 1 a n. 1 10 3 1
Page 523 and 524:
⎛ ⎝ − x y ⎞ −3 ⎠ ⎛
Page 525 and 526:
a (a m ) n = a m · n . b c (y
Page 527 and 528:
⎛ ⎝5x −3⎞ 2 ⎠ (ab) m = a
Page 529 and 530:
2 ⎛ ⎜ 4p−3 ⎞ ⎝ q 2 ⎟
Page 531 and 532:
(x 3 ) 4 (x −2 ) 5 (x 6 ) 5 (a m
Page 533 and 534:
3.7 × 10 4 3.7 × 10,000 37,000 b
Page 535 and 536:
a ⎛ ⎝−4 × 10 5⎞ ⎠ ⎛
Page 537 and 538:
a b 4 b −8 b ⎛ ⎝w 4 x −5⎞
Page 539 and 540:
a b a b a b a b a 5.2
Page 541 and 542:
⎛ ⎝ 5 6 x3 y ⎞ ⎠ ⎛ ⎝12x
Page 543 and 544:
a ⎛ ⎝y −7 ⎞ ⎠ ⎛ ⎝y +4
Page 545 and 546:
a ⎛ ⎝y 2 + 7 ⎞ ⎠ ⎛ ⎝⎛
Page 547 and 548:
(a + b) 2 = ___ + ___ + ___
Page 549 and 550:
a (2x +5)(2x −5) b (5m −9n)(5m
Page 551 and 552:
d (5x −6)(6x +5) (5x −6)(6x +5
Page 553 and 554:
a ⎛ ⎝6y 7⎞ ⎠ ⎛ ⎝−3y 4
Page 555 and 556:
(r 2 − s 3 )(r 3 + s 2 ) ⎛
Page 557 and 558:
3 d + x d . 30xyx 3 . 5xyx
Page 559 and 560:
y 5 + 2 5 y +2 5 .
Page 561 and 562:
x 3 0x 3 x 4 x. x 3 , x 3
Page 563 and 564:
x. x − c 2x 2
Page 565 and 566:
f (x) g(x). ⎛ ⎝ f g ⎞ ⎠ (
Page 567 and 568:
f (x) = x 3 − 7x + 12 x + 3.
Page 569 and 570:
2x 4 −9x 3 +5x 2 −3x −6 x
Page 571 and 572:
(a − b), (a + b).
Page 573 and 574:
a m · a n = a m + n (a m ) n = a m
Page 575 and 576:
f (x) x − c, f (c). f (x),
Page 577 and 578:
⎛ ⎝y 4⎞ 3 ⎠ ⎛ ⎝3 2⎞
Page 579 and 580:
(3y + 5)(3y −5) (6x + y)(6x −
Page 581:
8y 4 −3y 2 +1 ⎛ ⎝5a 2 +2a
Page 585 and 586:
25m 4 , 35m 3 , 20m 2 . 14x 3 ,
Page 587 and 588:
8x 3 y, −10x 2 y 2 , and 12xy 3
Page 589 and 590:
a x 2 +3x −2x −6 b 6x 2 −3x
Page 591 and 592:
−18xy 2 −27x 2 y −4x 3 y 5
Page 593 and 594:
x 2 + bx + c. x 2 + bx +
Page 595 and 596:
u 2 − 9u + 18. y 2 − 16y + 6
Page 597 and 598:
u 2 −9uv −12v 2 u, v. (u v)(u
Page 599 and 600:
1x ·3x =3x 2 ?
Page 601 and 602:
6b 2 −13b +5 (b −1)(6b −5)
Page 603 and 604:
−5y 2 . −5y 2 ⎛ ⎝y +4 ⎞
Page 605 and 606:
ac. ac =28 ac (−4)(−7) = 28
Page 608 and 609:
x 2 + bx + c x 2 +bx+c. p 2 +11p
Page 610 and 611:
x 2 + bx + c (x + m)(x + n).
Page 612 and 613:
9x 2 +12x +4. 4x 2 + 12x + 9.
Page 614 and 615: 49x 2 + 84xyx + 36y 2 . 64m 2 +
Page 616 and 617: 144x 2 −49y 2 . 144x 2 −49y 2
Page 618 and 619: ⎛ ⎝x − y −3 ⎞ ⎠ ⎛ ⎝
Page 620 and 621: 27u 3 − 125v 3 . 8x 3
Page 623 and 624: 16y 2 +24y +9 25v 2 +20v +4 36s 2
Page 625 and 626: x 2 + bx + c? ax 2 + bx + c?
Page 627 and 628: 24y 2 − 150 6 ⎛ ⎝4y 2 −25
Page 629 and 630: 12x 3 y 2 +75xy 2 3xy 2 3xy 2
Page 631 and 632: 4x 2 +8bx −4ax −8ab 4 ⎛ ⎝
Page 633 and 634: 2n 2 +13n −7 8x 2 −9x −3 a
Page 635 and 636: 5y − 3 = 0. n 3 − 9n 2 −
Page 637 and 638: ax 2 + bx + c =0. 2y 2 =13y +
Page 639 and 640: (k + 1)(k − 1) = 8.
Page 641 and 642: f (x) =0, f (x) =0, (x, 0)
Page 643 and 644: n = the first integer. n + 2 = next
Page 645 and 646: ⎛ ⎝a 2 + b 2 = c 2⎞ ⎠.
Page 647 and 648: c t =2 a h(t) =0. h(t) =0 h(t
Page 649 and 650: (3a −10)(2a −7) =0 (5b +1)(6b
Page 651 and 652: a b
Page 653 and 654: x 2 + bx + c x 2 + bx
Page 655 and 656: x 2 + bx + c? ax 2 + bx + c?
Page 657 and 658: x 2 +bxy+cy 2 . x 2 +12xy +35y 2
Page 659 and 660: f (x) =64x 2 −49 f (x) =6x 2 −
Page 661 and 662: 90y 15y 2.
Page 663: 8a 2 b 3c 3c =0 8a 2 b 3c c =0 is
Page 667 and 668: p q · rs pr = qs
Page 669 and 670: x 3 − 8 3x 2 − 6x + 12 ÷ x2
Page 671 and 672: 4m + 4 3m − 15 · m2 − 3m − 1
Page 673 and 674: R(x) = f (x) · g(x) f (x) = 3x
Page 675 and 676: 5p 2 p 2 −5p −36· p2 −16 10p
Page 677 and 678: a b
Page 679 and 680: 11x +28+ x +4 x x2 +4 , x ≠−4
Page 681 and 682: m2 −6m m 2 −1 − 3m +2 1−m
Page 683 and 684: 3 x −3 + x −2 2 . 2 x − 2
Page 685 and 686: Find the LCD. y 2 −16= ⎛ ⎝y
Page 687 and 688: Find the LCD. a 2 +6a +5 =(a +1)(a
Page 689 and 690: R(x) = f (x) − g(x) f (x) = x +
Page 691 and 692: 6 a 2 +14a +45 , 5a a 2 −81 4 b
Page 693 and 694: 3 5 . 9 10 1 − 1 3 4 2 + 4
Page 695 and 696: 1 3 + 1 6 1 2 − 1 . 3
Page 697 and 698: n − 4n n +5 1 n +5 + 1 . n −5
Page 699 and 700: 1 a + 1 b a b + b . a 1 x 2 −
Page 701 and 702: (m −3)(m −4). 3 x 2 +
Page 703 and 704: 2a a +4 4a 2 a 2 −16 3b b −5 b
Page 705 and 706: 1 6 x + 1 2 = 1 3 . n 2 − 5n
Page 707 and 708: 1− 5 y =−6 y 2.
Page 709 and 710: x =−1. 2 x + 1 + 1 x − 1 = 1
Page 711 and 712: (y −6)(y +6). y =4. x
Page 713 and 714: x ≠−1,x ≠ 1 3 , x ≠3 (3x
Page 715 and 716:
m = y − y 1 x − x 1 Multiply bo
Page 717 and 718:
1 a + 2 5 = 1 2 6 3 − 2 d = 4 9
Page 719 and 720:
a b 1 − 10,
Page 721:
y y + 55 = 3 8 . z z − 84 =
Page 725 and 726:
D = rt
Page 727 and 728:
Tailwind 150 + 30 = 180 mph 300 180
Page 729 and 730:
D = r · t, t t = D r .
Page 731 and 732:
1 10 1 8
Page 733 and 734:
s =15h
Page 735 and 736:
a b a
Page 737 and 738:
x = 7 56 56 8 72 = y 9 72 156 =
Page 740 and 741:
y x y = 14, x =3. x y. a
Page 742 and 743:
a m. b
Page 744 and 745:
x −1 x +3 ≥0. x −1 x +3
Page 746 and 747:
4x x −6
Page 748 and 749:
(x +3)(x −5)=0 x =−3,x =5
Page 750 and 751:
R(x) ≤0 R(x). x +3 x −5 ≤0 x
Page 752 and 753:
x −3 x +4 ≥0 x +6 x −5 ≥0
Page 754 and 755:
q p , q ≠0. R(x) =
Page 756 and 757:
a b = d c , b ≠0,d ≠0.
Page 758 and 759:
4q 2 − q +3 q 2 +6q +5 − 3q2
Page 760 and 761:
x = 3 3 4 5 y = 9 5 s s +20 = 3 7
Page 762 and 763:
R(x) = x x −5 −2 , R(x) = x
Page 765 and 766:
a (−9) 2 b −9 2 c (−9) 3 .
Page 767 and 768:
144 12 2 = 144. 12 b − 289 17 2
Page 769 and 770:
3 a 64 a 4 b 81 5 c 32. 3 64 4 3
Page 771 and 772:
105 b 3 43 3 a 38 b 93 3
Page 773 and 774:
4 625 =5.
Page 775 and 776:
y 16 ⎛ ⎝y 8⎞ ⎠2 = y 16 .
Page 777 and 778:
4 16q 12 4 ⎛ ⎝ 2q 3⎞ 4 ⎠
Page 779 and 780:
a 64 b −81 a 169 b − 100 a 19
Page 781 and 782:
x 9 x 4. y 3 y 11. ⎛
Page 783 and 784:
500 100 · 5 100 · 5 10 5 b 2
Page 785 and 786:
72n 7 36n 6 ·2n 36n 6 · 2n 6 |
Page 787 and 788:
a 98a 7 b 5 3 b 56x 5 y 4 4 c 32x 5
Page 789 and 790:
45 80 ⎛ ⎝ 3 ⎞ 4⎠2 = 9 .
Page 791 and 792:
a a8 b a 6 4 x7 x 3 c 4 y17 y 5 .
Page 793 and 794:
c 4 48x 10 y 8 4 48x 10 4 y 8
Page 795 and 796:
4 5a 8 b 6 80a 3 b 2 4 a 5 b 4 16
Page 797 and 798:
27 80 125 96 147 450 800 675
Page 799 and 800:
a b
Page 801 and 802:
1 a n = n a
Page 803 and 804:
1 2 25 25 5 b 1 3 64 3 64 3 4 3
Page 805 and 806:
1 (a m n ) a m n . m a n = ⎛
Page 807 and 808:
32 − 2 5 a −n = 1 1 a n. 2 5 3
Page 809 and 810:
2 1 5 1 a x 2 · x 6 b ⎛ ⎝z 9
Page 811 and 812:
⎛ ⎜m ⎝ 2 3 1 n 3 ⎞ 2 2 ⎠
Page 813 and 814:
1 n a 1 1 1 a x 2 b y 3 4 c z 1
Page 815 and 816:
a b
Page 817 and 818:
5 3 3 y +4 y 3 9 y c 4 7 x −2 4
Page 819 and 820:
a 950m 2 −6 48m 2 3 b 54n 5 a 3
Page 821 and 822:
⎛ ⎝ 10 6p3 ⎞ ⎠ ⎛ ⎝ 43p
Page 823 and 824:
⎛3 ⎝ x −2 ⎞⎛3 ⎠⎝ x +4
Page 825 and 826:
⎛ ⎝ ⎛ 3 − 2 5 ⎞ ⎠ ⎞
Page 827 and 828:
a 7 ⎛ ⎝5+2 7 ⎞ ⎠ b a 11
Page 829 and 830:
30 48 . x 2 · x 4 . (7 +
Page 831 and 832:
147ab 8 3a 3 b 4 147ab 8 3a 3 b 4
Page 833 and 834:
a 4 3 b 3 20 c 3 6x .
Page 835 and 836:
3 3 2 . 3 3 3 =3. c 3 2·x 2
Page 837 and 838:
a 1 4 b 3 4 3 64 c 3 . 4 125x a
Page 839 and 840:
q − 10 q + 10
Page 841 and 842:
8 1− 5 7 2− 6 6 3− 7 5 4
Page 843 and 844:
3m + 2 − 5 = 0. 10z + 1 − 2
Page 845 and 846:
3 5x +1+8=4. 3 5x +1+8=4 3 5x
Page 847 and 848:
=0 r =5 r =0 m + 9 − m +
Page 849 and 850:
3 − x = x − 3. x + 2 = x + 1
Page 851 and 852:
t = h 4 .
Page 853 and 854:
s = 24d
Page 855 and 856:
x +7− x −5=2 x +5− x −3=2
Page 857 and 858:
f (x) = 2x −1 f (−2), x. f (
Page 859 and 860:
f (x) = 3x −4. f (x) = 3x
Page 861 and 862:
c [0, ∞). f (x) = x + 2, a
Page 863 and 864:
f (x) = 4x −4, a f (x) = 6x −
Page 865 and 866:
i −4, − 7, 0. 5 - , 7 , 3
Page 867 and 868:
a + bi, b =0, a + bi a +0·
Page 869 and 870:
4i(5 − 3i). −3i(2 + 4i).
Page 871 and 872:
a + bi, a − bi. a + bi,
Page 873 and 874:
−3 5+2i . −3 5+2i −3(5
Page 875 and 876:
i n = ⎛ ⎝i 4⎞ ⎠q · i r ,
Page 877 and 878:
(4−5i)(4+5i) (7−2i)(7+2i) (
Page 879 and 880:
i i = −1.
Page 881 and 882:
n ab = n n a · b n n n a · b = a
Page 883 and 884:
3 a 225 b −16 a − 169 b −8
Page 885 and 886:
3 2 a 25 b 9 − 3 2 2 3 c (−64)
Page 887 and 888:
s = A
Page 889:
3 125x 9 169x 8 y 6 3 72x 8 y 4
Page 892 and 893:
32 5 9x 2 − 12x + 4
Page 894 and 895:
3z 2 = 108. 3z 2 = 108 3z 2 3 =
Page 896 and 897:
1 2 x2 + 4 = 24. 3 4 y2 − 3 =
Page 898 and 899:
⎛ ⎝ x − 1 ⎞ 3⎠2 = 5 9 x
Page 900 and 901:
2n +1= ± 16 2n +1= ±4 n 2n =
Page 902:
2r 2 =32 4t 2 =16 (a −4) 2 =28
Page 905 and 906:
1 (6). 2 x 2 + bx
Page 907 and 908:
Find ⎛ ⎝ 1 2 b⎞ ⎠2 . ⎛
Page 909 and 910:
x 2 +4x = −21. ⎛ ⎝ 1 2 (4)
Page 911 and 912:
a 2 + 4a + 9 = 30. b 2 + 8b −
Page 913 and 914:
⎛ ⎝ 1 2 (−4)⎞ ⎠2 =4
Page 915 and 916:
ax 2 + bx + c =0 a
Page 917 and 918:
a m 2 −24m b x 2 −11x c a n 2
Page 919 and 920:
2 − 4ab a = 3 b = −2. 10
Page 921 and 922:
3y 2 − 5y + 2 = 0 4z 2 + 2z
Page 923 and 924:
3m 2 + 12m + 7 = 0 5n 2 + 4n
Page 925 and 926:
x(x + 2) − 5 = 0. 3y ⎛ ⎝y
Page 927 and 928:
2 −4ac 2x 2 +9x −5=0 9 2
Page 929 and 930:
ax 2 = k a(x − h) 2 = k
Page 931 and 932:
4m 2 + m −3=0 4n 2 −9n +5=0 2
Page 933 and 934:
y 4 − y 2 − 20. ⎛ ⎝y
Page 935 and 936:
(x −2) 2 +7(x −2) +12=0. u =
Page 937 and 938:
1 x 3 . x 2 x 3 1 − 5x 3
Page 939:
x 4 −7x 2 +12=0 x 4 −9x 2 +18=
Page 942 and 943:
Consecutive even integers Consecuti
Page 944 and 945:
A = 1 2 bh.
Page 946 and 947:
a, b, c a, b, c
Page 948 and 949:
x ≈ 7.1
Page 950 and 951:
= D = r · t t t = D r
Page 952:
x =12
Page 955 and 956:
f (x) = x 2 2x 2 + 3x − 2 =
Page 957 and 958:
a f (x) =−3x 2 +2x −4 b f (x) =
Page 959 and 960:
− 2a b .
Page 961 and 962:
f (x) = ax 2 + bx + c 0 = ax 2 + bx
Page 963 and 964:
f (x) = ax 2 + bx + c : y-intercept
Page 965:
f (x) =5x 2 + x +4. x =0 f (x)
Page 968 and 969:
f (3) (3, 0). x =0 f (0) x =0
Page 970 and 971:
x =− b 2a x =−2 x =−2. f
Page 972 and 973:
f (x) =0 f (x) =0
Page 974 and 975:
2.5, 0 −0.6, 0 .
Page 976 and 977:
f (x) = x 2 − 8x + 12. f (x) =
Page 978 and 979:
f (x) =x 2 +3 f (x) = x 2 −3 y
Page 980 and 981:
f (x) = x 2 f (x) = x 2 −1
Page 982 and 983:
g(x) = x 2 +2 f (x) = x 2 h(x) =
Page 984 and 985:
f (x) = x 2 f (x) = x 2 − 5
Page 986 and 987:
f (x) = x 2 f (x) = x 2 f
Page 988 and 989:
f (x) = x 2 f(x) =ax 2 f (x)
Page 990 and 991:
x 2 −3 ⎛ ⎝ 1 2 ⎠2 ·2
Page 992 and 993:
f (x) =−2x 2 −4x +2 f (x) =
Page 994 and 995:
a =2 x = h (h, k) f (0) x =
Page 997 and 998:
f(x) =x 2 + k a b
Page 1000 and 1001:
f (x) =a(x−h) 2 +k f (
Page 1002 and 1003:
2x − 3 = 0. 2y 2 + y =15
Page 1005 and 1006:
a x 2 + 2x − 8 < 0 b a x 2
Page 1007 and 1008:
x 2 + 2x − 8 ≥ 0 x 2 − 2x
Page 1009 and 1010:
a ≠0.
Page 1011 and 1012:
a b x 2 +6x +5>0 x 2 +4x −12
Page 1013 and 1014:
a ≠0 x = −b ± b2 −4ac 2a
Page 1015 and 1016:
y-intercept x-intercepts Let x = 0
Page 1017 and 1018:
m 2 +10m − 4 = −13 n 2 −6n +
Page 1019 and 1020:
y = x 2 −2 y =−x 2 +3 a y =
Page 1021 and 1022:
f (x) =3x 2 −12x +7 a f (x) =a(
Page 1023 and 1024:
f (x) = 2x − 3 g(x) = x 2 + 2x
Page 1025 and 1026:
⎛ ⎝f ∘g ⎞ ⎠(x). b ⎛
Page 1027 and 1028:
a {(−3, 27), (−2, 8), (−1, 1)
Page 1030 and 1031:
f {(0, 5), (1, 6), (2, 7), (3
Page 1032 and 1033:
(−5, −3), (−3, −1), (−1,
Page 1034 and 1035:
5x −1 f (x). x +1 5 g(x).
Page 1036 and 1037:
f (x) = 5 2x −3 y f (x) 5 y =
Page 1038 and 1039:
a a b b a a b b {(2, 1), (4, 2
Page 1040 and 1041:
f (x) = 1 x +2 f (x) = 1 x −6 f
Page 1042 and 1043:
f (x) = (−4) x f ⎛ ⎝ 1 1 ⎞
Page 1044 and 1045:
f (x) = ⎛1⎞ x ⎝ 4⎠ . g(x
Page 1046 and 1047:
f (x) = 2 x g(x) = 2 x − 1 .
Page 1048 and 1049:
π e ⎛ ⎝
Page 1050 and 1051:
(x −3)(x +1) =0 x =3, x =−1
Page 1052 and 1053:
5%, a b c
Page 1054 and 1055:
f (x) =2 x f (x) =6 x f (x) = (1.
Page 1056 and 1057:
$5,000 20%
Page 1058 and 1059:
a 2 3 1 =8, b 5 2 = 5, c ⎛ ⎝ 1
Page 1060 and 1061:
a log 5 25, b log 9 3, c log 2 1 1
Page 1062 and 1063:
y 2 y = x x, y −2 2 −2 = 1 2 2
Page 1064 and 1065:
y 1 3y = x x, y −2 ⎛ ⎝ 1 3
Page 1066 and 1067:
y = x.
Page 1068 and 1069:
log 2 (3x −5) =4 2 4 =3x −5
Page 1070 and 1071:
R = log I 1906 earthquake 7.8 = log
Page 1072 and 1073:
log 14 1 16 = x log 13 1 9 = x lo
Page 1074 and 1075:
a a 0 b a 1 . 3 x 2 y.
Page 1076 and 1077:
M >0,N >0,a>0 a≠1, log a (M ·
Page 1078 and 1079:
M >0, a>0, a≠1 p log a M p = p
Page 1080 and 1081:
4 log x 3 2 3y 2 z 4 log x 3 2 3
Page 1082:
log a M y = log a M log a M y =
Page 1085 and 1086:
log 5 ⎛ ⎝ 4x 6 y 4⎞ ⎠ log
Page 1087 and 1088:
x 2 = 16. x 2 − 5x + 6 = 0.
Page 1089 and 1090:
log 3 x + log 3 (x −8) =2 log a
Page 1091 and 1092:
5 x = 11 x x. log5 x = log11
Page 1093:
A = A 0 e kt . k
Page 1096 and 1097:
log 4 64 = 2log 4 x log49 = 2log x
Page 1098 and 1099:
3 x +1 = 81, 3 x +1 = 75.
Page 1100 and 1101:
f (x) = a x : a >1 0
Page 1102 and 1103:
M >0,N >0,a>0 a≠1, log a M N =
Page 1104 and 1105:
a a b b {(−3, 10), (−2, 5),
Page 1106 and 1107:
7 = log 2 128 5 = log100,000 4=ln
Page 1108 and 1109:
$18,000 $30,000
Page 1110 and 1111:
y = log 3 x. log(x 2 −39)=1
Page 1112 and 1113:
x 2 − 12x − 12 = 0.
Page 1114 and 1115:
a 2 + b 2 = c 2 ⎛ ⎝|x 2 −
Page 1116 and 1117:
⎛ x 1 , y 1 ⎞ −5, −4 ⎝
Page 1118 and 1119:
(0, 0). (x − h) 2 + ⎛ ⎝y
Page 1120 and 1121:
(x − h) 2 + ⎛ ⎝y − k ⎞
Page 1122 and 1123:
(2, 3) a b x 2 + y 2 − 6x
Page 1124 and 1125:
(2, 0) (5, 4) (−4, −3) (2, 5
Page 1126 and 1127:
y = −3x 2 + 12x − 12. x 2
Page 1128 and 1129:
−1, x =− b 2a . x =3. x =3.
Page 1130 and 1131:
y = −x 2 + 5x − 6 y = −x
Page 1132 and 1133:
x = ay 2 + by + c x = a y − k
Page 1134 and 1135:
x = y 2 x = −y 2 x =−y
Page 1136 and 1137:
x = a ⎛ ⎝y − k ⎞ ⎠2 + h.
Page 1138 and 1139:
(0, 0). (0, 0) (0, −2) x =
Page 1140 and 1141:
a x = 3y 2 + 6y + 7 b a x =
Page 1143 and 1144:
y =−x 2 +4x −3 y =−x 2 +8x
Page 1145 and 1146:
y = x 2 x = y 2
Page 1147 and 1148:
y = (x − 1) 2 − 2 x 2 −
Page 1149 and 1150:
(a, 0) (−a, 0). (0, b) (0,
Page 1151 and 1152:
x 2 16 + y2 4 =1 (0, 0). 16 > 4
Page 1153 and 1154:
(h, k) (h, k), (x − h) 2 a 2 +
Page 1155 and 1156:
(x − h) 2 a 2 + ⎛ ⎝y − k
Page 1157:
a =40 a 2 = 1600 b (10, 0) c
Page 1161 and 1162:
(x +1) 2 4 + ⎛ ⎝y +6 ⎞ 2 ⎠
Page 1163 and 1164:
a b
Page 1165 and 1166:
⎛ ⎝(−c, 0), (c, 0) ⎞ ⎠
Page 1167 and 1168:
0, 0 x 2 a 2 − y2 b 2 =1 y 2 a 2
Page 1169 and 1170:
4y 2 −16x 2 =64 4y 2 64 − 16
Page 1171 and 1172:
(x − 3)2 25 − ⎛ ⎝y − 1
Page 1173 and 1174:
x 2 - (h, k). (3, −2) a =3
Page 1175 and 1176:
a x 2 + y 2 − 8x − 6y = 0 b 4x
Page 1177 and 1178:
⎛ ⎝y −3 ⎞ 2 ⎠ (x +2)2 x
Page 1179 and 1180:
⎧ x − y =−2 ⎨ ⎩y = x 2 .
Page 1181 and 1182:
(x −2) 2 + ⎛ ⎝y +3 ⎞ ⎠2 =
Page 1183 and 1184:
(0, −3) 9x 2 + y 2 = 9 y = 3x −
Page 1185 and 1186:
x 2 , −1. x 2 . y =0 y =
Page 1187 and 1188:
⎛ ⎝−2, 3 ⎞ ⎠, ⎛ ⎝2,
Page 1189 and 1190:
y 2
Page 1191 and 1192:
⎧ ⎨ x2 + y 2 =16 ⎩x 2 − y
Page 1193 and 1194:
(x 1 , y 1 ) (x 2 , y 2 ) d = (x
Page 1195 and 1196:
x = ay 2 + by + c x = a y − k
Page 1197 and 1198:
0, 0 x 2 a 2 − y2 b 2 =1 y 2 a 2
Page 1199 and 1200:
(1, −4) (5, −5) (−2, −6
Page 1201 and 1202:
25x 2 +4y 2 + 150x + 125 = 0 4x 2
Page 1203 and 1204:
(−4, −3) (−10, −11) (6, 8
Page 1205 and 1206:
2n + 3 (−1) n
Page 1207 and 1208:
n a n a n 2·1 2 2·2 4 2·3 6
Page 1209 and 1210:
3, 6, 9, 12, 15, … 5, 10, 15,
Page 1211 and 1212:
(n +1)! a n = (n −1)! . a n =
Page 1213 and 1214:
3 ∑ 2 k ! . k = 0 3 ∑ 3 k !
Page 1215 and 1216:
a n =2n −7 a n =5n −1 a n =3n
Page 1217 and 1218:
3−6+9−12+15 −5+10−15+20−
Page 1219 and 1220:
c 10, 3, −4, −11, −18, −25,
Page 1221 and 1222:
a 15 , a 1 = 3 and d =6. a n = a
Page 1223 and 1224:
a 5 a 11 , n = 11. n =5 a 5 =19
Page 1225 and 1226:
a n =3n −4. S n = n 2 (
Page 1227 and 1228:
4, 12, 20, 28, 36, 44, … −7,
Page 1229 and 1230:
n 24 32 . ⎛ ⎞ 4 ⎠
Page 1231 and 1232:
a −150, −30, −15, −5, − 5
Page 1233 and 1234:
a 1 =3 3, 6, 12, 24, 48, 96, … 6
Page 1235 and 1236:
15 ∑ 2(3) i . i =1 S n
Page 1237 and 1238:
= 18 54 r = 6 18 … r = 1 3 a 1 .
Page 1239 and 1240:
S = a 1 1−r a 1 = 1,000 r = 0.8
Page 1241 and 1242:
P = 100 r = 0.05 n =12 t =
Page 1243 and 1244:
8, 24, 72, 216, 648, 1944, … 7,
Page 1245 and 1246:
a b
Page 1247 and 1248:
(a + b) 1 = a + b a 1 b 1 (a + b)
Page 1249 and 1250:
(x + y) 5 . (p + q) 7 .
Page 1251 and 1252:
⎛ n ⎝r ⎞ ⎠ = n! r !(n − r
Page 1253 and 1254:
(a + b) n = ⎛ n⎞ ⎝0⎠ an +
Page 1255 and 1256:
(r +1)st (r +1)st (r +1)
Page 1257 and 1258:
(x + y) 4 (a + b) 8 (m + n) 10 (
Page 1259 and 1260:
a n − a n −1 ,
Page 1261 and 1262:
⎛n⎞ ⎝1⎠ = n ⎛n⎞ ⎛n⎞
Page 1263 and 1264:
50 30 ∑ (4i −5) ∑ (−3i
Page 1265 and 1266:
(a + b) 9 (x − y) 7 y 4 ⎛
Page 1267:
(m −2n) 5 a ⎛8 ⎞ ⎝1⎠ b
Page 1270 and 1271:
a b a b a b c −10 a 4,
Page 1272 and 1273:
11 1 5 13 3 a 1 5 b 6 5 − 1
Page 1274 and 1275:
a b a b m =2 a =0 u =2 x =
Page 1276 and 1277:
a a a b b b c
Page 1278 and 1279:
a b a b y =5 w = −18 q =3
Page 1280:
a a a b b b c c c a a a b b b
Page 1283 and 1284:
x =2,x = 1 4 x = 3 2 , x =−1 2
Page 1285 and 1286:
10.8 −57, −55 30°, 60°, 9
Page 1287 and 1288:
a b (2, 0), (0, −2) (8, 0)
Page 1289 and 1290:
a b c d a b c 1 4 ,
Page 1291 and 1292:
a 10x +13y ≥ 260 b y
Page 1293 and 1294:
⎡ ⎣−5, 1 ⎤ ⎦. [−4, 2]
Page 1295 and 1296:
(3, 0), (0, 3) (5, 0), (0, −5)
Page 1297 and 1298:
a b c 1.75, $1.75 d
Page 1299 and 1300:
x + y ≥5 3x − y ≤6
Page 1301 and 1302:
a b a b c a b c c
Page 1303 and 1304:
a a a b b a b a a b b D: (
Page 1305 and 1306:
−6 5 2 m = 5 3 ; (0, −6) m
Page 1307 and 1308:
a 20x +15y ≥ 600 b a b a a
Page 1309 and 1310:
y =2x +5 y =− 4 5 x −5 a b
Page 1311 and 1312:
a C(x) =15x + 25, 500 b R(x) =32x c
Page 1313 and 1314:
a ⎧ +20p ≤ 160 ⎨30m ⎩2m +3p
Page 1315 and 1316:
(−2, 0, −3) x = 203 ;y = -25
Page 1317 and 1318:
⎧f ≥0 ⎪p ≥0 a ⎨ ⎪f + p
Page 1319 and 1320:
46 2 3 23 1 3 a b (−3, 2
Page 1321 and 1322:
a −7c 2 b −10y 2 z 3 a 5y 2 +3
Page 1323 and 1324:
12x 2 −5a 6w +19x 2 y a −22b
Page 1325 and 1326:
6r 3 +11r 2 s −8rs 3 4x +3 −5
Page 1327 and 1328:
(2x −3)(4x −1) ⎛ ⎝2y −7
Page 1329 and 1330:
(5w −6) 2 (m +7n) 2 7(b +3)(b
Page 1331 and 1332:
R(x) = 1 3 R(x) = 4(x x −2 x(x
Page 1333 and 1334:
3x(x +7) R(x) = x −7 r +8 m
Page 1335 and 1336:
a ≠ 2 3 x +3 x +4 y ≠0 1 6
Page 1337 and 1338:
a 7 9 b 2 5 c 1 3 2|p| 6p 7 a 3u3
Page 1339 and 1340:
a [2, ∞) b a (−∞,∞) b a
Page 1341 and 1342:
a 44 − 3 11 b 4 32 + 54 4 60 + 2
Page 1343 and 1344:
a (−∞, ∞) b c (−∞,
Page 1345 and 1346:
28 63 52i ⎛ ⎝y 2 +4 ⎞ ⎠
Page 1347 and 1348:
a b a b a x =2;b (2, −7) a
Page 1349 and 1350:
a a b g(x) = (x +2) 2 f (x) =
Page 1351 and 1352:
a (−∞, −4] ∪ [2, ∞) ⎡
Page 1353 and 1354:
a b a b a x =−4 b ⎛ ⎝
Page 1355 and 1356:
a b g(x) = x 2 +4 f (x) = x 2
Page 1357 and 1358:
a f (x) =(x +2) 2 −1 b a f (x) =
Page 1359:
u =−6±3 2 p =0,6 c =− 1 3 ±
Page 1362 and 1363:
w =−2,w =−8 m =1,m = 3 2 y =
Page 1364 and 1365:
a 64 = 4 3 a 27 = 3 3 b 1=x 0 b 1=
Page 1366 and 1367:
x =4 x =−1 x =−1,x =1 x =1
Page 1368 and 1369:
a b −4 a 3 b −1 a b log 5
Page 1370 and 1371:
a 48x −17 b 48x +5 c 48x 2 −10x
Page 1372 and 1373:
a (3, 1) b a (0, 0) b a (0,
Page 1374 and 1375:
y =− 1 20 (x −20)2 +20 y =−
Page 1376 and 1377:
a b (x +1)2 16 − ⎛ ⎝y −2
Page 1378 and 1379:
a (0, 0) b a (0, 0) b a (−
Page 1380 and 1381:
a x = ⎛ ⎝y +2 ⎞2 ⎠ −9 b
Page 1383 and 1384:
a b (x −1)2 4 − ⎛ ⎝y −1
Page 1385 and 1386:
(x −2) 2 + ⎛ ⎝y −2 ⎞ ⎠2
Page 1387 and 1388:
a b (x +1)2 16 − ⎛ ⎝y −3
Page 1389 and 1390:
−1,2,5,8,11 −3, −1, 1, 3, 5
Page 1391 and 1392:
a 11 = 59. a n =5n +4. a 1 = 21,
Page 1394:
3×3
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Intermediate Algebra - 2e, 2017a

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