new review guide (with answers).notebook · 2018-06-06 · y2 7y + 4y 28 y2 3y 28 x2 + 3x 10x 30...

NEW Review Guide (With Answers).notebook June 04, 2018

Answer Key

RealIntegerInteger

Integer

Natural

Rational

RationalRational

Rational

Irrational

Rational

RealRealRealReal

RealReal

AlwaysSometimes

AlwaysNever

102 2 = 100 |102 + 2||104| = 104

10 2 = 12 |40|40

the opposite of 3 squared 9 3 3

9negative 3 squared

32 12 14 7

99 105 5 6

110 + 85 = x25 = x 25 feet below sea level

22 (8) = x30 = x 30 degree difference

16 + 9 = x7 = x

6 + 3 106 + 30 36

8 6 + 248 + 2 50

25 (9 4) 25 5

213 (5)

6 + 3 +

(6)2 + (5)3

36 + 1255 6 2 5

36 125161

4030 + 10

undefined undefinedzero zero022

5x x2y 3y 75x x 2y 3y5 1 2 3

4a 10c 8 2a 74a 2a 8 74 10 28 7

21 28x + 8 + 10x 18x 13 10 18x 12 + 9x 9x 2

19x + 24 + 9x 13 19x 2610x + 11 12x 17 + 7x 9

15x 12y + 34 167x 140 19x 5

12x 145 15x 12y + 18

3 2x + 5 + x 7 5

1 4x y x y 1

3 20 x 1 y 1

1 ±13 -4

4 5 10 11 6 7

√ √4

-5 16 7

√-20 7√11

-33 -3 121

√-3 121

√ √3

9 7 x4

√3x2 7√

√ √5

x 25 6 x4 x1

√5x3 6x

√ √ √3

-3 9 5 y4 y1

√-9y2 5y√

√ √2

-2b 4 34 b8

√-4b5 34

√√ √6 36 5

√6 5

180 √

2 144 2 √24 22 288

√√

-4 49 6 √-28 6-4 294

√60n3

√ √2

4 15 n2 n1 √2n 15n

√√-6 2240x6

√ √8

-6 64 35 x6

√-48x3 35√

x3 34√240x6

√ √416 15 x6

√3x3 15√

√√

= 67 √ √

3 √√ √

49 x4 x1

√√x5

= √3

2 2 √

√ √y3

225 y6 y1

√8x2

15y3 y

√√ x28

12 3 √

√ √√4

8 3 + 2 16 3

3 11 -3 7√ √1 1

√ √8 3 + 8 3 16 3 √

√ √3

3 4 5 + 2 9 5

√ √6 5 + 6 5 12 5 √

√ √ √2

4 3 - 7 25 3

√ √2 3 - 35 3 -33 3 √

√ √2

24 s7 a5b2

41= 1 x8

29 46 105

k9 a6c7 10w5x5

21x6 16y7 30x9

42y416w10z6

a8c4 x6y8 m6n9

16x4y4 27x12y21 100x2y10

34 = 81 1 26

= 1 64

26 = 86 3n3

4x6 9y5 5x3y2

2y8 1 5x2y8

4x2 x2 3w4

2.204 x 1096.59 x 1034.7338 x 106

8.331 x 10-42.9 x 10-1 5.71 x 10-6

67 61,000 1600

0.0000291 0.0000008651

6 102 48 109

4.8 1010

5 102 11 1012

1.1 1013

polynomial 5x3 3x2 + 14x + 2 3

binomial

polynomial

trinomial

monomial

9z3 2z

7y5 + 3y2 + 2y + 2

7x5 + x3 2x2 + 4

5x2 + 2x 7

x2 - 7x - 20 5x4 - 15x3 + 10x2 -6y + 21y2 - 24 - 5y

21y2 - 11y - 24

4x + 16 - 3x4 + 9x2 - 2x + 5 n2 + 5n + 6n 2x2 + 3x + 4x2 - x + 1

-3x4 + 9x2 + 2x + 21 n2 + 11n 6x2 + 2x + 1

2x + 4y - 1 - x - 7 - 6yx - 2y - 8

5x2 + 12x - 17 - 13 + 4x2 - 8x9x2 + 4x - 30

3x + 10 + 6x - 159x - 5

x2 + 9x - 5x2 + 3x-4x2 + 12x

-5x2 + 8x + 12 + 3x2 - 4x + 8

-2x2 + 4x + 20

6x2 - 11x - 17 - 9x2 + 8x + 12

-3x2 - 3x - 5

5x + 3 + 2x + 5x + 3 + 2x

14x + 6 units 8y - 4 + 9y - 5 + 3y

20y - 9 units

x2 - 3x + 2 + x2 - 3x + 2 + 3x - 7 + 3x - 72x2 - 10 units

5x3 + 3y + 5x3 + 3y + 5x3 + 3y15x3 + 9y units

x5y - x2y2 -112m2n + 64mn2 -24mn x3z4 - 5x3z2

x3a5 - 8xa4ca5x3 - 8a4cx

8x5y2 + 60x2yz - 28x2y 3x3y2 + 6x4 + 3x3z

2x + 2x + 5x 2 + 5x 214x 4

Perimeter = 14x 4 feet

A = 2x (5x 2)

A = lw

Area = 10x2 4x feet2

P = add up all sides

A = 10x2 4x

x2 + 1x + 5x + 5x2 + 6x + 5

y2 7y + 4y 28y2 3y 28

x2 + 3x 10x 30x2 7x 30

a2 5a 4a + 20a2 9a + 20

2x2 2x + 6x 62x2 + 4x 6

12x2 + 2x + 12x + 212x2 + 14x + 2

25x2 35x + 35x 4925x2 49

6x2 + 18x + 12x + 366x2 + 30x + 36

4x3 + 12x2 8x + x2 + 3x 2

4x3 + 13x2 5x 2

GCF: 5 GCF: 3x GCF: 4 GCF: 4y

x (1 y) 5 (3m + 10) 6 (3n + 4) 7y (3x 4)

2x (2x3 11x + 9) 7x2 (3x3 + 5x + 7)

c3 (2c2d4 3c + 4) y (23y9 46y6 + 68y + 10)

x2 + 6x + 6x + 36

(x + 6) (x + 6)

x2 + 12x + 36

(x 6) (x 6)

x2 6x 6x + 36x2 12x + 36

x3 + 4x2 + 2x + 3x2 + 12x + 6x3 + 7x2 + 14x + 6

3x + 1 5a2 + ab 2b6z2 3y + 2z

4 + 5vw 4w5vw 4w + 4

x2 2x xy2z

2z + 6z2 3y

xy2z + x2 2x

Same Signs both positive Same Signs both negativeDifferent Signs Bigger positivemult. to 40, add to 14

(x + 10) (x + 4) mult. to 24, add to 5(x + 8) (x 3)

mult. to 20, add to 9(x 5) (x 4)

Same Signs both positive Same Signs Both negativemult. to 15, add to 16

(x + 15) (x + 1)mult. to 14, add to 9(x 7) (x 2)

mult. to 24, add to 11

(x 8) (x 3)

Same Signs both negative

4 (6x 5)24x 20 Perimeter = 24x 20 units

A = (6x 5)2A = s2

Area = 36x2 60x + 25 units2

P = add up all sides

A = 36x2 30x 30x + 25A = (6x 5) (6x 5)

36x2 60x + 25 36(2)2 60(2) + 25 36(2)2 60(2) + 25 144 120 + 25

The puppy will have 49 square feet of space to play.

2x 2x2x 7 = 15

+ 7+ 72x = 222 2 x = 11

22c + 88 = 22 88 88

22 22c = 5

22c = 110

20x + 16 2x = 14x 2822x + 16 = 14x 28

8 8x = 5.5

8x = 44

+12+ 12

x = 35

x = -15 73

2x - 53

= 5 (3)3

2x - 5 = 15+ 52x = 20

2 2x = 10

4x + 8 = 2x 16 2x 2x

6x + 8 = 16 8 86x = 24-6 -6x = 4

0.4y 3.6 = 0.3y + 1.23 (x + 2) = 7 (x 2)

4 4x = 5

4x = 20

+1.8x+1.8x5x 7.1 = 6.8+ 7.1 +7.15x = 13.95 5x = 2.78

3x + 6 = 7x 140.1

x = 48

0.1y = 4.8

3x + 7 = 3x + 6 3x

ContradictionNo Solution

3x7 ≠ 6

2x + 9 = 2x + 8 + 12x + 9 = 2x + 9 2x 2x

9 = 9Identity

Infinite Solutions

√x2 = 49√x = ± 7

x2 = 81-10 -10

√x2 = 81√ x = ± 92x2 = 50

2 2√x2 = 25√

x = ± 5

x = 2q

3x = 6q3 3

x = 6a

5x = 30a

5 r - 10y = x

r = 5x + 10yr - 10y = 5x y - z = 2x

2 y - z = x

Let c = the # of cups $7.50 + $2.50c = $12.50

7.50 + 2.50c = 12.50c = 2

You can buy 2 cups of food.

Let c = the # of chocolates $3c - $45 = $105

3c - 45 = 105c = 50

You must sell 50 chocolates.

Let w = the # of weeks $100 + $20w = $280

100 + 20w = 280

w = 9It will take you 9 weeks.

Let x = cost of 1st item Let x + 8 = cost of 2nd item x + x + 8 = $130

x + x + 8 = $1302x + 8 = $130

x = 61

The items cost $61 and $69.

Let n = 1st odd integer Let n + 2 = 2nd odd integer n + n + 2 = 84

n + n + 2 = 842n + 2 = 84

n = 43The integers

are -43 and -41.

0.5x + 6 < 9x < 6

60 -5 0

x ≤ -5

x ≤ -1

4x 3 > 21

5n + 3 ≥ 382x 4 > 17

2 + 7 ≤ 40 x

e ≤ 3600a ≥ 45a ≤ 50

Let x = # of tickets 12x + $2157 ≥ $4500

12x + 2157 ≥ 450012x ≥ 2343

x ≥ 195.25

They must sell at least

196 tickets.

Let x = # of boxes 3x + $12.75 ≤ $38

3x ≤ 25.25x ≤ 8.41666...

They can buy at most8 boxes.

3x + 12.75 ≤ 38

Let x = # of tickets 12x + $2157 ≥ $4500

12x + 2157 ≥ 450012x ≥ 2343

x ≥ 195.25

They must sell at least

196 tickets.

Let x = # of boxes 3x + $12.75 ≤ $38

3x ≤ 25.25x ≤ 8.41666...

They can buy at most8 boxes.

3x + 12.75 ≤ 38

0.5 pounds /week$20 /ticket

16x = 9

16x = 1441612

12x = 2512

50 n =1 3.2 1x = 160

1n = 1601 The actual distance between

the cities is 160 km.

Let n = the actual distance

14 ounces

10 teaspoons2 1

= 0.75 teaspoons/ ounce

6 laps

4 minutes2 1

= 0.75 minutes/ lap

20 pounds$14.99 = 0.7495 $0.75/ pound

50 pounds$37.99 = 0.7598 $0.76/ pound

The 20 pound bag is a better buy because it costs less per pound.

2 DVD's$26.50 = 13.25 $13.25/ DVD

3 DVD's$40.00 = 13.3333... $13.33/ DVD

The 2 pack of CD's is a better buy because it

costs less per DVD.

0.75 lb$6 $8/ pound

1 lb$8.50 $8.50/ pound

0.25 lb$2.25 $9/ poundC

4 oz = 0.25 lb

4 24 324

c = 4ty = 4x

The graph repersents a proportional relationship because it is a straight line that passes through the origin. (0, 0)

y = 2x b = 2c36

b = 2c b = 2 18b = 36

y = 0.99x c = 0.99a

n = 121.9047 ...

21n = 25602121 512 = 5 n You would expect

about 122 people to have green eyes.

Let n = # of people expected with green eyes

n = 4.5731 ...

1230n = 562512301230 375 = 15 n

You would expect about 5 cars to have headlight problems.

Let n = # of cars expected with headlight problems

3.6 = y

54 = 15y15 15

3.6 ft

little big x

9 28 12

21 = x

252 = 12x12 12

big little

0.875 87.5%

215% 220 3

2043OR

0.0425 1

0.666.6 %66 %3

2%50 1

0.2825 7

25 100

=48 = p

4800 = 100p100100 Mary earned $48 commission.

Let p = amount of commission

15 100

=12.75 = p

1275 = 100p100100 Jenny paid $72.25 for the boots.

discount = $12.75Sale Price = 85 - 12.75 = 72.25

Let p = amount of discount

p 99.50

7.5 100

7.4625 = p

746.25 = 100p100100

The bicycle costs $106.96.

tax = $7.46Total = 99.50 + 7.4625 = 106.9625

Let p = amount of tax

12 100

= 42 = p

4200 = 100p100100 42 people will

win a door prize.Let p = # of people who will win

5.25 100

= 1.155 = p

bill = 22+1.155 = 23.155

p 23.155

15 100

3.47325 = p

Total = 23.155 + 3.47325= 26.62825

= $26.63

Let p = tax Let p = tip

Find the discount first:

= 30 100

90 = n$300 - $90 = $210

Now find the sales tax on the discounted price:

= 8 100

16.8 = n

Let n = taxLet n = discount

discount = $90tax = $16.80

Total = 210 + 16.80= 226.80

= $226.80

I = PRTI = (1750)(0.0875)(2.5)I = 382.8125I = $382.81

Total = P + IT = 1750 + 382.81

Total = $2132.81

She started her bank account with $800.

I = PRT147 = P (0.1225)(1.5)147 = 0.18375P

0.18375 0.18375

800 = P

70 100

=92.8571 . . . = x

6500 = 70x7070 The original price

is $92.86.

Let x = original price

=650 = r

5200 = 8r8 It's a 650% increase

in weight.8

R = 650%

Let R = % increase

Percent error = 12.5%

Percent error = x 100 5 40 Percent error = 12.5%

Let R = % error

Percent error = 25%

Percent error = x 100 100 400 Percent error = 25%

Let R = % error

13.49 75.99

= 17.7523... = r

1349 = 75.99r

The price decreased about 17.8%.R ≈ 17.8%

75.99 75.99Let R = % increase

Total = 20 pens

1 40 (impossible)

1 (certain)3 + 4

= 3 20

#5 1 20

= 4 20

= 4 19

= 3 20

#8 3 50

= 8 20

#9 5 18

45 = n

900 = 20n20

Let n = # of times expected to land on the sun

20n = x 150 6

You would expect the spinner to land on the sun 45 times

n = 45

Total = 50 rolls

x 10,000 = 6800

skirtsblousesx3 4 = 12 12 outfits

coin #2coin #1x2 2 = 8 8 outcomesx

coin #32

= 17.5

11, 12, 15, 17, 18, 19, 20, 21, 25

median = 18mode = none

meanmean = 17.5

median

range 25 - 11 = 14

range = 14

1, 2, 3, 3, 4, 4, 5, 6, 6, 7 median = 4lower extreme = 1upper extreme = 7

1st Quartile = 33rd Quartile = 6

# of items

Electronics World

AIt's median time is 5 minutes faster, it also has a lower range and IQR (interquartile range)

50%75%

time is 5 minutes faster, it also has a lower range and IQR (interquartile range) so it's data are more clustered together.

A It's median

C = πdC = π 20C = 20π

C ≈ 62.8 mm

A = πr2

A = π (10)2

A = 100π

d = 20, so r = 10

A ≈ 314.2 mm2C = 62.8318... A = 314.1592...

C = πdC = π 10C = 10π C = 10π m

C = 2πr C = 2 π 10C = 20π C = 20π in

A = πr2 A = π (6)2

A = 36πd = 12, so r = 6

A = 36π in2

6 = rThe radius is 6 meters.

C = 2πr 12π = 2 π r 2π 2π

12π = 2 π r

radius = 6 in

√√A = πr2 36π = πr2

36π = πr2

36 = r2

±6 = r

The diameter is 12 inches

18 = d

C = πd18π = π d18π = πd π π

d = 18 so r = 9 A = πr2

A = π (9)2

A = 81πA = 81π cm2

A A = lwA = 9 8 A = 72

BA = 5 2A = 10

Total Area = 72 - 10Total Area = 62 yd2

A = lw

Total Area = A - B8 yd

SA = 550 m2

V = lwhV = (15)(5)(10)V = 750 m3

SA = 2lw + 2wh + 2hl = 2(15)(5) + 2(5)(10) + 2(10)(15) = 150 + 100 + 300

SA = 2πr2 + 2πrhSA = 2π(5)2 + 2π(5)(4)SA = 50π + 40πSA = 90π SA = 90π in2 SA ≈ 282.7 in2

V = πr2hV = π(5)2 4 V = 100π

V = 100π in3

V ≈ 314.2 in3

V = πr2h13

V = π(4)2 25

V = 133.3π

diameter = 8, so radius = 4

V = 133.3π ft3 V ≈ 418.9 ft3

Maxwell should find its volume because volume is the amount of space a 3dimensional figure occupies.

Area of front/backA = lw A = 3 x 2A = 6

frontside

top Area of Sides (2)A = lw A = 2 x 1A = 2

SA = 6 + 6 + 2 + 2

SA = 16 ft2

V = lwhV = (6)(2.5)(4)V = 60 in3

Volume of 1 box of crayons

240 60 = 14,400They need 14,400 cubic inches of space to store the crayons.

V = πr2h81π = π(3)2 h height = 9m81π = 9πh

81π = 9πh 9π9π

V = lwh40 = 4 2 h 40 = 8h

885 = h

height = 5m

48 + 37 + 111 = 196No

10 + 70= 80

8 10 = 80

180 - 80= 100

100 3 21 + 12= 75

21 - 6= 15 7 22 - 38

3 22 - 2= 64

vertical angles

x = 10

- x- 1x

8x = x + 70

7x = 70

complementary

x = 214

3x + 12 + x - 6 = 90

4x + 6 = 90- 64x = 84

supplementary

x = 2210

7x - 38 + 3x - 2 = 180

10x - 40 = 180+ 4010x = 220

38 + 68 + y = 180106 + y = 180

- 106 - 106y = 74

The other angle is 74

Let y = the measure of other angle

2x90 + 36 + 2x = 180

126 + 2x = 180- 126 - 126

2x = 542 2x = 27

x = 27

45 + 110 + 65 + x = 360220 + x = 360

- 220 - 220x = 140

The m W is 140

Let y = m W

x + x + 5 + x + 15 + 2x = 3605x + 20 = 360

- 20 - 20

x = 68

5x = 3405 5

m A = 68

m B = 68 + 5 = 73

m C = 68 + 15 = 83

m D = 2(68) = 136

12 - 21.

Vertical to 2 OR supp. to 4 or 1150 It is supplementary to 4 or 1

Alt. interior to 4 OR corresponding to 1 150

17 *The sum of the 3 angles of a triangle is 180

30Vertical to 5 OR alt. exterior to 1 OR

corresponding to 430

They are alternate exterior

They are correspondingThey are alternate interior

AB BAor

AC CAorC

Bscalene

AC CAor

AB BAorB

Cscaleneobtuse

6 + 8 > 914 > 8 (True) Yes

Sum: 6 + 9 = 15Difference: 9 6 = 3

The third must be greater than 3 inches, but less than 15 inches.

a2 + b2 = c2

162 + b2 = 302

256 + b2 = 900

b2 = 644- 256 - 256

√ b = ± 2 161 2 161 meters √√

a2 + b2 = c2

102 + 122 = c2

100 + 144 = c2

244 = c2√√ ± 2 61 = c √

2 61 feet√

50 fthouse

40 ftground

a2 + b2 = c2

402 + b2 = 502

1600 + b2 = 2500

b2 = 900- 1600 - 1600

√ b = ± 30

The tree hit the house 30 feet

above the ground.

y2 y1x2 x1

ΔyΔx

slope = =x1 y1 x2 y2

5 - 14 - -3 = 7

slope = 74

y2 y1x2 x1

x1 y1 x2 y2

5 - 63 - 2 = 1

slope = -1

y2 y1x2 x1

slope = -2y-intercept = 7

slope = y-intercept = -5

21 slope = 5

y-intercept = 1

xintercept (let y=0)

12 = 6x6

xint = 2

yintercept (let x=0)

y = 6x + 12

y = 122 = xyintercept = 12

y = 6(0) + 12

y = 6x + 120 = 6x + 12

4 4x = 4

xintercept = 4

y 4x = 3

y = 3yintercept = 3

y 4(0) = 3

y 4x = 30 4x = 34x = 3

y = x + 521 y = 5x 3 y = x 6

slope = -2y-intercept = 3up 2 left 1

down 2 right 1

ORslope = -2y-intercept = -4

up 2 left 1

down 2 right 1

y = 2x + 3

y = 2x + 3 TP

Test Point (3,2)x, y

y ≥ -2x - 4

2 ≥ -2(3) - 41 ≥ -10

12 = 6x6

xint = 2

y = 6x + 12

y = 122 = xyintercept = 12

y = 6(0) + 12

y = 6x + 120 = 6x + 12

4 4x = 4

xintercept = 4

y 4x = 3

y = 3yintercept = 3

y 4(0) = 3

y 4x = 30 4x = 34x = 3

y = x + 521 y = 5x 3 y = x 6

slope = -2y-intercept = 3up 2 left 1

down 2 right 1

ORslope = -2y-intercept = -4

up 2 left 1

down 2 right 1

y = 2x + 3

Test Point (3,2)x, y

y ≥ -2x - 4

2 ≥ -2(3) - 41 ≥ -10

y = x + 131

y = x 1slope = 1yintercept = 1

y = x 131y = x + 1

slope = yintercept = 1

(3, 2)

2 = 22 = 22 = (3) + 12 = 3 1Check (3, 2)

y = x 1 31y = x + 1

y = x + 2

down 2 right 3

∆y∆x

Slope23-

yintercept 2

up 2 right 1

∆y∆x

yintercept 3

y = 2x 3

down 2 right 3 up 2

right 1

Yes, every input has exactly one output

Not a function, the input -2 has 2 outputs

(2, 5)(2, -2) (4, 1)(3, 3) (6, 1){2, 3, 4, 6}{-2, 1, 3, 5}

Not a function, because the input 2 has 2 outputs.

y = 128 - 8x

If bottle is unopened, no servings have been poured, so x = 0.

y = 128 - 8(0)y = 128 - 0y = 128

has exactly one output.

Yes, every input

I agree with the boys claim. shown in the table is NOT a function

The relation

because some inputs have 2 outputs.If we reverse the x (input) and y (output),

the relation would be a function becauseeach inputs would have exactly 1 output.

Using the vertical line test -- Each vertical line drawn through the graph intersects at only 1 location.

Remember: The y-intercept is the value of y when x = 0

ΔyΔx

=slope = 44 = 1

Function Rule: y = x - 5

ΔyΔx

=slope = 24 = 2+2 +4

y-intercept = 1

y-intercept = -5 Function Rule y = 2x + 1

translationreflectionrotation

dilationlarger

smaller

translations, reflections and rotations are isometries

Rule: (x,y) (x, y) A' (3, 5)

Rule: (x,y) (x 2, y + 6) A' (5, 11)

Rule: (x,y) (2x, 2y) B' (4, 16)

Rule: (x,y) (y, x) R' (7, 4)

Rule: (x,y) (x, y) T' (3, 9)

A' (2, 8)T' (2, 2)

A (1, 4)T (1, 1)

M (3, 3)

H (3, 1)

M' (6, 6)

H' (6, 2)

Rule: (x,y) (2x, 2y)

B' (5, 5)C' (5, 8)

B (5, 5)C (5, 8)

A (2, 8) A' (2, 8)

Rule: (x,y) (x, y)

B' (2, 5)

D' (5, 2)

B (2, 5)

D (5, 2)

A (5, 5)

C (2, 2)

A' (5, 5)

C' (2, 2)

Rule: (x,y) (x, y)

new review guide (with answers).notebook · 2018-06-06 · y2 7y + 4y 28 y2 3y 28 x2 + 3x 10x 30...

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