Deck 10: Equations of Lines and Simplifying Radical Expressions

Question 1

Factor.

- $x^{3}-216$

A) $(x+6)\left(x^{2}-6 x+36\right)$
B) $(x+216)\left(x^{2}-1\right)$
C) $(x-6)\left(x^{2}+6 x+36\right)$
D) $(x-6)\left(x^{2}+36\right)$

Answer 1

$(x-6)\left(x^{2}+6 x+36\right)$

Question 2

Factor.

- $t^{3}+64$

A) $(t-64)\left(t^{2}-1\right)$
B) $(t+4)\left(t^{2}+16\right)$
C) $(\mathrm{t}-4)\left(\mathrm{t}^{2}+4 \mathrm{t}+16\right)$
D) $(t+4)\left(t^{2}-4 t+16\right)$

Answer 2

$(t+4)\left(t^{2}-4 t+16\right)$

Question 3

Factor.

- $27 p^{3}-1$

A) $(3 p+1)\left(9 p^{2}-3 p+1\right)$
B) $(3 p-1)\left(9 p^{2}+1\right)$
C) $(3 \mathrm{p}-1)\left(9 \mathrm{p}^{2}+3 \mathrm{p}+1\right)$
D) $(27 p-1)\left(p^{2}+3 p+1\right)$

Answer 3

$(3 \mathrm{p}-1)\left(9 \mathrm{p}^{2}+3 \mathrm{p}+1\right)$

Question 4

Factor.

- $216 s^{3}+1$

A) $(6 s-1)\left(36 s^{2}+6 s+1\right)$
B) $(6 s+1)\left(36 s^{2}+1\right)$
C) $(216 s+1)\left(s^{2}-6 s+1\right)$
D) $(6 s+1)\left(36 s^{2}-6 s+1\right)$

Question 5

Factor.

- $1000 y^{3}-729$

A) $(1000 y-9)\left(y^{2}+90 y+81\right)$
B) $(10 y-9)\left(100 y^{2}+90 y+81\right)$
C) $(10 y-9)\left(100 y^{2}+81\right)$
D) $(10 y+9)\left(100 y^{2}-90 y+81\right)$

Question 6

Factor.

- $27 \mathrm{c}^{3}+125$

A) $(27 c+5)\left(c^{2}-15 c+25\right)$
B) $(3 c+5)\left(9 c^{2}-15 c+25\right)$
C) $(3 c-5)\left(9 c^{2}+15 c+25\right)$
D) $(3 c+5)\left(9 c^{2}+25\right)$

Question 7

Factor.

- $125-8 y^{3}$

A) $(5+2 y)\left(25-10 y+4 y^{2}\right)$
B) $(125-2 y)\left(1+10 y+4 y^{2}\right)$
C) $(5-2 y)\left(25+10 y+4 y^{2}\right)$
D) $(5-2 y)\left(25+4 y^{2}\right)$

Question 8

Factor.

- $1000 x^{3}+y^{3}$

A) $(10 x+y)\left(100 x^{2}-10 x y+y^{2}\right)$
B) $(10 x-y)\left(100 x^{2}+10 x y+y^{2}\right)$
C) $(10 x+y)\left(100 x^{2}+10 x y+y^{2}\right)$
D) $(10 x+y)\left(100 x^{2}+y^{2}\right)$

Question 9

Factor.

- $64 a^{3}-125 b^{3}$

A) $(4 a-5 b)\left(16 a^{2}+20 a b+25 b^{2}\right)$
B) $(64 a-5 b)\left(a^{2}+20 a b+25 b^{2}\right)$
C) $\left(4 a+5 b^{2}\right)\left(16 a^{2}-20 a b+25 b^{2}\right)$
D) $(4 a-5 b)\left(16 a^{2}+25 b^{2}\right)$

Question 10

Factor.

- $n^{3}-\frac{1}{8}$

A)
B)
C)
D)

Question 11

Factor.

- $5 r^{3}-40$

A) $5(r-10)\left(r^{2}+10 r+20\right)$
B) $5(r-2)\left(r^{2}+2 r+4\right)$
C) $5(r+2)\left(r^{2}-2 r+4\right)$
D) $5(r-2)\left(r^{2}-2 r+4\right)$

Question 12

Factor.

- $3 k^{3}+192$

A) $3(\mathrm{k}-4)\left(\mathrm{k}^{2}+4 \mathrm{k}+16\right)$
B) $3(\mathrm{k}+4)\left(\mathrm{k}^{2}+4 \mathrm{k}+16\right)$
C) $3(\mathrm{k}+4)\left(\mathrm{k}^{2}-4 \mathrm{k}+16\right)$
D) $3(\mathrm{k}+12)\left(\mathrm{k}^{2}-12 \mathrm{k}+48\right)$

Question 13

Factor.

- $162 x^{3}+750$

A) $6(3 x-5)\left(9 x^{2}+15 x+25\right)$
B) $6\left(27 x^{3}+125\right)$
C) $6(3 x+5)\left(9 x^{2}+25\right)$
D) $6(3 x+5)\left(9 x^{2}-15 x+25\right)$

Question 14

Factor.

- $5 r^{3}-320 s^{3}$

A) $(5 r-4 s)\left(r^{2}+20 r s+80 s^{2}\right)$
B) $5(r-4 s)\left(r^{2}+4 r s+16 s^{2}\right)$
C) $5(r+4 s)\left(r^{2}-4 r s+16 s^{2}\right)$
D) $5(r-4 s)\left(r^{2}+16 s^{2}\right)$

Question 15

Factor.

- $375 x^{3}-81 y^{3}$

A) $3(5 x-3 y)\left(25 x^{2}+15 x y+9 y^{2}\right)$
B) $3(5 x+3 y)\left(25 x^{2}-15 x y+9 y^{2}\right)$
C) $3(5 x-3 y)\left(25 x^{2}+15 x y-9 y^{2}\right)$
D) $3(5 x-3 y)\left(25 x^{2}-15 x y+9 y^{2}\right)$

Question 16

Factor.

- $343 y^{3} z-z$

A) $z(7 y+1)\left(49 y^{2}-7 y+1\right)$
B) $z(7 y-1)\left(49 y^{2}+7 y+1\right)$
C) $z(343 y-1)\left(y^{2}+7 y+1\right)$
D) $z(7 y-1)\left(49 y^{2}+1\right)$

Question 17

Factor.

- $128 \mathrm{k}^{3} \mathrm{~m}-250 \mathrm{~m}^{4}$

A) $2 m(64 k-5 m)\left(k^{2}+20 k m+25 m^{2}\right)$
B) $2 m\left(4 k+5 m^{2}\right)\left(16 k^{2}-20 k m+25 k m^{2}\right)$
C) $2 m(4 k-5 m)\left(16 k^{2}+20 k m+25 m^{2}\right)$
D) $\left(8 \mathrm{~km}-10 \mathrm{~m}^{2}\right)\left(16 \mathrm{k}^{2}+25 \mathrm{~m}^{2}\right)$

Question 18

Factor.

- $b^{6}$ - 1

A) $\left(b^{2}+1\right)\left(b^{4}-b^{2}+1\right)$
B) $(b+1)(b-1)\left(b^{2}+b+1\right)\left(b^{2}-b+1\right)$
C) $(b+1)(b-1)\left(b^{4}+b^{2}+1\right)$
D) $\left(b^{3}+1\right)\left(b^{3}-1\right)$

Question 19

Factor.

- $p^{6}+1$

A) $\left(p^{2}+1\right)\left(p^{4}-p^{2}+1\right)$
B) $(p+1)(p-1)\left(p^{2}+p+1\right)\left(p^{2}-p+1\right)$
C) $\left(\mathrm{p}^{3}+1\right)\left(\mathrm{p}^{3}-1\right)$
D) $(p+1)(p-1)\left(p^{4}-p^{2}+1\right)$

Question 20

Factor.

- $\mathrm{x}^{9}+\mathrm{y}^{6}$

A) $\left(x^{3}-y^{2}\right)\left(x^{6}-x^{3} y^{2}+y^{6}\right)$
B) $\left(x^{3}+y^{2}\right)\left(x^{6}-x^{3} y^{2}+y^{6}\right)$
C) $\left(\mathrm{x}^{3}+\mathrm{y}^{2}\right)\left(\mathrm{x}^{6}+\mathrm{x}^{3} \mathrm{y}^{2}+\mathrm{y}^{6}\right)$
D) $\left(x^{3}-y^{2}\right)\left(x^{6}+x^{3} y^{2}+y^{6}\right)$

Question 21

Factor.

- $27 x^{6}+343 y^{6}$

A) $\left(3 x^{3}+7 y^{3}\right)\left(9 x^{3}-21 x^{3} y^{3}+49 y^{3}\right)$
B) $\left(3 x^{2}+7 y^{2}\right)\left(9 x^{4}+49 y^{4}\right)$
C) $\left(3 x^{2}+7 y^{2}\right)\left(9 x^{4}-21 x^{2} y^{2}+49 y^{4}\right)$
D) $\left(3 x^{2}-7 y^{2}\right)\left(9 x^{4}+21 x^{2} y^{2}+49 y^{4}\right)$

Question 22

Factor.

- $a^{6}-64 b^{6}$

A) $(a+2 b)(a-2 b)\left(a^{2}+2 a b+4 b^{2}\right)\left(a^{2}-2 a b+4 b^{2}\right)$
B) $\left(a^{2}-4 b^{2}\right)\left(a^{4}+4 a^{2} b^{2}+16 b^{4}\right)$
C) $\left(a^{3}+8 b^{3}\right)\left(a^{3}-8 b^{3}\right)$
D) $(a+2 b)(a-2 b)\left(a^{4}+4 a^{2} b^{2}+16 b^{4}\right)$

Question 23

Find an equation of the line having the given slope and containing the given point.

- $m=-2,(3,4)$

A) $y=-2 x+\frac{1}{10}$
B) $y=-2 x-10$
C) $y=-2 x+10$
D) $y=-\frac{1}{2} x+10$

Question 24

Find an equation of the line having the given slope and containing the given point.

- $m=3,(-3,-7)$

A) $y=3 x-2$
B) $y=3 x-12$
C) $y=3 x+12$
D) $y=3 x+2$

Question 25

Find an equation of the line having the given slope and containing the given point.

- $m=-8 ;(7,-3)$

A) $y=-8 x+54$
B) $y=-8 x+51$
C) $y=-8 x+53$
D) $y=8 x+52$

Question 26

Find an equation of the line having the given slope and containing the given point.

- $m=-4$ ; $(-6,7)$

A) $y=-4 x-17$
B) $x=-4 y+17$
C) $y=-4 x+17$
D) $x=-4 y-17$

Question 27

Find an equation of the line having the given slope and containing the given point.

- $m=6,(0,8)$

A) $y=6 x+15$
B) $y=-6 x+6$
C) $y=6 x+8$
D) $y=6 x+13$

Question 28

Find an equation of the line having the given slope and containing the given point.

- $m=3$ ; $(0,-3)$

A) $y=-3 x-1$
B) $y=3 x+5$
C) $y=3 x+3$
D) $y=3 x-3$

Question 29

Find an equation of the line having the given slope and containing the given point.

- $m=6 ;(-7,0)$

A) $y=6 x-45$
B) $y=6 x-43$
C) $y=-6 x+38$
D) $y=6 x+42$

Question 30

Find an equation of the line having the given slope and containing the given point.

- $m=0 ;(0,3)$

A) $x=3$
B) $x=3 y$
C) $y=3 x$
D) $y=3$

Question 31

Find an equation of the line having the given slope and containing the given point.

- $m=0,(4,-1)$

A) $y=4$
B) $y=-1$
C) $x=4$
D) $x=-1$

Question 32

Find an equation of the line having the given slope and containing the given point.

- $\mathrm{m}=-\frac{4}{7},(4,5)$

A) $y=-\frac{4}{7} x+\frac{7}{51}$
B) $y=-\frac{7}{4} x-\frac{7}{51}$
C) $y=-\frac{4}{7} x+\frac{51}{7}$
D) $y=-\frac{4}{7} x-\frac{51}{7}$

Question 33

Find an equation of the line having the given slope and containing the given point.

- $\mathrm{m}=\frac{5}{4},(0,6)$

A) $y=-\frac{4}{5} x+\frac{1}{6}$
B) $y=\frac{5}{4} x-\frac{1}{6}$
C) $y=\frac{5}{4} x+6$
D) $y=-\frac{5}{4} x+6$

Question 34

Find an equation of the line containing the given pair of points

- $(-8,-60)$ and $(9,59)$

A) $y=\frac{1}{7} x-\frac{412}{7}$
B) $y=7 x-4$
C) $y=-7 x-116$
D) $y=-\frac{1}{7} x-\frac{428}{7}$

Question 35

Find an equation of the line containing the given pair of points

- $(3,-1)$ and $(4,-3)$

A) $y=-\frac{1}{2} x+\frac{1}{2}$
B) $y=-2 x+5$
C) $y=2 x-7$
D) $y=\frac{1}{2} x-\frac{5}{2}$

Question 36

Find an equation of the line containing the given pair of points

- $(1,-1)$ and $(-3,3)$

A) $y=x$
B) $y=-x$
C) $y=-\frac{3}{1} x$
D) $y=-x-1$

Question 37

Find an equation of the line containing the given pair of points

- $(5,2)$ and $(0,-9)$

A) $y=\frac{1}{3} x-9$
B) $y=\frac{11}{5} x-9$
C) $y=-\frac{11}{5} x-9$
D) $y=-\frac{1}{3} x-9$

Question 38

Find an equation of the line containing the given pair of points

- $(-5,0)$ and $(-7,3)$

A) $y=\frac{3}{2} x-\frac{15}{2}$
B) $y=-\frac{1}{2} x+\frac{13}{2}$
C) $y=\frac{1}{2} x+\frac{13}{2}$
D) $y=-\frac{3}{2} x-\frac{15}{2}$

Question 39

Find an equation of the line containing the given pair of points

- $(-2,-5)$ and $(-9,-3)$

A) $y=-\frac{1}{2} x-\frac{15}{2}$

B) $y=-\frac{2}{7} x-\frac{39}{7}$

C) $y=\frac{1}{2} x-\frac{15}{2}$

D) $y=\frac{2}{7} x-\frac{39}{7}$

Question 40

Find an equation of the line containing the given pair of points

- $(0,0)$ and $(4,-7)$

A) $y=-\frac{7}{4} x-7$
B) $y=\frac{7}{4} x$
C) $y=-\frac{7}{4} x$
D) $y=-\frac{4}{7} x$

Question 41

Find an equation of the line containing the given pair of points

- $(-3,5)$ and $(1,-6)$

A) $y=\frac{8}{7} x-\frac{34}{7}$

B) $y=-\frac{11}{4} x-\frac{13}{4}$

C) $y=\frac{11}{4} x-\frac{13}{4}$

D) $y=-\frac{8}{7} x-\frac{34}{7}$

Question 42

Find an equation of the line containing the given pair of points

- $(-9,-4)$ and $(-9,1)$

A) $x=-9$
B) $y=-4$
C) $1 x-4 y=0$
D) $-4 x+1 y=0$

Question 43

Find an equation of the line containing the given pair of points

- $(1,-7)$ and $(-9,-7)$

A) $\mathrm{x}=1$
B) $-9 x+1 y=0$
C) $1 x-9 y=0$
D) $y=-7$

Question 44

Find an equation of the line containing the given pair of points

- $\left(\frac{1}{5}, \frac{4}{5}\right)$ and $\left(-\frac{1}{10}, \frac{1}{10}\right)$

A) $y=-\frac{7}{3} x$
B) $y=\frac{7}{3} x-\frac{1}{5}$
C) $y=\frac{7}{3} x+\frac{1}{3}$
D) $y=\frac{7}{3} x$

Question 45

Find an equation of the line containing the given pair of points

- $\left(-\frac{1}{5}, \frac{2}{5}\right)$ and $\left(\frac{1}{5}, \frac{7}{5}\right)$

A) $y=\frac{5}{2} x$
B) $y=\frac{5}{2} x+\frac{9}{10}$
C) $y=5 x+9$
D) $y=\frac{5}{2} x-\frac{1}{2}$

Question 46

Simplify. If an expression does not represent a real number, state this.

- $-\sqrt[3]{512}$

A) -8
B) not a real number
C) 64
D) 8

Question 47

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[3]{343}$

A) 7
B) 18
C) not a real number
D) 49

Question 48

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[3]{-216}$

A) 7.348
B) -6
C) not a real number
D) 14.697

Question 49

Simplify. If an expression does not represent a real number, state this.

- $-\sqrt[3]{-8}$

A) 2
B) not a real number
C) -2
D) 1.414

Question 50

Simplify. If an expression does not represent a real number, state this.

- $-\sqrt[4]{81}$

A) not a real number
B) -9
C) 4.264
D) -3

Question 51

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[4]{1296}$

A) 36
B) not a real number
C) 6
D) 10.645

Question 52

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[4]{-81}$

A) not a real number
B) 3
C) -3
D) 9

Question 53

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[5]{3125}$

A) 6
B) not a real number
C) 5
D) 625

Question 54

Simplify. If an expression does not represent a real number, state this.

- $\sqrt[5]{-1024}$

A) -204.8
B) not a real number
C) 4
D) -4

Question 55

Simplify. If an expression does not represent a real number, state this.

- $-\sqrt[5]{243}$

A) - 3
B) -48.6
C) not a real number
D) 3

Question 56

Simplify. If an expression does not represent a real number, state this.

- $-\sqrt[7]{\mathrm{t}^{7}}$

A) - t
B) $\mathrm{t}^{49}$
C) $-\frac{t^{7}}{7}$
D) $\mathrm{t}$

Question 57

Simplify

- $\sqrt[3]{375}$

A) 19
B) 7
C) $3 \sqrt[3]{5}$
D) $5 \sqrt[3]{3}$

Question 58

Simplify

- $\sqrt[4]{1536}$

A) 39
B) $4 \sqrt[4]{6}$
C) $6 \sqrt[4]{4}$
D) 6

Question 59

Simplify

- $\sqrt[5]{64}$

A) $2 \sqrt[5]{4}$
B) 2
C) $4 \sqrt[5]{2}$
D) $2 \sqrt[5]{2}$

Question 60

Simplify

- $\sqrt[3]{\frac{1}{125}}$

A) 5
B) $\frac{1}{25}$
C) $\frac{1}{5}$
D) $\frac{1}{\sqrt[3]{5}}$

Question 61

Simplify

- $\sqrt[3]{\frac{125}{64}}$

A) $\frac{25}{16}$

B) $\frac{125}{64}$

C) $\frac{5}{64}$

D) $\frac{5}{4}$

Question 62

Simplify

- $\sqrt[4]{\frac{16}{625}}$

A) $\frac{8}{125}$
B) $\frac{4}{25}$
C) $\frac{2}{5}$
D) $\frac{2}{625}$

Question 63

Simplify

- $\sqrt[3]{\frac{3}{125}}$

A) $\frac{\sqrt[3]{3}}{125}$
B) $\frac{\sqrt[3]{3}}{5}$
C) $\frac{3}{5}$
D) $\frac{27}{5}$

Question 64

Simplify

- $\sqrt[4]{\frac{3}{625}}$

A) $\frac{\sqrt[4]{3}}{625}$
B) $\frac{3}{5}$
C) $\frac{81}{5}$
D) $\frac{\sqrt[4]{3}}{5}$

Question 65

Simplify

- $\sqrt[5]{\frac{11}{1024}}$

A) $\frac{\sqrt[5]{11}}{1024}$
B) $\frac{11}{20}$
C) $\frac{\sqrt[5]{11}}{4}$
D) $\frac{11}{4}$

Question 66

Name the set using the roster method.

-The set of whole numbers 2 through 5

A) $\{3,4,5\}$
B) $\{3,4\}$
C) $\{2,3,4,5\}$
D) $\{2,5\}$

Question 67

Name the set using the roster method.

-The set of even numbers between 1 and 5

A) $\{2,4\}$
B) $\{2,3,4\}$
C) $\varnothing$
D) $\{1,2,3,4,5\}$

Question 68

Name the set using the roster method.

-The set of multiples of 3 between 10 and 16

A) $\{11,13,14\}$
B) $\varnothing$
C) $\{12,15\}$
D) $\{10,12,15,16\}$

Question 69

Name the set using the roster method.

- $\{x \mid$ the square of $x$ is 36 $\}$

A) $\{18\}$
B) $\{6\}$
C) $\{-6,6\}$
D) $\{18,18\}$

Question 70

Name the set using the roster method.

- $\{x \mid x$ is the cube of 2 $\}$

A) $\{6\}$
B) $\{6,6\}$
C) $\{8,8\}$
D) $\{8\}$

Question 71

Classify the statement as true or false.

- $8 \in\{x \mid x$ is an even number $\}$

Question 72

Classify the statement as true or false.

- $15 \in\{x \mid x$ is an even number $\}$

Question 73

Classify the statement as true or false.

- $9 \in\{6,8,10,12\}$

Question 74

Classify the statement as true or false.

- $8 \in\{8,10,12,14\}$

Question 75

Classify the statement as true or false.

- $\frac{2}{9} \in\{\mathrm{x} \mid \mathrm{x}$ is an integer $\}$

Question 76

Classify the statement as true or false.

-Algebra $\in$ The set of all mathematics topics

Question 77

Classify the statement as true or false.

-Box turtle $\in$ The set of all mammals

Question 78

Classify the statement as true or false.

-Ace of hearts $\in$ The set of outcomes of drawing a card from a deck

Question 79

Classify the statement as true or false.

- $\{10\} \subseteq\{8,10,12,14\}$

Question 80

Classify the statement as true or false.

- $\{5,10\} \subseteq\{4,6,8,10\}$