Multiply: ( 4 – 3 i ) ( − 7 – 2 i ) (4–3i)(-7–2i) ( 4 – 3 i ) ( − 7 – 2 i )

− 34 + 13 i -34+13i − 3 4 + 1 3 i

− 23 + 13 i -23+13i − 2 3 + 1 3 i

− 23 − 29 i -23-29i − 2 3 − 2 9 i

− 34 − 29 i -34-29i − 3 4 − 2 9 i

What is the complex conjugate of 4 − 3 i 4-3i 4 − 3 i ?

1 4 − 3 i \frac{1}{4-3i} 4 − 3 i 1

1 4 + 3 i \frac{1}{4+3i} 4 + 3 i 1

Solve: 10 − 13 x = x − 4 \sqrt{10-13x}=x-4 1 0 − 1 3 x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = x − 4

x = − 2 , − 3 x=-2,-3 x = − 2 , − 3

x = − 1 , − 6 x=-1,-6 x = − 1 , − 6

Find the domain and range: y = − x − 1 + 4 y=-\sqrt{x-1}+4 y = − x − 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 4

Domain: [ 1 , ∞ ) [1,∞) [ 1 , ∞ ) Range: ( − ∞ , 4 ] (-∞,4] ( − ∞ , 4 ]

Domain: ( − ∞ , ∞ ) \left(-\infty,\ \infty\right) ( − ∞ , ∞ ) Range: ( − ∞ , 4 ] \left(-∞,4\right] ( − ∞ , 4 ]

Domain: [ − 1. ∞ ) [-1.∞) [ − 1 . ∞ ) Range: [ 4 , ∞ ) [4,∞) [ 4 , ∞ )

Domain: [ 4 , ∞ ) [4,∞) [ 4 , ∞ ) Range: [ − 1 , ∞ ) [-1,∞) [ − 1 , ∞ )

Simplify: 4 x + 8 + 3 x − 5 \frac{4}{x+8}+\frac{3}{x-5} x + 8 4 + x − 5 3

7 x + 4 ( x − 5 ) ( x + 8 ) \frac{7x+4}{(x-5)(x+8)} ( x − 5 ) ( x + 8 ) 7 x + 4

7 x + 3 ( x − 5 ) ( x + 8 ) \frac{7x+3}{(x-5)(x+8)} ( x − 5 ) ( x + 8 ) 7 x + 3

2 x + 3 ( x − 5 ) ( x + 8 ) \frac{2x+3}{(x-5)(x+8)} ( x − 5 ) ( x + 8 ) 2 x + 3

2 x + 4 ( x − 5 ) ( x + 8 ) \frac{2x+4}{(x-5)(x+8)} ( x − 5 ) ( x + 8 ) 2 x + 4

Solve the rational inequality and state your solution in interval notation. 3 x − 7 x + 2 > 0 \frac{3x-7}{x+2}>0 x + 2 3 x − 7 > 0

( − ∞ , − 2 ) ∪ ( 7 3 , ∞ ) \left(-\infty,-2\right)\cup\left(\frac{7}{3},\ \infty\right) ( − ∞ , − 2 ) ∪ ( 3 7 , ∞ )

( − 2 , 7 3 ) \left(-2,\ \frac{7}{3}\right) ( − 2 , 3 7 )

( 7 3 , ∞ ) \left(\ \frac{7}{3},\ \infty\right) ( 3 7 , ∞ )

( − ∞ , − 2 ) ∪ [ 7 3 , ∞ ) \left(-\infty,-2\right)\cup\left[\frac{7}{3},\ \infty\right) ( − ∞ , − 2 ) ∪ [ 3 7 , ∞ )

Which function is graphed?

f ( x ) = − 3 ∣ x − 1 ∣ + 4 f(x)=-3|x-1|+4 f ( x ) = − 3 ∣ x − 1 ∣ + 4

f ( x ) = − ∣ x − 1 ∣ + 4 f(x)=-|x-1|+4 f ( x ) = − ∣ x − 1 ∣ + 4

f ( x ) = − 5 ∣ x + 1 ∣ + 4 f(x)=-5|x+1|+4 f ( x ) = − 5 ∣ x + 1 ∣ + 4

f ( x ) = − 3 ∣ x − 4 ∣ + 1 f(x)=-3|x-4|+1 f ( x ) = − 3 ∣ x − 4 ∣ + 1

Solve: − 2 ∣ 2 r + 4 ∣ = − 12 −2|2r+4|=-12 − 2 ∣ 2 r + 4 ∣ = − 1 2

{ 1 , − 5 } \left\{1,\ -5\right\} { 1 , − 5 }

{ ± 1 } \left\{\pm1\right\} { ± 1 }

Solve: ∣ 3 n + 12 ∣ = 2 n |3n+12|=2n ∣ 3 n + 1 2 ∣ = 2 n

− 12 , − 12 5 -12,-\frac{12}{5} − 1 2 , − 5 1 2

− 12 5 -\frac{12}{5} − 5 1 2

Solve: ∣ b − 8 ∣ + 10 > 22 |b-8|+10>22 ∣ b − 8 ∣ + 1 0 > 2 2

( − ∞ , − 4 ) ∪ ( 20 , ∞ ) \left(-\infty,\ -4\right)\cup\left(20,\ \infty\right) ( − ∞ , − 4 ) ∪ ( 2 0 , ∞ )

( − 4 , 20 ) \left(-4,\ 20\right) ( − 4 , 2 0 )

( − ∞ , − 4 ] ∪ [ 20 , ∞ ) \left(-\infty,\ -4\right]\cup\left[20,\ \infty\right) ( − ∞ , − 4 ] ∪ [ 2 0 , ∞ )

Write the logarithmic expression as a single logarithm log ⁡ 4 60 − log ⁡ 4 4 + log ⁡ 4 x \log_460-\log_44+\log_4x lo g 4 6 0 − lo g 4 4 + lo g 4 x

log ⁡ 4 15 x \log_415x lo g 4 1 5 x

log ⁡ 4 15 \log_415 lo g 4 1 5

log ⁡ 4 56 x \log_456x lo g 4 5 6 x

x log ⁡ 4 30 x\log_430 x lo g 4 3 0

Expand the logarithmic expression log ⁡ 5 x 4 y \log\frac{5x}{4y} lo g 4 y 5 x

log ⁡ 5 + log ⁡ x − log ⁡ 4 − log ⁡ y \log5+\log x-\log4-\log y lo g 5 + lo g x − lo g 4 − lo g y

log ⁡ 5 x + log ⁡ 4 y \log5x+\log4y lo g 5 x + lo g 4 y

log ⁡ 5 x − 4 log ⁡ y \log5x-4\log y lo g 5 x − 4 lo g y

5 log ⁡ x − 4 log ⁡ y 5\log x-4\log y 5 lo g x − 4 lo g y

Find the inverse of f ( x ) = log ⁡ 4 ( x + 4 ) f(x)=\log_4(x+4) f ( x ) = lo g 4 ( x + 4 )

f − 1 ( x ) = 4 x − 4 f^{-1}(x)=4^x-4 f − 1 ( x ) = 4 x − 4

f − 1 ( x ) = 4 ( x − 4 ) f^{-1}(x)=4^{(x-4)} f − 1 ( x ) = 4 ( x − 4 )

f − 1 ( x ) = 4 x + 4 f^{-1}(x)=4^x+4 f − 1 ( x ) = 4 x + 4

f − 1 ( x ) = 4 x f^{-1}(x)=4^x f − 1 ( x ) = 4 x

Solve for x: log ⁡ 6 x + log ⁡ 6 ( x − 5 ) = 2 \log_6x+\log_6(x-5)=2 lo g 6 x + lo g 6 ( x − 5 ) = 2

7 \sqrt{7} 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Solve for x. 8 + log ⁡ 6 ( x − 1 ) = 6 8+\log_6\left(x-1\right)=6 8 + lo g 6 ( x − 1 ) = 6

− 1331 8 -\frac{1331}{8} − 8 1 3 3 1

− 1 28 -\frac{1}{28} − 2 8 1

Solve for x: 3 e 2 x + 1 = 5 3e^{2x}+1=5 3 e 2 x + 1 = 5

x = 0.144 x=0.144 x = 0 . 1 4 4

x ≈ 0.131 x\approx0.131 x ≈ 0 . 1 3 1

x ≈ 0.187 x\approx0.187 x ≈ 0 . 1 8 7

x ≈ 0.151 x\approx0.151 x ≈ 0 . 1 5 1

Algebra 2 Final Exam

Authored by Teresa Fuston

Mathematics

9th - 11th Grade

CCSS covered

Used 37+ times

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50 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Multiply:
$(4–3i)(-7–2i)$

$-23+13i$

$-23-29i$

$-34-29i$

$-34+13i$

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the complex conjugate of $4-3i$ ?

$\frac{1}{4-3i}$

$\frac{1}{4+3i}$

$-4+3i$

$4+3i$

Tags

CCSS.HSN.CN.A.3

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify. $u^{-\frac{5}{4}}\cdot\left(u^{\frac{3}{2}}\right)^{\frac{3}{2}}$

$u^{\frac{1}{4}}$

$u$

$u^{\frac{7}{4}}$

$u^3$

Tags

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify the expression:
$3^{\frac{1}{3}}\cdot9^{\frac{1}{3}}$

1/3

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify:
$32^{\frac{3}{5}}$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Factor
$2x^2-13x-70$

$(2x-7)(x+10)$

$(7x+5)(x+2)$

$(2x+7)(x-10)$

$2(x+7)(x+10)$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Factor:
$x^2+16$

$\left(x+4\right)\left(x+4\right)$

$(x-4i)(x+4i)$

$(x-8)(x+8)$

$(x-4)(x+4)$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSN.CN.C.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve By Completing the Square:

$p^2-10p-52=0$

$5\pm\sqrt{77}$

$-5\pm\sqrt{77}$

$5\pm77$

$5+i\sqrt{77}$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve:
$x^2+12x-5=0$

$6\pm\sqrt{41}$

$-6\pm2\sqrt{41}$

$-6\pm\sqrt{41}$

$-6\pm\sqrt{164}$

Tags

CCSS.HSA.REI.B.4

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve:
$(2x+1)^{\frac{1}{3}}+3=6$

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.CED.A.1

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Algebra 2 Final Exam

Multiply: (4–3i)(−7–2i)(4–3i)(-7–2i)(4–3i)(−7–2i)

What is the complex conjugate of 4−3i4-3i4−3i ?

Simplify. u−54⋅(u32)32u^{-\frac{5}{4}}\cdot\left(u^{\frac{3}{2}}\right)^{\frac{3}{2}}u−45​⋅(u23​)23​

Simplify the expression: 313⋅9133^{\frac{1}{3}}\cdot9^{\frac{1}{3}}331​⋅931​

Simplify: 323532^{\frac{3}{5}}3253​

Factor 2x2−13x−702x^2-13x-702x2−13x−70

Factor: x2+16x^2+16x2+16

Solve By Completing the Square: p2−10p−52=0p^2-10p-52=0p2−10p−52=0

Solve: x2+12x−5=0x^2+12x-5=0x2+12x−5=0

Solve: (2x+1)13+3=6(2x+1)^{\frac{1}{3}}+3=6(2x+1)31​+3=6

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Multiply:
$(4–3i)(-7–2i)$

What is the complex conjugate of $4-3i$ ?

Simplify. $u^{-\frac{5}{4}}\cdot\left(u^{\frac{3}{2}}\right)^{\frac{3}{2}}$

Simplify the expression:
$3^{\frac{1}{3}}\cdot9^{\frac{1}{3}}$

Simplify:
$32^{\frac{3}{5}}$

Factor
$2x^2-13x-70$

Factor:
$x^2+16$

Solve By Completing the Square:

$p^2-10p-52=0$

Solve:
$x^2+12x-5=0$

Solve:
$(2x+1)^{\frac{1}{3}}+3=6$