algebra 2 semester 2 exam

simplify: (3x²/4y)⁻³

64y³/27x⁶

add: 5/x+4 + 2/x-4

7x-12/(x+4)(x-4)

simplify 10√162 - √405 -√200

80√2-9√5

expand (2x+1) using the binomial theorem and find the coefficient on the x² term

84

find the product: (8-2i)(5+i)

40-2t-2t²

solve: e0.05t=10

46.05

simplify: (4x⁸y⁸/2x³y¹⁰)²

4x¹⁰/y⁴

the following series: ∞∑3(2/3)k does this series coverage and what is the sum? k=1

6

the third term in the 5th row of pascal's triangle is

6

solve for x: -2x³+14x²-24x+20=0

5, 1+i, 1-i

solve for x: -1/2 - 4x/4 = 1/2 - 2x

5/6

find the y-intercept: y=2×4^x

2

simplify: 8e⁸/4e¹³

2/e⁵

simplify 6(4x+8y)+2(3x-6y)

30x+36y

simplify: 6d⁴/3e³f × 15e⁷f²/20d⁹

3e⁴f/2d⁵

multiply: x²-4/x+2 × 6x²/2x-4

3x²

what is the log₂16 ?

4

the ellipse: (x+1)/25 + (y-9)/4 = 1 is oriented and has focus at the ordered pair

(-1±√21, 9)

factor: 2x²+3x-9

(2x-3) (x+3)

factor: 4xy-3y-40x+30

(4x-3) (y-10)

find the focus for the parabola: x=1/32 y²

(8,0)

write the equation of an ellipse, in standard form, with vertices at (-7,0) and (7,0) and co-vertices at (0,-4) and (0,4).

(x-0)²/49 - (y-0)²/16 = 1

simplify: 5/x+5 / 1/x-6

- 5x/(6x+1)(x-5)

add: (5+i)-(6-12i)

-1+13i

add: -2x-6/9x + x+6/9x

-1/9

for an infinite geometric series to converge

-1<r<1

rationalize the denominator: √3 - √6 / √3 + √6

-3+2√2

if 2x³+4x⁴+11x-17=0 has 1 real root at x=1, what are the complex roots?

-3±5i/2

solve for x: -5x²-2=14x

-7±√39/5

the number of bacteria present in a culture, b, after t minutes is given by the equation: b=10e if there are 593 bacteria present after 9 minutes, find k

0.4536

how many positive zeroes does the following polynomial have? 5x²-3x-2

1 positive

given the binomial: (2y+3)¹⁰ find the coefficient on the y⁸ term

103680y⁸

what are the positive rational zeroes for 5x²-3x-2 ?

± 1/5, 2/5, 1, 2

simplify: √36x¹²y⁸

±6x⁶y⁴

what is the domain of a polynomial function?

all real numbers

for a hyperbola, the transverse axis is

always under the positive sequenced term

given the following series: -3, -3/2, 0, 3/2,... the series is

arithmetic difference = 3/2

find the 5th term for the geometric series: a₁=2, r=3

as=162

find the first term in the arithmetic series if the sum of the first 3 terms is 12 and the sum of the first 6 terms is 42

a₁=2

find the arithmetic sequence: -1, 1, 3, ...

a₈₀=157

given the equation of hyperbola: (y+3)²/16 - (x+1)²/25 = 1 the center of the hyperbola is the ordered pair

center (-1. -3)

the center of the following conic (x-3)²/36 - (y+2)²/81 =1 is

center (3,-2)

find the coordinates of the center and radius for the circle: x²+y²-4x+4y-17=0

center: (2,-2)

find the common difference for the arithmetic series if the 4th term is 3 and the 20th term is 35

d=2

what conic section is represented by the equation? x²+4y²=4

ellipse

write in exponential form: ln16=x

ex=16

given: f(x) = x³+4x²+2x-3 find f(-20)

f(-20)= -6443

the equation: -x²+4y²-2x-16y+11 when graphed is a

hyperbola

what conic section is represented by the equation? x²/25 - y²/9 =1

hyperbola

i⁵¹ is equivalent to

i⁵¹

which expression is equivalent to 3log4+log6-log48 write as a single log expression

log8

express as a single logarithm: logr12+logr45

logr540

write in logarithmic form: 3³=27

log₃27=3

the equation of a straight line is y=3/5x-7 the slope of the line is

m=3/5

any term in an arithmetic series can be found using the equation: an=a₁+(n-1)d what does the variable n represent in the equation?

n= number of terms

given the restricted domain for the polynomial function, f(x)=2x³-3x²-2x+1 as -3≤x≤3, what is the range of the function?

range -86≤f(x)≤34

find the sum of the arithmetic sequence with a₁=60; d=4; an=120

s= 1440

find the sum of the following arithmetic sequence: 8, 33/4, 17/2, 35/4,..., 50

s=4901

simplify: 3x²-12/4x²+8x / 6x-12/8x²+16x

x+2

multiply: (x-5)(x+2/x²-25)

x+2/x+5

simplify is possible: x²-2x-15/x²-x-20

x+3/x+4

find the roots of the polynomial equation x³-2x²+10x+136=0

x-3=±5i x=3±5i x=4

divide: x²+9x+20/x²-25 ÷ x+4/x-4

x-4/x-5

solve for x: 8x²=12x-4

x= 1/2 x=1

solve the following system of equations: 2x+5y=12 and x-3y=-2

x= 26/11 y=16/11

solve: 4³x-¹=1/256

x=-1

solve: 1/16=64^(3x+5)

x=-17/9

x⁵+2x⁴+2x³=0 has what kind of solutions

x=-1±i 3 real which are all 0 2 imaginary

solve for x: -6x-4x=6+5x

x=-2/5

solve for x: -2-2x=2+2x/5

x=-5/3

what are the zeroes for the polynomial?, 5x²-3x-2

x=1 x=-2/5

solve: ln(2x-1)=2

x=1+e²/2

what is the equation, in vertex form, of the parabola with vertex at (0,0) and focus at (5,0)?

x=1/20(y-0)+0

solve: x²-12x=28

x=14 x=-2

solve: x+1/5x - 2/4x = 1/20

x=2

solve the following equation: |x-2|=27

x=29 x=-25

evaluate: log₂8

x=3

solve: √2x-2+12=14

x=3

solve: log₂x+log₂(x-2)=log₂3

x=3 x=-1

solve: 2/x-5=x-6

x=4 x=7

find x to the nearest 0.01: 1.95^x=26

x=4.9

solve the following system of equations: -3x-9y=7 8x+9y=-1

x=6/5 y=-53/45

solve: 2^x+1-8^x-2

x=7/2

solve: x²/x+9 = 81/x+9

x=±9

find the equation of the polynomial with roots, 5, -4, 1

x³-2x²-19x+20=0

given the arithmetic series: an=-3{½} what is the common ratio

½