algebra 2 final

convert the point (15,5π/3) from polar coordinates to rectangular coordinates

(15/2, 15√3 /2)

factor (2x-1)³-27 as the difference of two of twos cubes . then, simplify each factor

(2x-4)(4x²+2x+7)

complete the square for the expression x² -16x + ___. write the resulting expression as a binomial squared

(x-8)²

evaluate log₄1/16 by using mental math

-2

an automobile insurance company claim that its rates for teenage drivers average $410 less per year than the same coverage from another company in a random sample of 35 customers, the average saving was $390 per year, with standard deviation

-2.15; enough to reject

solve inequality -8x²-14x+4>-11

-2.5<x<0.75

for h(x)=2x²+6x-9 and k(x)=3x²-8x+8, find h(x)-2k(x)

-4x²+22x-25

simplify 10-x²-3x/x²+2x-8 identify any x-value for which the expression is undefined

-x-5/x+4 undfine x=2 and x=-4

solve the equation 2x/x²-7x-18=6x/x²+x-2

0 or 13

solve the polynomial equation 3x⁵+6x⁴-72x³=0 by factoring

0,-6,4

a group of 4 students went to drink pearl tea and study at a local tea shop . the shop offer 12 different flavors of pearl tea. what is the probability that at least 2 student ordered the same flavor? express your answer as a decimal, and round to the nearest ten thousandths

0.4271

if the probability that player A rolles at last one six is 0.6651, what is the probability that player rolls at least three sixes? express your answer as a decimal, and round to the nearest ten thousandths

0.5973

use the table to estimate the probability that a randomly-selected male is between 67 and 74.5 inches tall.

0.77

solve √6x-2 ≤3

1/3≤x≤11/6

write the expression ¹¹√10⁸ by using rational exponents

10^8/11

use synthetic substitution to evaluate the polynomial p(x)=x³-4x²+4x-5 for x=4

11

given f(x)=x³ and g(x)=4x+3, find g(f(3))

111

solveⁿ⁺⁸=32

12

find the sum for the arithmetic sequence∑

1313

the speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by the formula s=√30fd, where f is the coefficent of friction and d is the length ....

14

a building has a triangular floor with sides of 150,200 and 280 feet. to the nearest square foot, what is the area of the floor of the building

14,464

find all the real fourth roots of 16

2 and -2

find the number and type of solutions for x²-9x=8

2 real solution

what is the expected value of rolling the six-sided number cube represented by the net? express your answer as a decimal rounded to the nearest hundredth

2.83

find the missing terms in the arithmetic sequence 18,_,_,_,42

24,30,36

there are 256 players competing in a national chess championship tournment. the player compete until there is one winner. how many matches must be scheduled in order to complete the tournament.

255

find the 7th term of the geometric sequence with a₃=16 and a₅=64

256

given f(x)=2x²+8x-4 and g(x)=-5x+6 find (f-g)(x)

2x²+13x-10

simplify 2z³-6z²/z²-3z. identify any z-values for which the expression is undefine

2z;z≠3 or 0

express log₃6+log₃4.5 as a single logarithm. simplify, if possible

3

simplify the expression log₄64

3

solve the equation x-9=18/x

3 or 6

the volume V of a cylinder varies jointly with the height h and the radius squared r² and V=157cm³ when h=2cm and r². Find V when h=3cm and r²=36cm². round your answer to the nearest hundredth

339.12cm³

find the measure of the reference angle for ∅=142

38

factor the expression 81x⁶+24x³y³

3x³(3x+2y)(9x²-6xy+4y²)

use inverse operation to write the inverse of f(x)=x/4 -5

4(x+5)

find the complex conjugate of 3i + 4

4-3i

simplify the expression⁴√256z¹⁶ assume all variables are positive

4z⁴

solve x⁴-3x³-x²-27x-90=0 by finding all roots

5,-2, 3i, and -3i

what expression is equivalent to (3-2i)²

5-12i

solve log ₅x¹⁰-log₅x⁶=21

5^21/4

find the product (5x-3)(x³-5x+2)

5x⁴-3x₃-25x²+25x-6

expand the series .∑. and evaluate

6

divide by using long division (5x+6x³-8)÷(x-2)

6x³+x²+5x-8

multiply 8x⁴y²/3z³×9xy²z⁶/4y⁴

6x⁵z³

write the arithmetic series 5+1-3-7-11-15-19 in summation notation

7 ∑(9-4k) k=1

identify the degree of the monomial -5r³s⁵

8

solve √11x=3√x+2

9

what expression is equal to log 50

In50÷In10

leading coefficent, degree, and end behavior of the function p(x)=-5x⁴-6x²+6

LC=-5, D=4, x→-∞, p(x)→-∞, x→+∞,P(x)→-∞

rewrite the polynomial 12x²+6-7x⁵+3x³+7x⁴-5x

LC=-7, D=5, N term=6, quintic polynomial/-7x⁵+7x⁴+3x³+12x²-5x+6

an oil company plans to add a chemical to its gasoline to make it burn more clearly. the company conducts an experiment to see whether adding the chemical affects the gasoline milage of cars using their gasoline. state the null hypothesis

adding chemical equation does not affect gasoline milage

to maximize her expected winning, on which question should the contestant use ask expert? on which question should she use simplify it? what are her expected winning if she use the strategy

ask expert on history, simplify on math, =43925

the distance d in meters traveled by skateboard on a ramp is related to the time traveled t in seconds. this is modeled by the function d(t) =4.9t²-2.3t +5. what is the maximum distance the skateboard can travel, and at what time would it achieve this distance? round your answer to the nearest hundredth

d(t)= 4.73

evaluate the piecewise function

f(-1)=11 f(9)=1

write a quadratic function thats fits the points (0,6),(2,4) and (3,6)

f(x)= x²-3x+6

let g(x) be the transformation, vertical translation 3 units down, of f(x)= -4x + 8. Write the rule for g(x)

g(x)= -4x +5

let g(x) be a vertical shift of f(x)=-x up 4 units followed by a vertical stretch by a factor of 3. write the rule for g(x)

g(x)=-3x+12

write the exponential equation 2³=8

log₂8=3

solve the equation 6x/x-3=4x+6/x-3

no solution

solve x²+x-30/x-5=11 check your answer

no solution; undefine 5

add x+9/x-2 +-8x-39/x²+x-6 identify any x-values for which the expression is undefined

x+6/x+3; undefine -3

identify the roots of -3x³-21x²+72x+540=0. state the multiplicity of each root

x-5 factor once x+6 factor twice

substract 2x²-48/x²-16-x+6/x+4 identify any x-values for which the expression is undefined

x-6/x-4; undefine x=4 and x=-4

divide by using synthetic division (x²-9x+10)÷(x-2)

x-7+-4/x-2

solve the inequality 5/x+3<6 algebraically

x<-3 or x>-13/6

find the roots of the equation 30x-45=5x² by factoring

x=3

write an expression that represents the width of a rectangle with length x+5 and area x³+12x²+47x+60

x²+7x+12

simplofy -5/x-4+x-6/10/ x+3/x-4 assume that all expression are defined

x²-10x-26/10(x+3)

the daily profit of a bicycle store can be modeled by f(x)=x³-5x²+2x+2 where x is the number of bicycles sold. let g(x)=f(x+4). find the rule for g, and explain the meaning of the transformation in terms of daily profit

x³+7x²+10x-6

write the simplest polynomial function with zeros 5,-4 and ½

x³-3/2x²-39/2x+10

find the end behavior of the function p(x)=-8ⁿ

x→-∞,p(x)→0,x→+∞, p(x)→-∞

determine by composition whether f(x)=1/5x+4 and g(x)=5x-20

yes; f(g(x))=g(f(x))=x

find the geometric mean of -1/48 and -1/75

±1/60

solve the equation sin∅=0.3 to the nearest tenth. use the restriction 90°<∅<180°

∅=162.5

find the absolute value |-7-9i|

√130