2nd semester study guide - Algebra 2 - Reeves

You have a coupon good for $6 off the price of any large pizza. You also get a 20% discount on any pizza if you show your student ID. How much more would you pay for a large pizza if the cashier applies the coupon first?

$1.20

How much money invested at 5% compounded continuously for 3 years will yield $820

$705.78

Y^2/ y-3 • y^2 - y - 6 / y^2 + 1y

(X-4)^2 / (x+3)(x+1) ; x cannot equal -3, -1

N^4 - 10n^2 + 24 / n^4 -9n^2 + 18

-(n^2 - 4) / n^2 - 3 ; n not equal +- root 6, +- root 3

8e ^4x+8 = 15

-1.843

Find the exact values of cos(3pi/4 radians) and sin(3pi/4 radians)

-1/2 , root 3/2

Find the 110 term of the sequence -7, 3, 13, 23, ...

-1097

Find the 2nd and 3rd term of the sequence -7, _,_, -22, -27, ...

-12, -17

Find the radian measure of an angle of -340

-17pi/9

-4/x+1 = -1/x+5

-19/3

Root 3 - root 6 / root 3 + root 6

-3 + 2 root 2

Find all the real square roots of 9/16

-3/4 and 3/4

6/x^2-9 - 1/x-3 = 1

-4

Find all the real fourth roots of 256/2401

-4/7 and 4/7

3 root of -125/343

-5/7

Log(x+9) - log x =3

0.0090

125^9x-2 = 150

0.3375

Find the cosine 315. Round to the answers to the nearest hundredth is necessary

0.71

The formula for the volume of a cone is V=1/3pir^2h. Find the radius, to the nearest hundredth, of a cone with a height of 3 in. And a volume of 12in^3

1.13 in

The formula for the volume of a sphere is V=4/3pir^3. Find the radius, to the nearest hundredth, of a sphere with a volume of 15 in^3

1.53

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers

1/q + 1/q+2 = 7/24 ; 6 and 8

In how many ways can 3 singers be selected form 5 who came to an audition?

10

Lynn are nd dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn's dm dawns results?

11/20

What is the sum of the geometric series 10 sigma x=1 6(2)^x

12,276

A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?

120 cartons

Find the degree measure of an angle of 7pi/10 radians

126

Justine earned 26,000 during the first year of her job at city hall. After each had she received a 3% raise. Find her total earnings during the first five years on the job.

138,037.53

Use the summation notation to write the series 19 + 54 + 59+ ... for 14 terms

14 sigma n=1 (44 + 5n)

65 degrees

155

A garden has width root 13 and length 7 root 13. What is the perimeter of the garden in simplist radical form?

16 root 13 units

Evaluate the series 8 sigma n=3 5n

165

Kepler's Third Law of Orbital Motion states that you can approximate the period P (in Earth years) it takes a planet to complete one orbit of the sun using the function P=d3/2, where d is the distance (in astronomical units, AU) from the planet to the sun. How many Earth years would it take for a planet that is 6.76 AU from the sun?

17.58

What is S7 for 6 - 24 + 96 - 384 + ...

19,662

Teesha is in the French club. There are 21 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that teesha will not be picked as a guide?

19/21

The sales of lawn mowers t years after a particular model is given by the function y = 5500 ln(9t + 4), wher ybis the number of mowers sold. How many mowers will be sold 4 years after s model is introduced? Round the answer to the nearest whole number.

20,289 mowers

Let f(x) = 3x + 2 and g(x) = 7x + 6. Find f• g and it's domain

21x^2 + 32x + 12; all real numbers except x= -6/7

55 degrees

235

If R is the total resistance for a parallel circuit with two resistors of resistance r1 and r2 then 1/R = 1/r1 + 1/r2. Find the resistance r2 if the total resistance R is 35 ohms and r2 is 80 ohms. Round your answer to the nearest ohm if necessary.

24 ohms

1250, __, 50, ...

250

21 root (x+6)^3 + 3 = 19

26

Evaluate the series 4 sigma n=1 (n+4)

26

-10 + root x + 8 = -4

28

3^1/3 • 9^1/3

3

3 root 162 / 3 root 2

3 3 root 3

This is a spinner used ina board game. What is the probability that the spinner will land on a multiple of 3 and 4?

3/8

The booster club sells a basketball games. Each meal comes with a choice of hamburger, pizza, hot dogs, cheeseburgers, or tacos, and choice of root beer, lemonade, milk, coffee, tea, cola. How many possible meal combinations are there?

30

4 root of 81x^20y^8

3x^5|y^2|

For the function g(x) = 14/x+3 find (g^-1 • g) (4)

4

3 root 48 + 3 root 2058 - 3 root 750

4 3 root 6

4 root 11 • 4 root 3

4 root 33

Root 20 + root 45 - root 5

4 root 5

Suppose you drop a tennis ball from a height of 8 feet. After the ball hits the floors, it rebounds to 89% of its pervious height. How high will the ball rebound after it's third bounce? Round to the nearest tenth

4.1 feet

Use the change of base formula to evaluate log3 91

4.106

In how many different orders can you line up 8 cars on a table

40320

(-5) + 0 + 5 + 10 + ... + 65

450

Solve log(4x+10) = 3

495/2

Log4 1/16 = -2

4^-2 = 1/16

3 root of 128a^13b^6

4a^4b^2 3 root of 2a

Log3 243

5

Use the graph of y= e^x to evaluate e^1.7 to four decimal places

5.4739

A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find p(red or blue)

5/8

(7 - root 2) (8+ root 2)

54 - root 2

Verne has 6 math books to line up on a shelf. Jenny has 4 english books to line up on a shelf. In how many more orders can Verne line up husband books than Jenny?

696

1/16 = 64^4x -3

7/12

A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single servejng of frozen yogurt with in topping?

72

2 4 root 2x + 6 4 root 2x

8 4 root 2x

Write the exponential expression 3x^3/8 in radical form

8 root 3x^3

-27^2/3

9

There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?

90 ways

What is the theoretical probability of being dealt exactly three 4s in a 5- cade Hans from a standard 52- card deck?

94/54145

Y = log5 (x-2)

A

The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria.

An= 21n

Y = -4/x+2 - 3

C

Y= 4/x

C

Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% communes continuously after that. Credit card B has an interest rate of 0.7% also compounded continuously. If you are going to make a $500 purchase and plan to nat make a single payment for 2.5 years which credit card should you go with? Write the equation showing the total balance at the end of 2.5 years for that card.

Card A; $514.20 = 500 • e^(0.8 • 2.5 + 1)

Find the exact values of cos 150 and sin 150

Cos = - root 3/2, sin = 1/2

Find the exact value of cos 300

Cos = 1/2

For the function f(x) = root x - 5, find f^-1. What is the range of f^-1?

F^-1(x) = x^2 + 25 ; y > 5

K^2 - k - 2 / k^2 - 4K - 5

K-2 / k-5 ; k cannot equal -1, 5

125^4/3 = 625

Log125 625 = 4/3

Log3 11p^3

Log3 11 + 3 log3 p

3 logb q + 6 logb v

Logb (q^3v^6)

2, -4, -16, -36, ...

No

4 3 root 3x + 5 3 root 10x

Not possible to simplify

Find the exact value of sin 120

Sin = root 3/2

Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2 inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length of less than 29 inches?

Triangle 4

What is the solution of root 2x + 4 - root x = 27

X = 0 and x = 16

Y = 7x^2 - 3

X = root y + 3/ 7

a group of college students is volunteering for help the homeless during their spring break. they are putting the finishing touches on a hosie they built. working alone, kaitlin can paint a ceraint oom in 3 hours. briana can paint the same toom in 7 hours. write an equations that can be used to find how long it will take them working together to paint the toom. how many hours will it take them to paint the room? if necessary, round your answer to the nearest hundredth.

X/3 + x/7 = 1; 2.1 hours

3 root 7x^7 • 3 root 9x^4

X^3 • 3 root 63x^2

Square root 7x (square root x - 7 square root 7)

Xroot 7 - 49root x

This graph of a function is a translation of y=2/x. What is an equation for the function

Y=2/x-5 -3

The half life of a certain radioactive material is 32 days. An initial amount of the material has a max of 361 kg. Write and exponential function that models the decay of this material. Find Joan much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

Y=361(1/2)^32x;0 kg

Y^2/ y-3 • y^2 - y - 6/y^2 + 1y

Y^2 + 2y/ y + 1; y cannot equal 3,0,-1

-2.4, 9.8, 22, 34.2, ...

Yes ; 12.2

Graph y = -2x + 3 and it's inverse

a