Geometry Questions

has a vertical transverse axis of length 6 and asymptotes A hyperbola 8 8 of y 5and y x 8 Find the center of the hyperbola X 3 3 ts focal length and its eccentricity The center of the hyperbola is The focal length is 9 16 OF I

Write the equation for the graph shown 0 5 10 8 6 4 2 Oy 2 x 5 Oy 2 x 5 Oy 2 x 5 10 8 6 2 2 4 9 6 8 2 10 4 1 for 4 6

Solve the logarithmic equation algebraically log 3x log x 2 2 Enter the correct number in the box to complete your answer x Show Hints

23 Cameron deposits 120 000 in a bank account that earns 0 5 interest compounded yearly At the same time John deposits 135 000 in another bank account that earns 0 4 interest compounded yearly After one year who earns a greater amount of interest How much more He earned earns more interest 0 more dollars after one year

2 Mr Grindles invested 2 200 into an account compounded continuously at a rate of 4 How long until his money in the bank doub

4 1 Solve the following equation using properties of logarithms log loga z 6 2 H 2 Find the extraneous solution of the above equation if any HI no extraneous 4 2 2 no extraneous solution

Condense each expression to a single logarithm 3 log 2 2 log 5 2 log z 12 log y log 12 logg 7 4log 5 3 log 3 12 log 7 DRAG DROP THE log z y 2 3 712 logg log 84 54

3 The function y e 2 5 translates left left right ar

2 Consider the function g x 0 5 log x 8 12 Part A Which statement describes the transformation of the parent function f x log x to the given function A stretch by a factor of 0 5 translation 8 units to the left and 12 units down B compression by a factor of 0 5 translation 8 units to the right and 12 units up stretch by a factor of 0 5 translation 8 units to the right and 12 units up D compression by a factor of 0 5 translation 8 units to the left and 12 units down a b Part B What is the asymptote of the function g x

7 What is the value of x if log5x 2 A 25 B 10 C 100 D 2 2 E 5

21 Limone s Lemonade Corp has a savings plan for its employees If an employee makes an initial contribution of 1 000 00 the company pays 8 interest compounded quarterly What is the value of the account after 5 years A 1 485 95 B 59 049 000 C 1 500 00 D 1 469 33

Expand each logarithm 2 m n A 10 log m 2log n B 2logm 2logn 2log m 2 log n D 7log m 2log n log

1 For what value of x is the equation 22x 7 215 true A 16 B 4 11 D 44 E 2

Simplify condense the logarithm log 4 2 log a into a single logarithm

Expand Rewrite as a sum or difference of multiples of logarithms without exponents In x y

3 Which of the following is the solution to the equation 12e z 200 50 3 A In B In D ln 25 3 50 3 100 3

4 The graph of an exponential function g z is shown 343 Which statement best describes the value of g x as z approaches infinity A The value of g z approaches 1 B The value of g x equals 1 The value of g x equals 0 The value of g x approaches 0

Simplify the logarithm 2log a 3 log b log c

10 Select all the solutions to the equation In x ln 24 2x A 0 B 8 ce D 4 E 6

Use properties of logarithms to evaluate log4 6400 log4 100 A 2 41 B 6 31 1 81 D 3

Solve the following logarithmic equation for x log 2z 8 logs 42 10 X SHOW HINT

2 Solve the following logarithmic equation for x 3 log x 4 6 X

1 Question 1 23 Ov Find the range of y 2 1 SHOW HINT

5 Rewrite the equation in exponential form log b c A b c B C b a Dat b

5 The equation 34 81 rewritten in logarithmic form would be A log4 3 81 Blogg1 3 4 log4 81 3 log 81 4

Need Help Talk to a Tutor cos 2x 1 cos 2x O 0 1 points Previous Answers SPreCalc6 7 3 016 My Notes Ask Ye Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine as in Example 4 cos x

13 Prove these quadrilateral are parallelograms using the following formulas 2 x x x 325 40 6 5 A 6 2 y y 2 5 8 8 I

What is the volume of a hemisphere with a radius of 4 8ft rounded to the nearest tenth of a cubic foot Answer ft 3

Compound propositions s t and u are made of two atomic propositions p and q The truth table is given below What conclusion s can you make from this truth table about s t and u Write your answer in the space below Tip Consider the type of propositions tautology contradiction contingency whether they are logically equivalent or not as well as any other relation q u S F 201 F F p T T F LL T F T T F F T F F

The angles shown are compleme angles Determine the measures 42 What are the measures of 41

Suppose an arc of length s lies on the unit circle x y2 1 starting at point 1 C and terminating at the point x y Use a calculator to find the approximate coordinates x y Round coordinates to four decimal places when appropriate X COS B y sina 1 0 00 1 0 1 Are of lengths The unit circle x2 y2 1 1 0

1 Given that y y x is a function of x Find dy dx using implicit differentiation if y 2xy x 2 Find the tangent line to the graph y y x at the point 1 3 2 Given that x x t and y y t are two functions in the variable t and that

3 Given the following sign chart of the 1st derivative f x of y f x with f x 0 at x a b c d and e Draw a graph of y f x over the sign chart Label the points on your graph y f x corresponding to x a b c d and e f x 6

5 A box is shown below where x is in meter 2x 2x A Find total surface area S and the volume V in terms of x then express S in terms of V B Find dS in terms of dV and approximate the change in the surface S when

8 Is the following function continuous at x 1 Give the reason for your answer clearly If it s not continuous at x 1 is the discontinuity removable 9 Find the following anti derivatives A x x dx c f 1 dx dx x 4 ln x S E x 2x 3 x 1 1 x 3 x 1 x 1 5 x Show all steps B Stan x sec x dx D fxe dx

Find the supplementary The supplementary and Simplify your answer

Find the value of x and the value of both angles 13 5x 2 x 8

5 In the circle C above mzBCA x 12 and mAB 3x 24 What is the mZAFB X 12 3x 24 a 15 b 30 C 48 d 60 B 08 cup 12 H28 403 681 PP pp up A

e diagram belo Which of the following best describes line AB a Arc b Chord C Radius d Tangent Line Which of the following best describes line FD a Secant Line b Chord C Radius d Tangent Line Which of the following best describes EC a Arc b Chord C Radius d Tangent Line hich of the following best describes line BE a Secant Line b Chord B A D C F

6 Given the area of Circle Pis 128 cm determine the diameter to the nearest whole number de Area of a circle 128cm a b C d 41 cm 13 cm 20 cm 6 cm 2

Use the diagram below to answer 7 and 8 In circle B below the radius is 6 inches and the mzABD What is the area of sector CBD 7 a b C a d b C d 117 6 25T 6 117 2 8 What is the arc length of AD 25T 2 117 6 25T 6 117 2 25 2 Central angle 180 55 125 55 Area 125 TI X 360 2 of sector

In the circle below m2F 6x 40 and mzG 2y What is the mHEF 6 points 6x 20 8x 34 6x 40 180 20 94 180 94 94 20 20 20 M HEF 1 H being 8x134

4 Claire is considering investing in a new business In the first year there is a probability of 0 2 that the new business will lose 10 000 a probability of 0 4 that the new business will break even 0 loss or gain a probability of 0 3 that the new business will make 5 000 in profits and a probability of 0 1 that the new business will make 8 000 in profits a Claire should invest in the company if she makes a profit Should she invest Explain using expected values b If Claire s initial investment is 1 200 and the expected value for the new business stays constant how many years will it take for her to earn back her initial investment

5 Tanya is considering playing a game at the fair There are three different ones to choose from and it costs 2 to play a game The probabilities associated with the games are given in the table Game 1 Game 2 Game 3 Lose 2 0 55 0 15 0 20 Win 1 0 20 0 35 0 60 Win 4 0 25 0 50 0 20 a What is the expected value for playing each game b If Tanva decides she will play the game which game should she choose Explain

X 3 The point guard of a basketball team has to make a decision about whether or not to shoot a three point attempt or pass the ball to another player who will shoot a two point shot The point guard makes three point shots 30 percent of the time while his teammate makes the two point shot 48 percent of the time 3 P x X P x 0 30 2 0 48 0 0 70 0 0 52 a What is the expected value for each choice b Should he pass the ball or take the shot himself Explain

2 A game at the fair involves a wheel with seven sectors Two of the sectors are red two of the sectors are purple two of the sectors are yellow and one sector is blue Landing on the blue sector will give 3 points landing on a yellow sector will give 1 point landing on a purple sector will give 0 points and landing on a red sector will give 1 point a Let X the points you have after one spin Fill out the missing values in the table X P X b If you take one spin what is your expected value c What changes could you make to values assigned to outcomes to make the name fair

1 Miguel is playing a game in which a box contains four chips with numbers written on them Two of the chips have the number 1 one chip has the number 3 and the other chip has the number 5 Miguel must choose two chips and if both chips have the same number he wins 2 If the two chips he chooses have different numbers he loses 1 1 a Let X the amount of money Miguel will receive or owe Fill out the missing values in the table Hint The total possible outcomes are six because there are four chips and you are choosing two of them C X P x 2 7 1 b What is Miguel s expected value from playing the game Based on the expected value in the previous step how much money should Miguel expect to win or lose each time he plays d What value should be assigned to choosing two chips with the number 1 to make the game fair Explain your answer using a complete sentence and

holastic Student 1 i SRI College Career use the Fossil Life An In NG METHODS Tell whether you would us metric ratios to solve the triangle with the 5 a 12 b 21

ESTIONS Item 1 Item 2 Item 3 Item 4 8 CCSS G MG 3 Find the Area of regular polygon 6 ft

TIONS em 1 em 2 em 3 m 4 m 5 n6 n7 6 Find the area of each of the regular polygons shown be Polygon 14 49 ft 12 ft 9 63 in 337 05 695 52