Algebra Questions

4 Find the eigenvalues and eigenvectors for the matrix 35 3 046 001

Combine all 10 equations into one piecewise function Include correct domains for each part of the piecewise function y 2 x 1 5 x 3 y x 5 8 3 x 7

You observe a plane approaching overhead and assume that its speed is 550 miles per hour The angle of elevation of the plane is 16 at one time and 58 one minute later Approximate the altitude of the plane Round your answer to two decimal places miles

Find the exact location of all the relative and absolute extrema of the function Order your answers from smallest to largest x g x 2x 6x 3 with domain 2 2

Find the exact value of the sin 23 if 3 is in standard position with its terminal arm in Q2 and tan 21 20 5

Use the figure to evaluate a b a b and a a b b a 1 0 5 LO LO b

Use the properties of logarithms to condense the following logarithmic expression The solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions 2 log 4 log b log 5 2 log 4 log b log 5

Write the expression as a sum and or difference of logarithms Express powers as factors In x 3 5 x 0 x 5 In x 3 5 x Simplify your answer

Solve the equation Write the answer in terms of the natural logarithm 5e0 2x 6 In 12 0 2 www The solution set is Type an exact answer Simplify your answer Use a comma to separate answers as needed

Solve the following exponential equation Use logarithms to express the solution in its exact form In addition use a calculator to approximate the solution 7 97 The exact solution is given by z The approximate solution rounded to four decimal places is given by

Solve the equation Write the answer in terms of the natural logarithm 5e0 2x 13 ww The solution set is 4 7 Type an exact answer Simplify your answer Use a comma to separate answers as needed

18 An equation of a line is y x b Find the value of b if the line passes through the point 1 3

Ex 2 To join the local gym Karen pays a start up fee of 99 plus a monthly fee of 29 a Write an equation for the total cost C dollars for n months at the gym b Suppose Karen went for 23 months what was the total cost c If Karen paid a total of 505 how many months did she use the gym d Could the total cost ho exactly 6002 Justify your answor

Find the slope and y intercept of each line 1 y 2x 5 52 y 2 x M X S X 5 24 21312 5 Z Z 3 x y 1 0 M 1X4 17 2 12 23b 2 4 x 5 2y

Find the inverse function and graph both f x and f x on the same set of axes Check your work by looking for the required symmetry in the graphs f x 9 8x The inverse function is f1 x Choose the correct graph for f x and f x below Notice that the graph of f x is a solid blue line and the graph of f x is a dashed red line OA 16 Ay X 9 8 B 10 LC A 5 OC OD Ay

Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions log log7

12 The coordinates of point A are 1 5 If the slope of the line is name the coordinates of another point on the line

17 The slope of a plane taking off is 0 02 Assume the slope is constant What is the vertical height of the plane after it has travelled a horizontal distance of 450 m

Caitlyn wants to have 20 000 She deposits 14 000 into an account earning 8 1 interest and makes no additional deposits or withdrawals How long would the money need to be in the account for her to reach her goal Round the answers to 2 decimal places a simple interest years b compounded quarterly years c compounded continuously years

14 Marnie throws a softball straight up into the air The ball leaves her hand when it is exactly 5 ft from the ground The height h of the ball in feet can be written as a function of time t in seconds as h 1612 40t 5 a What is the maximum height the ball reaches b Marnie catches the ball 5 ft from the ground How long was the ball in the air

Solve the following exponential equation Express irrational solutions in exact form and as a decimal rounded to three decimal plac 41 6x 7x What is the exact answer Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an exact answer B There is no solution OA The solution set is What is the answer rounded to three decimal places Select the correct choice below and if necessary fill in the answer box to con A The solution set is Simplify your answer Type an integer or decimal rounded to three decimal places as needed B There is no solution

2 Graph f x 1 Write the equations of the asymptotes Write the domain and range 3 points 4 3 2 1 x 2 Domain Range La Equation of Horizontal Asymptote y Equation of Vertical Asymptote x GN S

Solve the following logarithmic equation Express irrational solutions in the exact form and as decimals 2 log 3 x 1 3 log 35 log 325 www Use a comma to separate answers as needed Simplify your answers Type exact answers using radicals as needed Express irrational solutions as decimals Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Use a comma to separate answers as needed Round to three decimal places as needed B The solution set has no irrational solutions

1 Is the table below an example of inverse variation Justify your choice 2 pts X 3 9 12 Justification y 24 86

Solve the following exponential equation Express irrational solutions in exact form and as a decim rounded to three decimal places 6 8 0 1 Ommy your answer Type all chans B There is no solution What is the answer rounded to three decimal places Select the correct choice below and if necessary fill in the answer box to complete your choice A The solution set is Simplify your answer Type an integer or decimal rounded to three decimal places as needed

Use a proportion to solve the problem below 41 of 78 is what

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A policeman is positioned on a highway without a radar gun He knows the distance from the construction zone to an exit is a quarter mile and the speed limit is 60 mph He times a car taking 10 seconds to go the quarter mile He times a truck taking 12 seconds to go the quarter mile Could he ticket them for speeding Justify your answer

S 1 2 and T Fun S R be the linear transformation defined by Find bases for Ker T and Im 7 Basis of Ker 7 Basis of Im 7 Enter functions using characteristic funtions writing 4 for y etc T f 2 21 2 4f 1 3f 2 6f 1

11 Use the synthetic division method to find the result when 2x 3x 4 is divided by x 2 If there is a remainder express the result in the form q x r x b x

3 2x a 86 b C

2 3x x 6 a b C

1 7x 3x 4 0 2 2x 6x 1 0 3 x2 5x 0 4 x 11 0 O b

6 x 4x

5 2x 5x 7 0

6 3 2x 9 a b

2 3x x 6

10 Factor to find all x intercepts of the function f x 2x 4x 8x 16

Solve the logarithmic equation log 20 x 5 1 log 20 X 6 Determine the equation to be solved after removing the logarithm x 5 x 6 20 Type an equation Do not simplify Select the correct choice below and if necessary fill in the answer box to com OA The solution set is Simplify your answer Type an exact answer Use a comma to separat B There is no solution

Solve the logarithmic equation log 20 x 5 1 log 20 X 6 Determine the equation to be solved after removing the logarithm Type an equation Do not simplify

If f x In x g x e x and h x x find the following a fog x What is the domain of fog b gof x What is the domain of g o f c fog 7 d foh x What is the domain of f o h e foh e c fog 7 21 Simplify your answer d f oh x 2 Simplify your answer The domain of fo h is 2 Type your answer in interval notation

Write the expression as a single logarithm log 4 x 49 5log 4 x 7 log 4 x 49 5log 4 x 7 Simplify your answer

3x If f x In x g x e x and h x x find the following a fog x What is the domain of fog b gof x What is the domain of g of c fog 7 d foh x What is the domain of f o h e foh e a fog x Simplify your answer The domain of fog is b gof x Simplify your answer The domain of g of is Type your answer in interval notation c fog 7 Simplify your answer d f x Simplify your answer Type your answer in interval notation

Express y as a function of x The constant C is a positive number In y In x In x 10 In C

Use the change of base formula and a calculator to evaluate the following logarithm log 5 Use the change of base formula with common logarithms logarithms with a base 10 to rewrite the given expression What is the resulting expression log log Use a calculator to evaluate the following logarithm log 5 log 5

Write the expression as a sum and or difference of logarithms Express powers as factors log 2 8x log 2 8x Type an exact answer in simplified form

Using the graph of f shown below find three intervals on which f is one to one making each interval as large as possible 2 Ay Q G The intervals on which f is one to one are 2 00 Simplify your answers co 41 4

Select the correct choice that completes the sentence below When the inequality 4x 7y 28 is solved for y the result is y Use integers or fractions for any numbers in the expression and the points the boundary line are sha

Use analytical and or graphical methods to determine the largest possible sets of points on which the following function has an inverse 3 f x 2 2 x BRESSER List the intervals on which the function has an inverse Make each interval as large as possible 2 Use a comma to separate answers as needed

The magnitude and direction of two forces acting on an object are 120 pounds S70 E and 60 pounds N68 E respectively Find the magnitude to the nearest hundredth of a pound and the direction angle to the nearest tenth of a degree of the resultant force