Quadratic equations Questions and Answers

1 An election is being held for Pr Bailey Cate and Dan Each member votes by means of a ballot indicating their 1st choice 2nd choice en Ballot 1st A 1st 2nd B 2nd 3rd C 3rd 4th D 4th Ballot Ballot 1st 2nd 3rd 4th Ballot B A 1st 1st D 2nd B 2nd C C 3rd 3rd A 4th D 4th Ballot A 1st B 2nd C 3rd D 4th Ballot Ballot C 1st B 2nd D 3rd A 4th Ballot D 1st C 2nd Ballot C 1st B 2nd D 3rd A 4th B A 4th Ballot A 1st B 2nd 3rd C 3rd D 4th Ballot B 1st D 2nd C 3rd A 4th Ballot A 1st B 2nd C 3rd D 4th Ballot C 1st B 2nd D 3rd A 4th Construct the preference schedule for the election of Voters 1st Choice 2nd Choice 3rd Choice 4th Choice a Determine the number of 1st choice votes each member received Ballot C 1st B 2nd D 3rd A 4th Ballot A 1st B 2nd C 3rd D 4th CA A 1st B 2nd C 3rd D 4th Ballot Ballot B 1st D 2nd C 3rd A 4th Ballot C 1st B 2nd D 3rd A 4th

Find the SVD of A 2 3 2 2 2 3 Give an SVD for matrix A below Hint Work with AT A Type an exact answer using radicals as needed

Simplify cot x 1 sec x csc x to a single trigonometric func

Add Assume all variables are greater than or equal to zero 9 8x 3 x

1 Graph the function f x Use the graphing tool to graph the function Give the domain and range The domain of the function f x 3 Type your answer in interval notation The range of the function f x 1 X 4 1 X 4 3 Type your answer in interval notation is 0 00 is C 10 8 6 4 D 4 10 8 6 4 2 2 44 6 8 10 10

K Graph the function f x 2 3 Give the domain and range Which transformations are needed to graph the function f x 2x 4 3 Choose the correct answer below www OA The graph of f x 2 should be shifted to the left by 4 units and shifted down by 3 units B The graph of f x 2 should be shifted to the right by 4 units and shifted down by 3 units OC The graph of f x 2 should be shifted to the left by 4 units and shifted up by 3 units D The graph of f x 2x should be shifted to the right by 4 units and shifted up by 3 units Use the graphing tool to graph the function Click to enlarge graph 1 0 1 8 6 1 4 1 2 4 10 8 6 14 2 2 4 6 8 40 X 10

Solve the equation for x 8 9 125 64 The solution set is Simplify your answer Type an integer or

Graph the function f x 3x 1 Give the domain and range Use the graphing tool to graph the function The domain of the function f x 3x 1 is 0 00 Type your answer in interval notation The range of the function f x 3 1 is Type your answer in interval notation 10 B D 10 8 z 6 4 2 4 6 8 10

Graph the function f x 3 Give the domain and range Use the graphing tool to graph the function The domain of the function f x 3 1 is Type your answer in interval notation CXII 10 4 104 8 6 4 14 2 4 6 8 10 10

1 3 5 If g x find g 2 68 g 2 68 Type an integer or decimal rounded to the nearest thousandth as needed

For g x 1 find g Simplify your answer Type an integer or a fracti

5 10 points For the information given state the value of the five remaining trig functions of 0 If cos 0 and sin 0 0

11 Find the shortest distance between the following pairs of parallel lines x y z 2 1 3 t 1 1 4 x y z 1 0 1 t 1 1 4 a b c 1 d e 2 9

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

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

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

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

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

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

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

Sketch the graph of the inverse function 8 Ay 72225 Choose the correct graph below SOA OC A OB OD

Using the graph of f shown below find three intervals on which f is one to one making each interval as large as possible 6 Ay EXTE The intervals on which f is one to one are Simplify your answers and 1

Determine which graph is a function that is one to one on the interval co 1 but is not one to one on 00 00 Choose the correct graph below OA O C AY SEEEE OB OD Ay 2

K Wity that is not one to one on an interval I cannot have an inverse function on I Choose the correct answer below ACCE OA If a function is not one to one then at least one of the domain values of the function has more than one image OB If a function is not one to one then at least one of the range values of the function has more than one image OC The function can have an inverse as it is not one to one on the interval I

Simplify 5 3 2 26a b c 3 8a bc

Find the area of the triangle using the formula A bh 1 and verify that the formula A absin C gives the same result O Points 0 of 1 A 2 2 45 2 B 2 1 The area using bh is Simplify your answer Type an integer or a fraction Type an exact answer using radicals as needed Sav

Select the correct choice that completes the sentence below For any triangle ABC its area can be found using the formula A 1 zab LE ab sin C ab sin B

e A ZA LB LC 43 33 104 b degrees a 10 543 b C C 15 B

11 a 2 x 3y 9 a 1 x 6y 12 a K SS A 2 D 1 B 1 E 2 C 0

Find the explicit particular solution of the differential equation for the initial value provided dy x y 7x 0y y 1 10 10 dx The explicit particular solution of the differential equation is y

3

0 10 pts 399 Details Write an expression of the type A log x B or A log x B for the transformed logarithmic function shown below 5 4 3 2 1 6 5 4 3 2 1 1 2 3 A 5 6 1 2 3 4 5 6 f x Hint Use the vertical asymptote to find B To solve for A use a point on the graph and substitute the coordinates into y A log x B or y A log x B as appropriate

The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building Using this information find the height of the Empire State Building Your answer is feet

18 s 0 n 0 ec 0 sc 0 cot 0 6 1 10 18 d the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 6 1

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

First determine the quadrant for 0 then find x y and r and finally give all six trigonometric ratios for given the following information tan 0 and sin 0 0 e lives in quadrant I K 11 11 1 sin 0 2 cos 0 3 tan 0 4 sec 0 5 csc 0 6 cot 0