Quadratic equations Questions and Answers

Which Pythagorean identity is correct O sin 9 1 cos e tan 8 1 sec 8 O 1 cot csc 8 O 1 cos 4 tan 8

Which functions are correctly graphed 0 0 4 2 4 2 2 2 4 4 4 2 4 2 2 4 20 2 y 2 y Y 2 2 4 4 4 x f x x f x f x f x 1 8 H 1 3x2 3 1 I 3 0 x 2 x 1 2 2 0 0 3 1 0 x x 2 0 x 0 0 x

A student is asked to find the solution to this equation 2x 6 12 The student s work is shown 2x 6 12 6 12 9 18 equation because it is The student s equation is One way we know this is that the sum of 12 and 6 is to 9

Each side of the regular hexagon below measures 8 cm What is the area of the hexagon 60 963 square centimeters 1923 square centimeters 384 3 square centimeters 7683 square centimeters

Which set of transformations is needed to graph f x 2sin x 3 from the parent sine function O vertical compression by a factor of 2 vertical translation 3 units up reflection across the y axis O vertical compression by a factor of 2 vertical translation 3 units down reflection across the x axis O reflection across the x axis vertical stretching by a factor of 2 vertical translation 3 units up O reflection across the y axis vertical stretching by a factor of 2 vertical translation 3 units down

ighest monthly payment he can budget 3 EDJJ 18U spend What I

Fatima wants to find the value of sine given cot O cos 8 1 sece O sin cos e 1 csce O 1 cot csc 4 7 Which identity would be best for Fatima to use

1 0 O y x O y x O y x 1 V 0 1 Z 2 37 2 0 1 l 8 x y R 4 0 X 1 0

Which of the following is a simpler form of the expression O sec 0 O cos 0 CSC 8 tan o sin sec 8 cos a tan 8

In the triangle below which is equivalent to sinA A B OsinC OsinB cosA cosC C

What is 720 converted to radians 1 O 4 O X 4 4 W

Stan guessed on all 10 questions of a multiple choice quiz Each question has 4 answer choices What is the probabilit that he got at least 2 questions correct Round the answer to the nearest thousandth O 0 211 O 0 244 O 0 756 O 0 944 P k successes C p 1 p n x n k l kl

If generator polynomial is g x 1 x 2 x 3 find 1 design cyclic encoder 2 codeword if m 0110

Find the length x to the nearest whole number 46 500 27 X

Two students used synthetic division to divide 2 8 by I 2 Determine which solution is correct 2 1 0 2 8 244 1 2 2 12 ONeither student is correct Student B is correct B 210 2 2 4 4 2 1 2 2 4

5a x intercepts b y intercept c All vertical asymptotes d All horizontal asymptotes e a rational equation in expanded form 10 ONE OGORO 10 9 baadhi4

the second week of May Susan Simmons worked 52 hours Susan earns 7 70 an hour Her employer pays overtime for all hours worked in excess of 40 s per week and pays 1 5 times the hourly rate for overtime hours ulate the following for the second week of May round your responses to the nearest cent if necessary Regular pay amount Overtime pay 0 X S

Let the cost of producing a books be 100 x and a price demand equation be p a P x 100 z b P x 800 100 x c P x x 800 x 100 x d P x 800z 100 z 100 x Ob d

y AX B x C JAZX y A x Question is if y Ax 2 Bx c and the summation formula is shown in the image What if Ax 2 B x What is our summation formula

1 Solve log 35 x log 5 x 3 5 marks

2 The equation x y 2 is graphed to the right Reflect the graph across the line y x to obtain the graph of its inverse relation Use the graphing tool to graph the inverse of x y 2 Click to enlarge graph 10 6 2 10 8 6 4 2 2 14 6 10

fits a normal distribution with a mean of 70 beats per minute and standard deviation of 15 beats per minute Use this information and the normal curve to answer the questions below a What percentage of heart rates in this sample was below 85 beats per minute b What percentage of heart rates in this sample was above 100 beats per minute c What percentage of heart rates in this sample were between 40 and 85 beats per minute d Out of 300 participants how many of them would you expect to have a resting heart rate between 55 and 85 beats per minute

Given the function f x 6x 7 a Find f 1 b Graph f and f1 in the same rectangular coordinate system c Use interval notation to give the domain and the range of f and f 1 X 7 6 Use integers or fractions for any numbers in the expression a The inverse function is f1 x b Choose the correct graph which shows f x and f1 x graphed in the same coordinate system The graph of f x is shown as a solid line and the graph of f is shown as a dotted line O A OB O C D

2 T R5 R is a linear transformation with the standard matrix A a Find a basis and the dimension for Row A b Find a basis and the dimension for kernel T c Find a basis and the dimension for range T 11 1 10 2 102 1 1 14 0 1 10 2

Solve and write interval notation for the solution set Then graph the solution set 6x 1 5 OA The solution set is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression OB There is no solution Choose the correct graph below OA 5 OC 5 OE 4 4 3 N 2 2 3 3 4 4 OB 5 OD 5 OF 2 2 0 0

Refer to the following figure Draw the sign diagram for f and find the relative extrema of f Select 4 Ins ha x 3 increasing X 7 6 5 4 3 2 1 Select Select f x 0 f x 0 relative minimum relative maximum horizontal tangent undefined 0 1 2 tead It 3 4 5 X 3 Select 7 x 9 Select 6 7 8 9 10 11 12 Watch It 3 x 5 Select X 9 Select X 5 Select 9 x 12 Select 5 x 7 You are given the graph of a function f Determine the intervals where fis increasing constant or decreasing Enter your answers using interval notation If an answer does not exist enter DNE Select

Solve 4 sin x 3 2 sin x for 0 sx 360 Which of the following statements about the solution set is true 240 is the larger of two solutions O240 is the smaller of two solutions O 210 is the larger of two solutions 210 is the smaller of two solutions

You are given the graph of a function f Determine the intervals where fis increasing constant or decreasing Enter your answers using interval notation If an answer does not exist en ncreasing Constant decreasing 1 i

4 66 12 8 4 0 4 4 8 12 2 y x 2 2 x 4 5 k Launch 16 Change two numbers in the row below to fix the Marbleslide 20 X X

To solve for the lengths of the right triangle sides which equation is correct A x 5x 7 4x 7 B x 4x 7 5x 7 C x 5x 7 2 4x 7 D x 5x 7 4x 7 To solve for the lengths of the right triangle sides equation is correct Type A B C or D 5x 7 4x 7

et U 2 5 1 3 0 4 b u 39 0 8 2 7 4 c 2u 3u3 18 X 43 Compute each of the following A graphing calculator is recommended a U 3 18 d 4u 5u 43 3 0 3 4 4 8 20 4 12 40 10 35 20

6 Determine the surface area of the following shape 4 cm 6 cm 8 cm 5cm

C 1 C G Yukar daki e it aral klarla b l nm olan ekilde ka tane dik gen vard r A 6 B 7 C 8 D 9 E 10 35

g r 7 Q Write an equation for the function graphed above Round to 4 decimal places as needed

Math 1 Find the x intercept and y intercept of the line 2x 3y 12 and y int x int Add or subtract the following polynomials 5pts each

A sales person makes a base salary of 200 per week plus 14 commission on sales a Write a linear function to model the sales person s weekly salary S x for x dollars in sales b Evaluate S 7000 and interpret the meaning in the context of this problem

occurs Which of the following is the probability distribution Px x Px x 0 25 0 5 0 25 O X 0 2 X 0 1 2 X Z10X 2 X 0 1 2 Px x 0 33 0 33 0 33 Px x 0 25 0 75 0 Px x 0 0 5 0 5

Which inequality corresponds to the following graph 16 15 14 13 12 x 14

Car insurance companies want to keep track of the average cost per claim The current data in use for Auto Insurance F Us is an average of 2 200 for each claim with a standard deviation of 500 With this average the company can stay competitive with rates but not lose money However the statistician for the company believes that the cost of the averag claim has increased He pulled 40 recent claims and found the average to be 2 350 Which most restrictive level of significance would suggest that the company should raise rates a Critical z values O 1 O 2 5 5 10 Upper Tail Values 5 1 65 2 5 1 96 1 2 58

Use exponential regression to find an exponential function that best fits this data

12 h x 3x 2 g x 3x 3 Find h g x 14 h x x 5 g x x 5 Find h g x 16 g x x 5 h x x 4 Find g h x 18 g x 4x 5 h x x 2x Find g h x 20 g x 2x 5 h x 3x 4 Find g h 3

dentities 13 of using Other directions and hints This DQ is very similar to Example 5 and the subsequent Progress Check in Section 8 3 of the LabBook text Use this Example and or Progress Check to help you explain how to find the exact value of the given expression using Method 2 Using Identities You must show the method of using identities in your DQ Response You will not receive any credit if you use any other method such as sketching right triangles in your DQ Response However it is a good idea to check your final answer on your own by using the method of sketching right triangles Do NOT show this check in your DQ Response

Suppose that you decide to borrow 16 000 for a new car You can select one of the following loans each requiring regular monthly payments Installment Loan A three year loan at 6 3 Installment Loan B five year loan at 6 4 Use PMT C 1 1 n nt to complete parts a through c below

First find f g f g fg and 1 Then determine the domain for each function g f x 3x 5 g x x 1 f g x 4x 6 Simplify your answer What is the domain of f g 0 00 3 O 2 u 12 00 00 00 Simplify your answer

raph the trigon y sec Start by drawing three consecutive asymptotes Then plot two points one on each side of the second asymptote Finally click on the graph a function bu 2 4T

The graph below shows the experimental probability of a runner finishing in first place 1 in second place 2 in third place 3 or not placing 4 Which of the following describes the probability distribution PX X 08 0 7 0 6 05 04 0 3 0 2 01 0 1 Finishing Place constant symmetric O negatively skewed positively skewed 2 X 3 4

A city s cable cars travel by clamping onto a steel cable that circulates in a channel beneath the streets This cable is driven by a large 14 foot diameter pulley called a sheave The sheave turns at a rate of 2 revolutions per minute Find the speed of the cable car in mies per hour by determining the inear velocity of the cable 1 mi 5 280 ft Round your answer to the nearest tenth mph

Two numbers total 71 and have a difference of 13 Find the two numbers The larger number is and the smaller number is

Determine the domain and range of the function T 3 2 3 2 PE 4 2 3 A 20 3 4

Solve the system of equations by the substitution method 20x 4y 10 5x y 10 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution is Type an ordered pair Simplify your answer OB There are infinitely many solutions x y 20x 4y 10 or x y 5x y 10 OC There is no solution or