Quadratic equations Questions and Answers

Find the multiplicative inverse or reciprocal of 9 What is the multiplicative inverse of 9 Type an integer or a simplified fraction

Find the value of the expression 64 24 64 24 Simplify your answer

Question 5 Construct three different quadratic forms over R that has a matrix representation with eigenvalues 2 1 Answer

1 2 Use the auxilliary equation to find three solutions of the following difference equation yk 37yk 2 7yk 1 15yk 0 for all k Find a basis for the solution space of the equation in Question 1 2 Justify your answer by referring to the appropriate theorems

year Initial cost P Annual M O year Refurbishment cost Trade in value S of P Life years A 15 000 6 000 0 20 4 B 20 000 9 000 2 000 every 4 years 40 12 5 Company X has two options A and B for the manufacture of switches The estimated cash flows for each option are given below Use an annual worth comparison to determine which option is preferable at an interest rate of 20 per year First cost Annual cort ar A 30 5 B 10 12

Equations When a new charter school opened in 1990 there were 820 students enrolled Using function notation write a formula representing the number N of students attending this charter school t years after 1990 assuming that the student population N t a Decreases 30 students per year b Increases 17 per year c Increases 8 3 per year d Decreases 8 6 per year e Remains constant does not change g Increases 46 students per year N t N t N t N t N t

3 Neville and Luna go to a used book sale where every book is the same price Neville buys 5 books and Luna buys 4 books They run into their friend Hermione who really loves to read and discover that she has bought 19 books Hermione received a 10 discount but she still spent 5 more than Neville and Luna combined How much does one book cost

Replace the question mark by or whichever is correct 3 3 N 4 3 4

Replace the with the correct symbol 3 4 11

Fill in the blank below The symbols and are called absolute values

Replace the question mark by or whichever is correct 3 8 0 4 0 4

In the following problem replace the question mark with or whichever is correct 6 30 25 6 5 5 30 25

The point on the real number line whose coordinate is 0 is called the scale

For the following division ladder a Fill in the factor tree to complete each problem b Express the original number as a product of the prime factors 495 a 3 33 33 495 3 Simplify your answers 5 5

Write the fraction as a decimal rounded to the nearest hundredth 14 14 3

Write the decimal as a fraction in lowest terms 0 718 0 718 Type an integer or a simplified fraction

Simplify the fraction to lowest terms 10 35

Write the fraction in lowest terms 245 80 Select the correct choice below and fill in any answer boxes within your che O A www 245 The fraction written in lowest terms is 80 Simplify your answer Type an integer or a fraction 245 B The fraction is already in lowest terms 80

Rewrite the fraction 1 1 with 12 as the denominator 2

In an all boys school the heights of the student body are normally distributed with a mean of 67 inches and a standard deviation of 2 5 inches What percentage of the students are between 65 and 72 inches tall to the nearest tenth Watch Video Statistics Calculaton Show Examples

How much money will there be in an account at the end of 4 years if 16000 is deposited at 3 compounded semi annually Assume no withdrawals are made How much money will there be in the account at the end of 4 years Round to the nearest cent

full An object is thrown upward at a speed of 80 feet per second from a height of 90 feet off the ground following the path indicated by the red parabola The height h of the object after t seconds can be found using the equation h 16t 2 80 t 90 When will the height be 110 feet blue line Note that there are two times when this happens Enter your answers as decimals rounded to the nearest tenth of a second First time t Second time t When will the object reach the ground Enter your answer as a decimal rounded to the nearest tenth of a second t

Two shops rent canoes for a rental fee plus a fee per hour How many hours must a canoe be rented for the total costs to be the same Shop A Rental fee 8 Hourly fee 7 Shop B Previous Rental fee 2 Hourly fee 9 The total costs are the same when a canoe is rented for hours Ne

Translate the sentence into an equation using n to represent the unknown number Then solve the equation for n a number subtracted from 46 is 21 a b C d 46 2 21 72 67 46 21 72 72 67 46 21 22 72 25 46 2 21 72 75

Ive the equation below Check your solution s and clea x 2 4x 12 x 2 x 4 x 6x 8

12 1 point Alex originally paid 5200 for her car 1 year ago The value of her car now is 4 420 What is the percent of decrease in the value of her car 44 10 8 15

1 1 point The appropriate translation of the phrase 11 more than 20 percent of a number is 0 2n 11 True False

1 point The oil tank in your car is leaking at a rate of 1 2 oz per mile driven You drove 15 miles over to your grandma s house How many cups of oil did your car leak 18 cups 2 25 cups 144 cups 2 cups Previour

3 1 point Translate the phrase into an expression 11 more than one third of a number On 11 n 11 3n 11 11 3n Previous

2 1 point A rectangle has a length of 7 and a width of w What is an expression for the perimeter 7 w 7 2w 14 2w 14 4w

Click the following link to view nominal GDP data from FRED Then use that data to answer the following questions Real time data provided by Federal Reserve Economic Data FRED Federal Reserve Bank of Saint Louis For this exercise you will need to enter data from FRED for nominal gross domestic product GDP The following table gives the GDP deflator for the second quarter of 2023 and 2022 Using data from FRED enter the values for nominal GDP Series ID GDP for the two periods shown as 2023 04 01 and 2022 04 01 in FRED Enter your responses exactly as they appear in FRED Period 2023 Q2 GDP Deflator 131 52 Value bil

Show that the map RCX given by exp ix is a group homomorphism Determine its image and kernel

8 Use Laplace Transform to solve o t 2 cos t 7 7 dt e for o t Sho 0 all work Note Let s o t 20 points

and alternative hypothesis are as follows Ho p 0 02 Ha p 0 02 Suppose the manager inspects 120 products and finds that 3 are faulty What is the value of the z statistic Please round your standard error to five decimal places for calculations and round your answer to two decimal places O z 0 03 z 0 65 O z 0 39 O z 0 01 Question 6 A manufacturer must ensure that the rate f faulty products is less than 0 02 Suppose we do a hypothesis test with a significance level of 0 05 Symbolically the null and alternative hypothesis are as follows Ho p 0 02 H p 0 02 Suppose the manager inspects 120 products and finds that 3 are faulty A researcher gives a p value of 0 652 in her analysis Which of the following definitions is the correct definition of p value The population proportion The sample proportion O The probability of rejecting a true null hypothesis diste 3 pts of 100 IE the true faultymto in 0 02

Which function below has the greatest average rate of change from x 0 to x 5 1 Asymptote y 0 Asymptote yad 6 Asymptate y Asymptote y 4 7

Given the function x 3 4x determine the average rate of change from x 1 to x 2 O 0 2

The function f x x 6x 9x 3 is graphed at the right What is the complete set of interval s of increase for the function f x 00 3 u 1 00 3 1 1 3 O 00 00 N 4 N 3 f x x 6x2 9x 3

Find all distinct eigenvalues of A Then find the basic eigenvectors of A corresponding to each eigenvalue For each eigenvalue specify the number of basic eigenvectors corresponding to that eigenvalue then enter the eigenvalue followed by the basic eigenvectors corresponding hat eigenvalue 4 6 8 3 4 Number of distinct eigenvalues 1 Number of Vectors 1

5 4 1 x 3 x 3 3 x 4 x 4 xs 3 7 x 2 3 x 0 xz0 2 2 T 6 3x 3 x 0 0 x 4 x 4 1 3 2 1 3 5 1 3 2 1 2 AM Ky

3 Generate two additional pairs of values that belong in each proportional relationship Lemonade I cups Lemon Juice j cups Number of Days d 0 5 1 5 1 3 2 2 3 334 Number of Hours h 4 1 12 36 24 72 10 5 114 Writing Equations from Tables Use table 1 to write an equation to show how the number of hours h relates to the number of days d

3 Homework 1 5 To write and graph linear piecewise functions Graph or write the following piecewise functions x 3 x 2 x 2 1 2x 2x 5 x 3 15 x 3 y x 3 x 0 x 0 2 1 Period

Find the length of a www Type an exact answer using radicals as needed a 201

Add Simplify by removing a factor of 1 when possible 5z 2 3z 2 3z 18 6 2 3z 12z 9 The sum is Type your answer in factored form if factorable

Solve the following equation for x 5 3 22 MA LAUN SHARE CON 3 8 5

Solve the following equation for 2 16 Ox 1 x 2 A Ox 4 Ox 8 F

Given g x is a transformation of the graph f x determine which of the below correctly describe q x Asymptote y 0 34 3 2 1 1 9 C f x 4 34 g x 32 x 3 1 g x x 1 3 q x 32 x 3 1 O g x 1 2 x 1 3 Asymptote y 1 54 2 1 1 9 x

Review If the linear function is of the form g x mx b and the following points are on the function 4 3 and 6 2 which function correctly describes g x g x 2x 5 8 x x 1 8 x x 5 g x 2x 5 Question 2 14 4 points Review Below is a table of a partial set of values of the linear function x h x 1 1 1 2 5 6 1 If the function is of the form h x mx b what is the value of the parameter b 0 E 4 0 2 8 10

54 3 Or P 5x OY 5x Ov 2 Ov y Review What is the equation of the following parabola in vertex form T n 3 5 CURGE XA MEDIANGLE HOSINGE SZENIE C JODE PUBE Pente

A boat moves in the direction of a lighthouse whose windows are located 50 m apart above sea level From a window in the lighthouse you can see at 02 45 p m the boat at an angle of 7 8 below the horizontal plane At 3 p m is the corresponding angle 42 4 How fast is the boat traveling Answer in km h

a Given the complex numbers z 1 5 3 i and w 0 5 0 75i find the moduli and principal arguments of zu and answer in 3 decimal places b Solve the equation 25 24 4 4 0 and plot the solutions in the complex plane w giving your