Basic Math Questions and Answers

1 Which one of the following is the correct sign diagram for the function y x 2x O O O O y y O 2 0 0 0 2 Y 0 0 I 02 0 0 2 0 131 Y 0 0 02

A parabola can be drawn given a focus of 8 5 and a directrix of y 3 Write the equation of the parabola in any form 12 11 10 9 8 7 6 5 4 3 directrix 12 11 10 9 8 7 6 5 4 3 10 11 8 1 2 3 4 5 F 8 5 6 7 8 9 10 11 12 x

Watch help video A parabola can be drawn given a focus of 10 6 and a directrix of x 2 Write the equation of the parabola in any form F 10 6 111 12 directrix 54421 OPN 11 10 12 11 10 9 8 7 6 5 4 3 2 1 2 9 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12

A parabola can be drawn given a focus of 3 8 and a directrix of x 3 What can be said about the parabola 12 11 10 9 8 7 F 3 8 12 11 10 874 2 4 3 2 1 1 2 The parabola has a vertex at 2 3 4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12 1 directrix 10 has a p value of and i opens up

A parabola can be drawn given a focus of 0 6 and a directrix of x 6 Write the equation of the parabola in any form 2H098 75 321 directrix 12 11 10 4 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 7 8 9 10 F 0 6 11 12

A parabola with focus F 10 3 and directrix x 4 contains the point P x y X 4 D 4 y F 10 3 P x y First we will find an expression for the distance from P a random point on the parabola to the directrix Write an expression for PD and simplify if necessary PD

atch help video A parabola can be drawn given a focus of 6 1 and a directrix of x 2 Write the equation of the parabola in any form A 4 12 11 10 9 8 7 6 5 4 2 1 12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5 6F 6 1 9 10 11 12 1 1 I V

Name Daniela a True b False March 27 2023 z 1 2 points When foreign real national income rises domestic Real GDP rises ceteris paribus a increase left b C Benavides increase right decrease left decrease right 2 2 points Business optimism about future sales tends to expenditures shifting the AD curve to the ALWAYS Full grade 25 points AD right investment increase curve 2 investment shifts to the 3 2 points A simultaneous rise in both aggregate demand and short run aggregate supply will definitely a raise the price level but there is not enough information provided to know how Real GDP will change ric b lower Real GDP but there is not enough information provided to know how the price level will change c raise the price level and Real GDP d raise Real GDP but there is not enough information provided to know how the price level will change e raise the price level and lower Real GDP z

3 1 Is x 3 a factor of P x x x 17x 15 If so write P x as a product of two factors 4 2 Use synthetic division to divide 2x 3x 2x 8x 1 by x 1

3 3 Find all complex roots of x 2x 19x 20 0 3 4 Find all complex roots of x 2x 9x 18 0

7 In a theater there are 15 rows of chairs The first row has 20 chairs and each row after that has 4 more chairs than the previous row How many chairs are in the theater 8 What transformations of parent function f x 2 2 x result in g x x 43

In Exercises 47 52 find each expression for u 2i5j and v 3i 2j 47 u v 48 u v 49 2u 3v 50 2v 3u 51 2u 3v 52 2v 3u

for each transformed function g x fie the Parent function f x the transformation Parameters a b h k the massing rotation a transformation fable With three points domain range of a sketch and the Transformed a 9 x 2 3 x 4 1 Function b 9 x x 7 5 7 Parent Function a F x B F X Mapping notation Transformation table transformed Domain Transformed

Problem a Factor completely the quadratic polynomial b Factor completely the quartic polynomial 81 3x 10

Problem a Find a minimal smallest degree polynomial with integer coefficients whose real roots are 4 7 2 pts b Find a minimal smallest degree polynomial with integer coefficients whose real roots are 2 1 3 3 ots

According to Nieto and Bode 2008 the complex nature of schooling and the sociopolitical context of our schools can be unfair to many young people and their families and the situations that the live and go to school but teachers do not simply have to go along with reality The authors believe that our primary role as educators is to interrupt the cycle of inequality and oppression They believe that it will take courage creativity hard work and on going collaboration with like minded educators and other to change things We can begin the process by teaching well and with heart and soul by asking questions and by seeking social justice in our school p 29 Reflect on the statement above and describe ways you embark on changing structures in your classroom Identify the stakeholders you would have to bring on board to effect change

1 Which of the following are solutions to the inequality below Select all that apply 4d 45 d 7 d 12 d 2 d 3

elix is tohe townhouse for 2 200 000 To obtain the mortgage Felix is required to make a 17 down payment Felix obtains a 25 year mortgage with an interest rate of 5 5 Click the icon to view the table of monthly payments a Determine the amount of the required down payment b Determine the amount of the mortgage c Determine the monthly payment for principal and interest a Determine the amount of the required down payment b Determine the amount of the mortgage c Determine the monthly payment for principal and interest Round to the nearest cent Monthly Principal and Interest Payment per 1000 of Mortga 4 Rate 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 10 0 10 5 11 0 30 4 21604 4 49045 Number of Years 10 15 20 25 9 65607 6 90582 5 54598 4 74211 9 88859 7 14883 5 79960 5 00624 10 12451 7 39688 6 05980 5 27837 4 77415 10 36384 7 64993 6 32649 5 55832 5 06685 10 60655 7 90794 6 59956 5 84590 5 36822 10 85263 8 17083 6 87887 6 14087 5 67789 11 10205 8 43857 7 16431 6 44301 5 99551 11 35480 8 71107 7 45573 6 75207 6 32068 11 61085 8 98828 7 75299 7 06779 6 65302 11 87018 9 27012 8 05593 7 38991 6 99215 12 13276 9 55652 8 36440 7 71816 7 33765 12 39857 9 84740 8 67823 8 05227 12 66758 10 14267 8 99726 8 39196 12 93976 10 44225 9 32131 8 73697 13 21507 10 74605 9 65022 9 08701 13 49350 11 05399 9 98380 9 44182 13 77500 11 36597 10 32188 9 80113 7 68913 8 04623 8 40854 8 77572 9 14739 9 52323

One serving of a certain brand of yogurt contains 6 g of fat The low fat version contains 40 75 less fat per serving How many grams of fat does one serving the low fat yogurt contain The low fat yogurt contains g of fat Type an integer or decimal rounded to the nearest tenth as needed

Determine the simple interest The rate is an annual rate Assume 360 days in a yea p 330 r 6 25 t 2 75 years The simple interest is Round to the nearest cent as needed

According to the Original Tipping Page www tipping org it is appropriate to tip waiters and waitresses 15 2 of the pre tax restaurant bill The Leeseburgs dinner costs 53 00 before tax and the tax rate is 6 a What is the tax on the Leeseburgs dinner b If the Leeseburgs decide to tip 17 of the pre tax bill how much is the tip c What is the total cost of the dinner including the tax and tip www Round to the nearest cent as needed a The amount of tax paid is b The tip is Round to the nearest cent as needed c The total cost is Round to the nearest cent as needed

wed 35900 from a bank for 6 months A friend was cosigner of the man s personal note The bank collected 4 simple interest on the date of maturity a How much did the man pay for the use of the money b Determine the amount he repaid to the bank on the due date of the note a The man paid for the use of the money b On the due date of the note the man repaid to the bank

by a piece of string of length 33 metres The kite is flying 12 metres directly above the ground 0 O one 1 7 with the ground O 1 COS Which one of the following is a good estimate for the angle of inclination of the piece of string with the ground O 1 sin O 1 COS sin 33 m 1 1 tan 11 11 4 1 El 4 21 12 m 4 ground

2 Consider the following polynomial x x 12 p x Which one of the following is correct O p 4 0 Op 6 0 O p 3 0 O p 4 0 O p 1 0

1 Find f 0 when f is the function given by the rule x 2 f x x 1 O 1 O 0 O 2 0 2 O 1

Find the argument of the complex number 0 4i in the interval 0 0 360 rounding to the nearest tenth of a degree if necessary

mework Question 25 6 3 93 Find the exact value of sin 1 sin 2 sin 3 sin 358 sin 359 sin 10 sin 2 sin 3 sin 358 sin 359

If tan 0 4 find the value of tan 0 tan 0 tan 0 2 tan 0 tan 0 tan 0 2 E Simplify your answer

mework Question 23 6 2 95 HW Score 56 76 21 of 37 points O Points 0 of 1 f 0 sin 0 g 0 cos 0 Find the exact value of the function g 0 if 0 45 Do not use a calculator Select the correct choice below and fill in any answer boxes within your choice OA g 0 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression OB The function value is undefined E

10x Find the average rate of change of f from 0 to 3 f x sin The average rate of change is Simplify your answer including any radicals Type an exact answer using as needed Use integers or fractions

omework A one lane highway runs through a tunnel in the shape of one half a sine curve cycle The opening is 24 feet wide at road level and is 20 feet tall at its highest point a Find an equation for the sine curve that fits the opening Place the origin at the left end of the opening Part 1 of 2 b If the road is 12 feet wide with 6 foot shoulders on each side what is the height of the tunnel at the edge of the road 24 ft 20 ft 12 ft

Find fog x and gof x and graph each of these functions f x 3x g x cos x fog x 3 cos x Simplify your answer gof x Simplify your answer

Use transformations to graph y 5x Use the graphing tool to graph the function

Solve for n n 2 31n 0 Write each solution as an integer solutions separate them with con

A parabola can be drawn given a focus of 8 7 and a directrix of Y 1 Write the equation of the parabola in any form F 8 7 4 I I i 12 11 10 9876 5 4 3 2 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 y 11 12 1 I 1 1 directrix 1 2 3 4 5 6 7 8 9 10 11 12 X

osage The doctor orders 60 mg of a certain medication The vials of this medication contain 1 gram of the drug in a 10 mL solution How much of the drug does the nurse need to draw in ml mL Round to one decimal place The nurse should draw

Prove mathematically that sample correlation is between 1 and 1

decimals Your Answer Answer Question 5 2 points Suppose that 8 arcsin 1 9 in the first quadrant What is cos 0 2 round to 4 decimals Your Answer

Find the inverse function of f x Of x 1 Of x log2 x 2 Of x 2x 2 1 2 2 None of the above 2 2

Consider f x 2x 7 fog 3 gof 3 fog x go f x g x 3x 2

0 Select one 01 Economic Indicators Question 7 What was the inflation rate between 2013 and 2014 O 1 1 6 1 5 O 2 6 The following data comes from the U S Department of Labor Bureau of Labor Statistics via the US Inflation Calculator https www usinflationcalculator com inflation consumer price index and annual percent changes from 1913 to 2008 Accessed 5 27 20 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 YEAR 218 1 224 9 229 6 233 0 236 7 237 0 240 0 245 1 251 1 255 7 CPI Inflation Rate X

2 Give a formula using correct function notation for the SINE function represented by the following graph 3 2 a KIN TT 3TT N

Which number is NOT a solution for x 5 15

DISCUSSION PROMPTS Repeated Doubling Teni Answer each question using any appropriate math notation noisonin erit of telaional notiomut aid 1 If you were asked to start with the number 5 and double it three times how would you write this problem using math notation 2 If you were asked to start with the number 5 and double it nine times how would you write this problem using math notation 1130 3 If you were asked to start with the number 5 and double it one hundred times how would you write this problem using math notation

1 Find the first 4 terms and the 8th term of the sequence n 2n

3 A sequence is defined recursively by a 6 a2 2 ak 2 4ak 1 3ak Find the first 5 terms rbr3 est TE Blea voy tud len and slae aed629000 2 ti lisz goy bib 290000 vnen

What is the shape of the base rectangle with dimensions What is the formula for the area of this shape What is the area of the base 3 in 2 in 4 in

Write down the three inequalities satisfied by all the points in the unshaded region X y 2x y 000 2 2 2 y 10 9 8 7 6 LO 5 4 3 2 1

1 Drawing the line On the grid below draw the graph of x 2y 7 3 y 10 9 8765 3 N 4 2 1 0 1 2 3 4 5 6 7 8 9 10 x Your line will turn blue when you have plotted it correctly Click to shade the region for which x 2y 7 2

9 a b The waiting times at a local coffee shop have a mean of 1 25 minutes and a standard deviation of 0 38 What is the z score for a wait time of 1 45 minutes Explain what your answer for part a means If a wait time had a z score of 1 35 what was the original wait time