Basic Math Questions and Answers

What additional information do you need to prove that triangle ABC is congruent to triangle DEF using the HL theorem A O ZA O AC OZB O ZA O AB AB C ZF DF ZE ZD DE F D

question 4 of 5 What additional information do you need to prove that triangle ACD is congruent to triangle DBA using the HL theorem A B D AD AD OBA CD ZBAD ZADB BD CD OZCAD ZADB Next

question 5 of 5 What is the value of cos 30 C 0 3 4 2 3

Use the rules of differentiation to solve the following equations You must clearly identify the rules y have used and show all your working a y b y 9x 4x z 9 2x 3 c y x 7x 4 14 4x x

question 4 of 5 What is the value of tan 3 01 HIN 2 C 0 2 2 0 3 2 0 3

for ALG 2 Period 4 due on Apr 17 2023 question 1 of 5 You can find the cosine value of an angle by looking at what value on the unit circle O x coordinate The angle in radians O y coordinate

James Furniture Company has two departments that produce lumber used in manufacturing tables and chairs In 1 day of operation department A can produce the lumber required to manufacture 19 tables and 63 chairs while department B can produce the lumber required to manufacture 26 tables and 53 chairs In this production run the company needs enough lumber to produce at least 208 tables and 519 chairs If it costs 829 per day to operate plant A and 875 per day to operate plant B what is the minimum cost of this production run Round to the nearest cent

Watch help video Which point would not be a solution to the system of linear inequalities shown below Y 3 2 x 7 0 9 O 0 10 2 y x 6 3 0 0 8 O 6 9

Avani s school is selling 100 raffle tickets to raise money for a new gymnasium The grand prize is a ten speed mountain bike Which word or phrase describes the probability that she will win the raffle if she buys 1 ticket O unlikely an equal chance or 50 50 O impossible

Convert 10 yards into meters Round your answer to the nearest tenth Note you must use these exact conversion factors to get this question right 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 mile mi 5280 feet ft 1 meter m 100 centimeters cm 1 kilometer km 1000 meters m 1 inch in 2 54 centimeters cm 1 foot ft 0 305 meters m 1 mile mi 1 609 kilometers km

Circumference in terms of pi Apr 17 9 30 24 AM Watch help video The radius of a circle is 12 ft Find its circumference in terms of Answer C

Julia is playing a board game The probability that Julia will lose a turn on her next turn is 0 15 Which word or phrase describes the probability that Julia will lose a turn O impossible O certain O unlikely likely

Riley read 1 book in 2 months If she reads at a constant rate how many books did she read in one month Give your answer as a whole number or a FRACTION in simplest form On the double number line below fill in the given values then use multiplication or division to find the missing value books O O months 1

A B C 0 6 is flying at an altitude of 32 000 feet The distance between the plane and a radio tower on the ground is 50 000 feet What is the angle of elevation between the radio tower and the plane round to 1 decimal place 32 6 39 8 D 39 7 50 000ft 1 32 000ft F 0 7 plane Radio tower

2 Lancaster Savings offers a 25 000 certificate of deposit at 5 compounded quarterly

Basic Trigonometry Determine the approximate value of A C 36 40 28 1 25 points 76 80 2045 104 Question 2 25 points Law of Sines Determine the approximate value of x 12 40 36 B

3 For the function f x x 4 x24 a Find the inverse of f x 3 marks b Graph f x and f x 3 marks c Determine the domain and range of f x and f x 1 mark each for a total of 2 marks f x x Domain Range Domain Range

3 Determine the number of zeros of the following functions a y 3x 2x 1 b y 2x 6x 20

2 The profit function of a company is P x 2x 6 4x 5 12 Determine if the company can break even hint use the discriminant If the company can break even determine how it can do so hint find the zeros

Give the equation of the inverse of each function a f x 3x 5 b f x x 2 x20 5

are 68 years old There are 45 years from the time you started investing saving until you retire You have no previous or other retirement savings when you start to save Assume there are 365 days and 52 weeks in each year from 2023 to 2067 Ignore leap years Assume that taxes will not affect any of the amounts or your savings You invest 75 at the end of each week into a retirement account paying 7 5 compounded weekly from January 1 2023 until you retire Show all work and answer the following questions 1 Assuming no withdrawals or additional payments were made how much money will be in your retirement account after 45 years 2 Assuming you made all the weekly payments for45 years how much did you pay into your retirement account 3 Assuming you made all the weekly payments for 45 years how much interest did you earn over the 45 years Enter the amounts from this strategy in Row 1 of the Comparison Table in Activity 3 of the Project STRATEGY 1 SAVING LATER PLAN Assume that you are 23 years old but decide to wait before saving for retirement You decide to start saving later when you are 42 years old As a result you start saving on January 1 2042 You plan to retire on December 31 2067 when you are 68 years old There are 26 years from the time you started investing saving until you retire When you start investing in 2042 you have no previous or other retirement savings Assume there are 365 days and 52 weeks in each year from 2042 to 2067 Ignore leap years Assume that faxes will not affect any of the amounts or your savings You invest 75 at the end of each week into a retirement account paying 7 5 compounded weekly from January 1 2042 until you retire Show all work and answer the following questions 1 Assuming no withdrawals or additional payments were made how much money will be in your retirement account after 26 years 2 Assuming you made all the weekly payments for 26 years how much did you pay into your retirement account

An equipment costing P250 000 has an estimated life of 15 years with a book value of P30 000 at the end of the period Compute the depreciation charge and its book value after 10 years using straight line method Answer A d P14 666 67 BV 333 30 P103

A man bought an equipment which cost P524 000 00 Freight and installation expenses cost him P31 000 00 If the life of the equipment is 15 years with an estimated salvage value of P120 000 00 find its book value after 8 years Answer A P323 000 00

1 A man bought an equipment which cost Php 524 000 Freight and installation expenses cost him Php 31 000 If the life of the equipment is 15 years with an estimated salvage value of Php 120 000 Find its book value after 8 years

Question 4 14 28 points Sine Graphs Determine the period of the following graph O 1 5 O X 2 2 01 5

Question 3 14 28 points Sine Graphs Determine the period of the following graph 4 O 3x 2 2x 4 O 0 5 O 1 5 Her Sino Granho 0 5 0 5 T h 2 Z 1 2 Question 4 14 28 points 7 2 2x 5 2 3

Sine Graphs Determine the vertical shift of the following Sine graph 5 www 1 O 1 5 3 4 4 5 Question 7 14 28 points 2

Sine Graphs Determine the vertical shiftt of the following Sine graph 27 0 1 02 O 3 3 11 1 20 K B12

Sine Graphs Determine the amplitude of the following Sine graph A ww O 1 5 3 6 7 211 129 pointel

Construct a stem and leaf plot for the data Stock prices rounded to the nearest dollar 22 65 34 98 77 24 67 75 82 54 53 66 71 68 51 55 33 70 43 36 Select the correct choice below and fill in the answer boxes to complete your choice B Stem 2 A Stem 2 3 4 5 6 7 8 Leaf blank blank Units 212 122 3 4 5 6 7 8 9 Leaf blank blank blank Units 212 22 Stem 2 8 Units 212

Suppose that a commuter drives 35 miles round trip to work for 20 days each month achieves a fuel economy of 31 mpg and drives an additional 300 miles each month Develop a spreadsheet model for the monthly gasoline usage using the data provided Apply the principles of spreadsheet engineering in developing your model Complete the spreadsheet below Round to the nearest integer as needed A 1 Data 2 3 4 additional miles month 5 6 Model 7 8 miles day days month fuel economy mpg Total miles month Gallons consumed B 35 20 300 31 B2 B3 B4 B2 B3 B4 B2 B3 B4 B2 B3 B4

I 6 1 Find and plot logz for the following complex numbers z Specify the principal value a 2 b i c 1 i d 1 i 3 2 Solution Suppose that n 0 11 12 log 2 log 2 i Arg 2 2nni log 2 12mn b Suppose that n 0 11 12 log 1 i log i log i i Argi 2nni in 2 12nn c Suppose that n 0 11 12 log 1 i i Arg 1 i 2nni log 2 in 4 i2 n log 2 2 in 4 12 n d Suppose that n 0 1 2 log i 1 i 3 log 1 i i Arg i 11 2ani

Determine whether the given matrix is orthogonal 1 1 Q Q 0 3525 141414 0 1475 0 0175 21 O O The matrix is orthogonal 2 5 The matrix is not orthogonal 25 0 Find its inverse If it is not orthogonal enter NA in any single blank 1 52 52 5 0 1475 0 3525 0 0175 0 0175 0 0175 0 2225

ulz TB MC Qu 10 68 Algo Kler Company Issued Kler Company Issued 580 000 in bonds on January 1 Year 1 The bor December 31 each year Based on this Information alone what are the

tributed with mean 11 grams and standard deviation 2 grams A About what percent of spiders in the colony weigh between 7 grams and 13 grams B About what percent of spiders in the colony weigh less than 9 grams C What is the z score of a spider in this colony that weighs 12 grams D What proportion of the spiders weigh more than 12 grams

4 Divide f x x 9x 5 by g x x 3x 4 both in the polynomial ring Z x

2 What is the remainder when 2x 3x 2x 1 is divided by x 2 2 both in Z x

Test for symmetry and then graph the polar equation rcos 0 6 a Is the graph of the polar equation symmetric with respect to the polar axis O A The polar equation failed the test for symmetry which means that the graph is not symmetric with respe the polar axis B Yes OC The polar equation failed the test for symmetry which means that the graph may or may not be symmet with respect to the polar axis

Test for symmetry and graph the polar equation r 6 6 sin 0 a Is the polar equation symmetrical with respect to the polar axis OA The polar equation failed the test for symmetry which means that the graph may or may not be symmetric with respect to the polar axis B The polar equation failed the test for symmetry which means that the graph is not symmetric with respect the polar axis C Yes

This year 10 years after you first took out the loan you check your loan balance Only part of your payments have been going to pay down the loan the rest has been going towards interest You see that you still have 172 628 left to pay on your loan Your house is now valued at 295 000 Your current situation How much of the original loan have you paid off i e how much have you reduced the loan balance by Keep in mind that interest is charged each month it s not part of the loan balance

The graph of a polar equation is given Select the polar equation for the graph Choose the correct equation below r 5 5 cos 0 Or 5 sin 0 5x 6 24 7x 10 3x 3 5x 4 4x 3x 2 3 4 K 6 7x 5x 4 11x

Test for symmetry and graph the polar equation r 3 cos 20 a Is the polar equation symmetrical with respect to the polar axis O A Yes OB The polar equation failed the test for symmetry which means that the graph may or may not be symmetr with respect to the polar axis OC The polar equation failed the test for symmetry which means that the graph is not symmetric with respe the polar axis

Plot the point given in polar coordinates 2 4 Select the graph that represents the point 2 A Q Q B 4 3 57 O C 5 D

2 Find the greatest common divisor in Z i 0 11 7i 4 7i 3 4i 4 7i

Identify the point with the given polar coordinates T Choose the correct graph below A Q B 57 C Q D 19

Divide f x 3x 2x 1 by g x 2x 4x both in Z x

Suppose three balls are drawn without replacement from a bag that contains 6 red balls and 4 blue balls The number of blue balls is counted Complete parts a and b below a Determine the histogram for the number of blue balls in the sample Choose the correct histogram below OA B APOS 0 5 01 N B Q APDO 05 0123 a C AP 05 b What is the expected number of blue balls in the sample Round to two decimal places as needed N 0 1 2 3 Q Q E OD APX 0 5 012

1 point We want to build 10 letter words using only the first n 6 letters of the alphabet For example if n 5 we can use the first 5 letters a b c d e Recall words are just strings of letters not necessarily actual English words a How many of these words are there total b How many of these words contain no repeated letters c How many of these words start with the sub word ade d How many of these words either start with ade or end with be or both e How many of the words containing no repeats also do not contain the sub word bed

According to a study a female driver in the United States will average 613 accidents per 100 million miles Regard an n mile trip as a sequence of n Bernoulli trials with success corresponding to having an accident during a particular mile What is the probability that a female driver will have an accident in a 1 mile trip Round your answer to eight decimal places

Let f x y 144 x y A Describe the cross sections of the surface z f x y produced by cutting it with the planes y 1 y 4 and y 7 B Describe the cross sections of the surface in the planes x 1 x 4 and x 7 C Describe the surface z f x y A Choose the best description of the cross sections in the planes y 1 y 4 and y 7 OA Upper semicircles whose centers lie on the y axis OB Up opening parabola in the xz plane OC Down opening parabola in the yz plane OD Lower semicircles whose centers lie on the x axis