Algebra Questions

A pole that is 3 5 m tall casts a shadow that is 1 52 m long At the same time a nearby tower casts a shadow that is 45 5 m long How tall is the tower Round your answer to the nearest meter m X 5

Uffit Stope Write the slope intercept form of the equation of the line through the given point with th slope 5 1 12 1 through 2 3 slope A y x 2 B y 4x 2 y x 2 D y 4x 2 2 2 through 1 3 slope 2 A y x 5 C y 2x 5 B y 2x 5 D y 4x 5

9 7 11 C y x 3 D y 7 through 2 2 and 1 3 A y x 8 C y 8x 1 B y 5x 1 D y 5x 8 Write the slope intercept form of the equation of 10 9 Slope 2 y intercept 1 A y x 2 C y 2x 2 11 Slope 2 A y 2x 2 C y 2x 2 B y 2x 1 D y 2x 2 y intercept 2 B y x 2 8 D y 2x 2 12

Describe any 3 out of the 4 features listed below for the function g x log x 4 1 Include a description of how you found those answers using complete sentences 1 Vertical Asymptote Name the equation of the asymptote and tell me how you found it from the equation or where you found it on the graph 2 X and Y Intercepts Name the x and y intercepts and tell me how you found them from the equation or where you found them on the graph 3 Transformations compared to its parent function f x log2 x You can just list the specific transformations that occurred such as vertical shifts horizontal shifts stretch or compress any reflections 4 Domain Name the domain of this function and tell me how you found it from the equation or where you found it on the graph

2 A school holds a lunch fundraiser The school has 350 students 70 of the students order lunch 15 of the students who order lunch select sandwiches The rest of the students who order lunch select pizza Determine the number of students who order lunch and select pizza Show your work

d 1 3 B y 5x 1 D y 5x 8 8 8 through 1 4 and 0 4 A y 4 C y 4x B y 2x D y 4x

11 Write the slope intercept form of the 9 Slope 2 y intercept 1 A y x 2 C y 2x 2 B y 2x 1 D y 2x 2 11 Slope 2 y intercept 2 A y 2x 2 C y 2x 2 B y x 2 D y 2x 2

Order each expression from the least value to the greatest value 12 2 4 8 12 2 4 8 12 2 4 8 START ORDER

Solve the system of equations by the method of your choice 5x y 3 20x 4y 7

26 y cotx Fig 2 6 i Fig 2 6 ii The following table gives the inverse trigonometric function principal value branches along with their domains and ranges Note sin 1 cos cosec sec 1 tan 1 cot 1 MATHEMATICS NCER repub Solution Let sin 2 1 1 1 1 R 1 1 R 1 1 R R Rationalised 2023 24 y Then sin y T T 1 2 2 0 EN EN T T 0 22 0 Y y cotx 1 1 sin x should not be confused with sin x In fact sin x sin x similarly for other trigonometric functions 2 Whenever no branch of an inverse trigonometric functions is mentioned we mean the principal value branch of that function T 3 The value of an inverse trigonometric functions which lies in the range of principal branch is called the principal value of that inverse trigonometric functions We now consider some examples Example 1 Find the principal value of sin 0 and ched

For the function g x solve the following inequality X 9 X 4 g x 0 Select the correct choice below and fill in the answer box within your choice OA The solution is Simplify your answer Use a comma to separate answers as needed OB The solution is Simplify your answer Type your answer in interval notation

2 x 14x 45 0 The solution is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals a

where S is the surface of the garden defined above and n is a unit normal to the surface S Evaluating this surface integral will measure the tendency for the air to circulate in the direction that Anna likes to walk around her garden Note that a negative value just means that she is walking into the breeze Hints An application of Stokes theorem suggests the answers in i and ii should be equal to each ther You may use the integrals sin u du u 2 1 4 sin 2u sinu sin u cos u du 1 4 cos2u Further hints on next page

K JWH payment on a mortgage reduces both the size of the monthly payments and the total interest paid Calculate a the reduction in the monthly payment by increasing the down payment by the amount specified and b the amount saved on interest over the life of the loan Assume the mortgage is for 30 years and use the amortization table to find the monthly payments Increase in Down payment 15 000 Click the icon to view a table of monthly payments on a 1 000 loan Amount of Loan Interest Rate Down Payment 162 000 5 38 000 COLLE a The monthly payment will be reduced by 80 55 when the down payment is increased by 15 000 Round to the nearest cent as needed b Increasing the down payment by 15 000 saved on interest over the life of the loan Round to the nearest cent as needed Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 3 29 53 29 97 30 42 31 34 32 27 Number of Years for the Loan 4 10 22 58 10 12 23 03 10 61 23 49 11 10 24 41 12 13 25 36 13 22 20 6 06 6 60 7 16 8 36 9 65 30 4 77 5 37 6 00 7 34 8 78 X

4000x The polynomial function defined by f x x 10xx can be used to find the depth that a ball 20 cm in diameter sinks in water The constant d is the density of the ball where the density of water is 1 The smallest positive zero of fix equals the depth that the ball sinks Approximate this depth for each material and interpret the results a A wooden ball with d 0 9 b A solid aluminum ball with d 22 e A spherical water balloon with d 1 a Select the correct choice below and fill in any answer boxes in your choice OA The depth is Type an integer or decimal rounded to the nearest hundredth as needed OB The answer is undefined

1 3 Point Slope Write the slope intercept form of the equation of the line through the given point with the given slope 1 through 2 3 slope 5232 A y x 2 B y 4x 2 5 C y x 2 D y 4x 2 3 through 3 3 slope undefined 1 A y x 1 3 B x 3 C y 3 D y x 1 3 2 2 through 1 3 slope 2 4 A y x 5 C y 2x 5 4 through 5 4 slope 7 A y x 2 3 2 7 3 B y x 2 2 7 3 C y x 2 2 B y 2x 5 D y 4x 5 3 7 D y x 2 2 3 2

7 through 3 1 and 1 3 A y 1 x 3 B y 1 5 x 3 C y 1 5 x 3 D y 3 5 x 1 11 Slope A y 0 C 0 x 1 2 B y 5 3x D y 5 4x Write the point slope form of the equation of each line given the slope and y intercept 9 Slope 0 y intercept 5 7 5 A y 5 3x C y 5 0 y intercept 0 8 1 B y x 2 D v 2x 8 through 3 4 and 0 4 A y 3 x 4 8 8 B y 4 x 3 3 12 C y 3 x 4 8 D y 3 x 4 4 10 10 Slope y intercept 5 A y 36x 5 5 7 B y 5 C y x 5 tx D y 5 x 5 12 Slope2 y intercept 1 A y 1 2x C y 1 4x B y 1 5x D y 1 4x

Point Slope Write the point slope form of the equation of the line through the given point with the given slope 2 1 through 1 0 slope 5 A y x 1 4 B y 1 5x C y 4 x 1 D y 5 x 1 3 through 5 4 slope A y 5 x 4 B y 5 x 4 C y 4 D y 4 5 x 5 x y x 5 6 5 B y x 1 5 C y 1 3x D y x 4 2 through 5 5 A 0 x 5 C y 5 0 slope undefined B 0 x 5 D y 5 0 Write the point slope form of the equation of the line through the given points 5 5 through 0 1 and 5 4 6 6 through 5 1 and 3 5 A y 1 x 5 B y 5 x 1 C y 1 x 5 D y 5 x 1 4 through 2 1 slope 3 A y 2 x 1 B y 1 3 x 2 C y 1 x 2 3 D y 2 2 x 1

Consider the min cost max flow problem where we have 6 nodes a b c d e f with supply on nodes b e f Sb 3 se 5 sf and demand on nodes c d 4 Sd The network has 9 arcs a c a d b a b c c e d b e a f b f d with associated costs Sc Cac 0 Cad 6 2 1 Cba 8 Cbc 3 Cce 2 Cdb 5 Cea 2 Cfb 0 Cfd 10

Find the domain and range for the following graphs 2 points each y 51 f 3 2 3 4 5 5 46 Domain Range 00 8 9 10 11 12 X Domain Range 2 1 4 3 2 1 0 2 4 1 2 B

Domain Range 3 4 2 1 10 1 2 3 4 5 2 3 5 Domain Range 2 O 6 Given f x x 4 and g x x 2 find the following 3 points f 2 g 2

4 Find the value of each unknown angle in this diagram There are five unknown angles 104 Z 56 Y X d of it all 41x12 b X y

12 5 xvr 1 sinh x Using the trial and error method the value of is obtained x 3 18

Given below is the principal owed on a student loan last month the annual interest rate and the way the minimum monthly payment is computed Find this month s minimum payment due Method for Calculating Minimum Monthly Payment finance charge 40 1 5 of principal Principal 23 700 Annual Rate 9 This month s minimum payment is Round to the nearest cent as needed CLIXE

Homework 3600 60x Part 1 of 4 Suppose that a parking attendant can wait on 60 cars per hour and that cars arrive randomly at a rate of x cars per hour Then the average number of cars waiting in line can be estimated by N x Complete parts a though c below a Evaluate N 33 and N 59 N 33 0 Round to two decimal places as needed Points 0 of 1

At a parking lot the attendant can wait on 50 people per hour If people arrive randomly at an average rate of x cars per hour the average number of cars N waiting to exit the lot is given by the equation below where x 50 Complete parts a and b x N x 3000 60x a Approximate x when N x 7 X Round to the nearest whole number as needed

Graph y f x Use division factoring or transformations as an aid Show all asymptotes and holes 2x 11x 15 2x 9x 10 f x Choose the correct graph below O A Ay O B Ay SOU MIXE O C Ay O Points 0 of 1 D

K Find the vertical and horizontal asymptotes of f and the graph of f that includes the asymptotes 8x x 25 Choose the correct asymptotes OA x 5 x 5 OC x 5 x 5 y 0 OB x8 x 8 OD x 8 x 8 y 0

K Drag each of the statements given below into the appropriate concept on the right Statements Concepts Rational function If x k is a zero of the denominator but not of the numerator a C is equivalent to ad bc b provided b and d are nonzero Continuous except at x values where the denominator equals zero p x f x where p x and q x are q x polynomials with q x 0 Occurs when the degree of the numerator is less than or equal to the degree of the denominator Vertical asymptote Horizontal asymptote Graph of a rational function Basic rational equation

Solve the equation x 12 X 4 X Type an integer or a simplified fraction Use a comma to separate answers as nee

y 9 6y x

For f x 1 xand g x 2x x 2 find the following functions a fog x b go f x c fog 3 d gof 3

2 Let g L M2 2 R R defined by g x x x 2x4 x x2 M 2 R E M2 2 3 mark 2 marl a Find the range and rank of g b Use the Rank Nullity Theorem to determine the nullity of g

The graphing calculator screen below displays the percentage of an adult brain y for a child at age x where 1sxs11 LnReg Use this information with numbers rounded to the nearest whole number to find the percentage of an adult size brain a child has at age 6 Round to the nearest whole number as needed 85 82 84 y a blnx a 29 23236624 b 30 26661497 83

the following Regression line Revenue and cost are the same Slope Scatter Plot Data presented in a visual form as a set of points The line that best fits the data points 3 Rate of Change 1 2 4 Breaking even

Express the given function h as a composition of two functions f and g so that h x fog x where one of the functions is 6x 9 h x 6x 9

For f x 8 X 4 1 and g x find X a fog x b the domain off og

10 Listen Find the y intercept of the line y 0 16 0 16 12 0 0 0 12 x 12

The function f t 1 5t 16 9 can be used to estimate the yearly sales of soccer equipment in billions of dollars as a function of time where t is the number of years after 1982 Determine the amount of sales made in the year 1991 28 9 Billion 16 9 Billion 1 5 Billion 30 4 Billion

The function P x 0 45x 87 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes Find and interpret P 900 Profit Made on Pretzel Sales 1000 900 800 700 600 500 400 Profit dollars 300 200 100 500 600 700 800 900 1000 Number of Pretzels Sold 813 813 is the profit the vendor makes from selling 900 pretzels 405 900 is the profit the vendor makes from selling 405 pretzels 900 900 is the profit thovendor makes from selling 900 pretzels

Listen Determine whether 0 2 is a solution of the system 2x 3y 6 4x 5y 10 Yes No

Listen Find the slope of the line that goes through the points 4 7 and 2 11 O 2 04 02 0 2 Pag

Question 5 4 Listen What ordered pair is shown plotted on the rectangular coordinate plane bela 10 8 7 8 7 7 8 7 8 10 5 0 5 10 5 10

Question 4 2 5 points f x 4x 5 Find f 3 O Listen 17 14 9 41

4 2 points The functions below are common streamfunctions for fluid flow which means that the level curves show trajectories of the fluid The first partial derivatives are related to the velocity components of the fluid in particular v 3 of For each streamfunction sketch several level curves enough to clearly see the shape and find the associated velocity vector v of the fluid for each pair x y a f x y 2xy b f x y x y

2 2 points For each of the following functions Find the function s domain i e the set of all input values Find the function s image i e the set of all output values Sketch several of its level curves on one set of axes a contour plot How many level curves At least 4 for each function generally sketch however many i sufficient to get a sense of the shape of the graph of f a f x y e y x b f x y ln x y 4

Divide 37i 2 12i 37i 2 12i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in t

6 22i 3i 6 22i 3i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in th

26 14i 2i 26 14i 2i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in the

68 1 4i 68 1 4i Simplify your onewer Tyng your cou Em