Algebra Questions

e 32 P and Q can do a piece of work in 15 days and 20 days respectively They work for 5 days and left then in how many days Q alone can finish the remaining work 8 days 7 days 8 days 8 days c e 33 The area of a square is 144 cm What is the perimeter of the square formed with the diagonal the original square as its side 48 2cm 24 2cm 48 cm 24 cm

16 What is 89 equal to can you make a about Values of in based on n general statement

Find 3 matrices to multiply to A so that you obtain an upper triangular matrix That is find My M and My such that M M M A is an upper triangular matrix Let a b c be real numbers Define the following matrices A a a ab and C aaa 87c Recall that you cannot divide by zero a Show that A 1 is invertible is a 0 and ab State the pivots of A b Find two values for e such that C is not invertible

Boris opened a savings account with 500 and was paid simple interest at an annual rate of 7 When Boris closed the account he was paid 70 in interest How long was the account open for in years If necessary refer to the list of financial formulas years X

The diameter of a circle is 8 mm Answer the parts below Make sure that you use the correct units in your answers If necessary refer to the list of geometry formulas a Find the exact area and circumference of the circle Write your answers in terms of Exact area 0 b Approximate the area and circumference of the circle To do the approximations use the button on the ALEKS calculator and round your answers to the nearest hundredth Approximate area Exact circumference 0 Approximate circumference 00 mm 8 mm X J mm mm

Jim is in charge of planning a reception for 2800 people He is trying to decide which snacks to buy He has asked a random sample of people who are coming to the reception what their favorite snack is Here are the results Favorite Snack Brownies Pretzels Potato chips Other Number of People 35 28 49 63 Based on the above sample predict the number of the people at the reception whose favorite snack will be brownies Round your answer to the nearest whole number Do not round any intermediate calculations people X Esp

Calculate the area of the triangle below 1 Area base base height x x 4 ft 8 ft 12 ft ft

Find the surface area of this rectangular prism Be sure to include the correct unit in your answer 2 in 6 in 3 in 1 in X in in

Find the area of the figure Sides meet at right angles 5 cm 9 cm 3 cm 4 cm 6 cm cm 2

To purchase 12 200 worth of machinery for her business Donna made a down payment of 1600 and took out a business loan for the rest After 2 years of paying monthly payments of 469 81 she finally paid off the loan a What was the total amount Donna ended up paying for the machinery including the down payment and monthly payments 12875 44 b How much interest did Donna pay on the loan X

Choose the property of addition that justifies the equation 0 8 8 5 b b 5 6 y 8 6 v 8 Choose one Commutative Property Associative Property Additive Identity Property Additive Inverse Property Choose one

Use the quadratic formula to solve for x 2x 7x 5 Round your answer to the nearest hundredth If there is more than one solution separate them with commas 8

Write a quadratic function f whose zeros are 4 and 3 f x

A fruit company packages its fruit into two types of boxes large and small This morning the company made two deliveries The table below shows the number of boxes in each delivery and the total weight in kilograms First delivery Second delivery Number of large boxes 2 5 Number of small boxes 12 3 Let x be the weight in kilograms of each large box Let y be the weight in kilograms of each small box x y 0 x y 0 Total weight in kilograms 199 133 a Write a system of equations that could be used to find the weight in kilograms of each type of box b How much does each type of box weigh in kilograms Weight of each large box kilograms Weight of each small box kilograms X

Graph the solution to the inequality on the number line u 6 24 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11

Divide 6x 13x 15x 8 2x 1 Your answer should give the quotient and the remainder Quotient Remainder 09

Find all real zeros of the function g x 2 x 5 x 36 x 5 If there is more than one answer separate them with commas zero s 8 0 0 None

Graph the equation y 6 x 6 10 F 10 X Ex

Let B 7 1 5 32 and C 7 C 2 1 6 Find 5B 4C 5B 4C 010 000 18

Graph the parabola y 3 x 2 1 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a functio button 10 8 6 12 10 8 6 10 12 10 12 X

1 Fill in the missing values for the weekly time card Mon Tues IN 8 15 8 30 OUT 12 00 12 30 IN 12 30 1 10 OUT 4 30 5 10 HOURS 7 75

Graph the parabola y x 10x 28 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a function button 10 8 12 10 N 6 22 2 8 10 12 10 12 X

Graph the line y x 3 3 2 10 6 10 N 6 10 X

The number of crimes that occurred in a certain city per 1000 people had decreased from 46 7 in 1920 to 46 1 in 1940 Find the average rate of change in the number crimes per 1000 people that occurred from 1920 to 1940 The average rate of change was Round to the nearest hundredth as n crimes per 1000 people cities years per crimes per 1000 people cities per year crimes per 1000 people per year years years per thousands of people years per city Clear all Check answ

The average rate of change between 1997 and 2001 was Simplify your answer Type an integer or a decimal in 1997 to 1 3 billion in 2001 Find the average rate of change in the number of public library visits from billion visits years years per library years per book books books per year libraries years per visit libraries per year

K Find the slope and the y intercept of the line with the following equation 4 y 5x 7 Find the slope of the line Select the correct choice below and if necessary fill in the answer box O A The slope is Type an integer or a simplified fraction OB The slope is undefined

Find the slope if it exists of the line Select the correct choice below and if necessary fill in the answer box to complete your choice OA m Type an integer or a simplified fraction OB The slope is undefined 1 3 3 3

Find the slope of the line containing the pair of points f 3 2 and f 1 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The slope of the line is Type an integer or a simplified fraction THE OB The slope is not defined

Determine the slope if it exists of the graph of the linear equation y 6 8x Select the correct choice below and fill in any answer boxes within your choice A The slope is B The slope is undefined Type an integer or a decimal

Find the slope of the line Select the correct choice below and if necessary fill in the answer box to complete your choice O A The slope of the line is m www Simplify your answer Type an integer or fraction OB The slope is undefined C B 64 2 2 s 6 8 10

Find power series solutions in power of x of each of the differential equation x 1 y xy 2xy 0 y 0 2 y 0 3

f x x g x x 3 G Choose the correct graph below O A 20 O C 20 OB O D 20 20 Q Q Q

Given that g x 2x2 3x 1 find each of the following a g 1 b g p 2 a g 1 Simplify your answer

Determine the domain and the range of the function shown below 6 4 2 6 4 2 2 6 2 Select the correct choice below and fill in the answer box to complete your choice A The domain is an interval The domain of the function is Type your answer in interval notation OB The domain is a list of values The domain of the function is Type an integer or a simplified fraction Use a comma to separate answers as needed

Find the domain of the following function Do not use a graphing calculator 1 2 x 2x 8 f x The domain is po your answer in interval notation

Determine whether the graph is that of a function An open dot indicates that the point does not belong on the graph CIT Is the graph the graph of a func No OYes

Given that g x a g 8 X 7 X 8 find each of the following b g 7 c g 8 OA g 8 Simplify your answer B g 8 does not exist Oc g 8 is not a real number d g 11 25 a Select the correct choice below and if necessary fill in the answer box to complete your choice e g x h

Determine if a graph is a function Is this the graph of a function OYes O No THE 2

2 B Show that the Borel algebra B is also generated by the collection of all half open intervals a b x R a x b Also show that B is generated by the collection of all half rays x e R x a ER

5 3 2 1 7 A cup of boiling water is placed outside at 1 00 pm One minute later the temperature of the water is 152 F After another minute its temperature is 112 F What is the outside temperature

b A 41 5 4 6 3 8 B M 6 0 The base of a vertical flagpole CM is at vertex C of the flower bed The flagpole is held in place by two cables AM and BM CM 6 0m i Show that AM 7 10m correct to 2 decimal places ii Given that BM 6 95 m find the angle of elevation of M from B iii Find angle AMB the angle between the two cables

1 point There are more inches on a football field 100 yards than there are centimeters on a 28 meter basketball court True False

B 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 2 cups 2 25 cups 18 cups 144 cups

1 point A square has side lengths of 9 use the Pythagorean theorem to find the length of the diagonal 18 2 18 9

15 1 point Simplify the radical expression 100 49 10 7 10 7 not possible 10 27 Previous

1 1 point Which of the following numbers can be classified as rational numbers 33 3000 3 0 1 1 234

13 1 point 49 the only possible answer for x is 7 True False If x Previous

10 1 point Multiply 2x 1 x x 3 2x 2x 6x 3 2x x 5x 3 2x 3x 7x 3 2x x 5x 3

4 1 point Simplify the radical expression 121 25 O 11 5 not possible 121 5 11

2 1 point The legs of a right triangle are 3 in and 4 in Use the Pythagorean theorem to find the length of the hypotenuse 6 in 12 in 7 in 5 in