Algebra Questions

point Convert the system ugmented matrix o an augmented matrix Then transform the system to reduced echelon form and determine if the system is consistent If the system is consistent then find all olutions educed echelon form the system consistent select olution x1 x 2x1 9x2 x1 4x2 1 lelp To enter a matrix use For example to enter the 2 x 3 matrix 44 20 1 1 2 3 6 5 4 ou would type 1 2 3 6 5 4 so each inside set of represents a row If there is no free variable in the solution then type 0 in each of the answer blanks directly

5 If y varies jointly as a and 2 and y 24 when x 3 and z 4 find y when z and z 8 O 12 O 48 O 64 O 36

You are given the cost of an item before and after tax Find the amount of tax and the tax rate Round both solutions to two decimal places if necessary Cost of item 127 Selling price 145 48 Tax amount Tax rate

After a 65 reduction you purchase a new television on sale for 198 What was the original price of the television Round your solution to the nearest cent

Rewrite the following equations using exponents instead of logs Estimate a solution fo calculator Round the value of x to the nearest integer a log x 1 153 x b log x 4 88 x i i

1 point Find the Laplace transform F L f of the function F s f 1 f 4 0 t 7 0 7 t 0

HOMEWORK Working with Fractions Perform the operations without using a calculator 22 9 18 11 1 4 7 8 7 10 10 2 5 s 2 70 8 8 12 6 2 1 20 4 3 6 10 11 5 Block 3 36 6 3 9 3 10 17 4 20 5 13 12 2 1 20 4 15

Activity A scientist needs to make 5 4 liters of saline solution salt water in which the salt level must be at 28 concentration meaning 28 of the water is salt Unfortunately the scientist only has two types of saline solution in his possession He has saline solution with a 12 concentration level and saline solution with a 30 concentration level How much of each type of saline solution should the scientist mix together to achieve 5 4 liters of saline solution at a concentration level of 28 Let a represent the amount 12 saline solution and let y represent the amount of 30 saline solution 10 Determine which two equations can be used to represent the system Before moving to the next question make sure that you write down the the two equations you ve chosen x y 28 12x 30y 1 512 12x 30y 5 4 12x 30y 28 x y 1 512 x y 5 4 1 point

1 3 2 45 3 3 rad rad 4 Y 2x 3

System 3 Stimulus 4 1 Understanding Systems Substitution Method Use the system of equations below to answer the following questions 2x 3y 15 x 3y 3 2 1 point 1st equation isolate x 1st equation isolate y 2nd equation isolate x 2nd equation isolate y cannot be determined DO Using the method of substitution which equation and which variable would be easiest to isolate

Which of the following scenarios have a reasonable solution Read each one carefully and select all that apply Scenario A student takes out two loans totaling 5000 at 4 and 6 annual interest The total interest after 1 year is 254 Find the amount of each loan Solution The loan at 4 interest is 2300 and the loan at 6 is 2700 Scenario An athlete ran for part of an hour at 6 miles per hour and for the rest of the hour at 8 miles per hour The total distance traveled is 7 miles How long did the athlete run at each speed Solution The athlete ran for half an hour at 6 miles per hour and one and a half hours at 8 miles per hour Scenario The perimeter of a rectangle is 40 feet The rectangle s length is 3 times as long as it s width Find the dimensions of the rectangle Solution The width of the rectangle is 5 feet The length of the rectangle is 15 feet Scenario If 2 bags of popcorn and 3 soft drinks cost 7 and 3 bags of popcorn and 2 soft drinks cost 8 find the price of a bag of popcorn and the price of a soft drink Solution A bag of popcorn costs 3 and a soft drink costs 2

5 1 point To solve by elimination we can choose to eliminate either the x variables or the y variables Use the system of equations below to answer the following 2 questions 4x 7y 2 3x 3y 6 Question 1 To eliminate the x variables with the lowest common value multiply the top and the bottom equation by the numerical value equation by the numerical value Question 2 To eliminate the y variables with the lowest common value multiply the top equation by the numerical value and the bottom equation by the numerical value Question 1 Values separate each value with a comma type your answer Question 2 Values separate each value with a comma type your answer

Consider the following scenario Choose the sentence that represents a reasonable You do not need to solve the system A plane flies 2400 miles from Orlando Florida to Los Angeles California against the wind in 4 hours and 10 minutes Then the plane flies back to Orlando with the wind in 3 hours and 45 minutes Find the speed of the plan with no wind and the speed of the wind The speed of the plane with no wind is 608 hours The speed of the wind is 32 hours The speed of the plane with no wind is 32 mph The speed of the wind is 608 mph The speed of the plane with no wind is 608 mph The speed of the wind is 32 mph The speed of the plane with no wind is 608 km h The speed of the wind is 32 km h

Stimulus 4 3 Application of Systems Chorus Concert Adults and Children Jennifer s school is selling tickets to a chorus concert On the first day of ticket sales the school sold 3 child tickets and 1 adult ticket for a total of 38 On the second day of ticket sales the school sold another 3 child tickets and 2 adult tickets for 52 Find the cost of each type of ticket Let represent the cost of a child ticket and let y represent the cost of an adult ticket S 7 8 1 point Determine which two equations represent the scenario Before moving to the next question make sure that you write down the the two equations you ve chosen 2x 3y 52 3x y 38 3x 2y 52 x y 38 x 3y 38 x y 52 10 1 point Using the two equations you chose from part 1 determine the solution to the system Enter a numerical value only The cost of a child ticket is type your answer dollars and the cost of an adult ticket is type your answer dollars D

1 point The sum of two numbers is 43 One number is 5 less than 3 times the other number What are the two numbers Need Help In the 4 2 Instructional Videos watch the videos showing examples of how to Solve Direct Translation Applications The smaller number is type your answer The larger number is

Use the system of equations below to answer the following questions 2x 3y 15 2 3y 3 3 4 easiest to is 1st equation isolate x 1st equation isolate y 2nd equation isolate x 2nd equation isolate y cannot be determined 1 point Using the equation you chose from part 1 rewrite the equation isolating the variable you determined was the easiest to isolate 00 Type your solution below If needed represent the constants in your equation as fractions using the backslash no decimals choose your answer type your answer 1 point Continuing with the substitution method find the solution to the system D

1 Do your best Take your time Meet with your lab instructor to discuss these questions 1 point Determine which method is MOST appropriate to solving the system Choose each method only once System 1 y x 3 y x 2 System 2 2x 3y 6 x y 4 System 3 x y 5 2x y 7 01 If you do not correctly match all 3 systems this question will automatically be marked incorrect therefore I wi be grading your submission and assigning partial credit System 1

Wayne is hanging a string of lights 59 feet long around the three sides of his rectangular patio which is adjacent to his house The length of his patio the side along the house is 7 feet longer than twice its width Find the length and width of the patio Width of the patio is Length of the patio is feet feet

Jotham needs 15 liters of a 40 alcohol solution He has a 30 and a 80 solution available How many liters of the 30 and how many liters of the 80 solutions should he mix to make the 40 solution Liters of 30 solution Liters of 80 solution

After four years in college Josie owes 12000 in student loans The interest rate on the federal loans is 2 8 and the rate on the private bank loans is 3 4 The total interest she owes for one year was 384 00 What is the amount of each loan Federal loan at 2 8 account Private bank loan at 3 4 account

blem 1 Which of the following is equal to 1 1 cos 2x ii 1 cot x 1 2 1 cos x tan x sin 2x A iii only B ii only C i and iii only D i and ii only E none of them F all of G 1 only H ii and iii only

plify 2 8 y 1 5y z 2 5yz 2 2 ution 5 5

Which combination of red and green apples can the person use 404 V 35 30 25 20 15 10 5 X 5 10 15 20 25 30 35 40 45 50 27 red apples and 17 green apples O 35 red apples and 25 green apples 25 red apples and 35 green apples 40 red apples and 10 green apples 040 red apples and 35 green apples 42 red apples and 22 green apples

6 5 4 3 515 4 3 2 6 5 4 3 2 1 24 NWS S 5 4 3 2 1 2 1 K 1 2 3 3 4 4 5 6 5 6 X 4 3 2 6 5 4 3 2 1 5 3 2 1 112 3 TO 4 56 6 5 4 3 2 1 12 3 4 56

Which system of inequalities represents the graph y 6 11x y 3x 4 2x 3y 15 y 11x 6 y 4 3x 2x 3y 15 y 11x 6 y 42 3x 2x 3y 15 y 6 11x y 3x 4 2x 3y 15 4 8 7 6 5 4 321 10 9 8 7 6 5 4 3 2 1 5 6 7 8 9 10 1 X 2 3 4 5 6 7 8 9 10

Enter an inequality that represents the graph in the box 8 6 4 2 8 6 4 2 2 4 6 8 2 4 H 6 8

O 5 4 3 2 1 5 4 3 2 1 2 3 2 1 2 1 1 2 3 2 3 1 2 N 3 4 5 4 5 O 5 4 3 2 1 2 1 2 3 5 4 3 2 1 1 1 2 3 1 2 3 4 5 2 3 45 X

Marty is 3 years younger than 6 times his friend Warren s age The sum of their ages is greater than 11 What is the youngest age Warren can be Enter your answer as a whole number in the box years

Solve for x 9 4x 3 27 Enter your answer as one inequality in the box

Which graph represents the inequality 24x8y 16 8 6 4 2 2 8 6 4 2 8 6 4 8 6 4 2 2 XAT y 1 2 4 6 2 4 6 X 8 8 6 4 8 6 4 2 8 6 4 2 4 68 2 1 8 6 4 2 1 2 2 4 6 8 X

Plot the inequality on the number line a 1 ora 8 Choose the proper tools with the correct endpoints then click and drag the endpoints to the correct location Notice the trash can is available if an error is made 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

What is the solution to the system of linear equations 6x 7y 59 4x 5y 41 Enter your answer by filling in the boxes

What is the interval notation for the compound inequality I 3 or 1 7 O 3 7 O 0 3 or 7 O 0 3 or 7 O 3 7

ATA YAYINCI 1 4 Selim bir torbadaki bilyeleri alt ar alt ar veya seki zer sekizer sayd nda her defas nda 3 bilye art yor Torbadaki bilyelerin say s 160 tan fazla oldu u na g re torbada en az ka bilye vard r A 165 B 171 C 192 D 195 8 76 25 ab

a Find the slope of the line and b interpret the slope a The slope of the line is b Interpret the slope 4 3 Simplify your answer C 3 3 KO Q K

Graph the line that contains the point P 2 1 and has slope m 0 Find the slope intercept form of the equation of the line point yrape at it Click to enlarge graph Write the slope intercept form of the equation of the line that contains the point P 2 1 and has slope m 0 Type your answer in slope intercept form 10 8 6 4 D P of 8 6 4 2 46 8

The slope m and a point P on a line are given Use the information to find three additional points on the line m P 5 6 3 Determine three points on the line with slope O A 2 8 2 11 6 14 O B 8 2 11 2 14 6 O C 9 1 12 3 15 7 On 1 0 2 121 1 7 151 and passing through 5 6

he slope and a point on a line are given Use this information to locate three additional points on Slope 3 point 2 4 etermine three points on the line with slope 3 and passing through 2 4 OA 1 1 3 7 4 10 O B 1 1 7 3 10 4 OC 5 5 3 1 2 4 O D 5 5 1 3 4 2

Calculate the change of enthalpy for the reaction CH4 g NH3 g HCN g 3H2 g from the following reactions Reaction 1 N g 3H2 g 2NH3 g Change in enthalpy 91 8 kJ mol Reaction 2 C s graphite 2H2 g CH4 g Change in enthalply 74 9 kJ mol Reaction 3 H g 2C s graphite N g 2HCN g Change in enthalpy 270 3 kJ mol To earn FULL POINTS you need to include ALL YOUR WORK used to complete the calculation the correct calculated value AND the correct units

Solve each inequality 5 8 7 x 3 27 A x 4 or x 7 B x 4 or x 10 C 4 x 7 D 6 x 5 7 7 5 46 4 53 A 3 b 5 B 1 b 3 8 C bs or b24 3 D 5b53 6 6 75 p 4 10 A 4 p 6 B 3 p 7 C p 2 or p26 D p 3 or p 7

1 A No solution C 4 9 or 2 26 D a 42 ora 23 7 11 2 9m 3 8 4 8 7 35 A 32 2 3 B RS 25 or x 2 0 5 C All real numbers 1 D 25 SNS 0 5 12 12 3 2 4 3 6 2 23 04 A 41 5 1 B All real numbers T C 08 or 25 6 D No solution 9 4 S um m HB 8 1221 TE T T

7 7 7 5 4b 4 53 A 3 b 5 B 1 b 8

8 5 4r 2 4 106 A srs1 B r21 orrs 9 C Sorr 26 D 5 r 6 9 10 4 10 8n 78 A All real numbers B 6 n 5 C ns 6 orn20 D 6 n 0 10 210

1 Solve each equation 1 x 6 10 A 4 16 C 4 B 8 26 D 20 0 3 0 6 b 0 2 2 9 3 98 B 2 D 0 6 2 A 1 84 1 2 C 2 1 6 2 4 2 A C 25 6552 43 10 2 11 2 24 B D 4 14 9a 14 13 209 A 6 2 28 C 9 B 0 18 D 6 1

0 9 10 4 10 8n 78 A All real numbers B 6 n 5 C ns 6 orn20 D 6 n 0 10 10 8 69x 45 38 A 7 x 1 B xs 4 orx23 49 1 C x 21 orxs 9 D x 7 or x 1 10 57472

3 5 3 0 6 b 0 2 2 9 3 98 A 1 84 1 2 C 2 1 6 Solve each inequality 5 8 7 x 3 27 A x 4 or x 7 B x 4 or x 10 C 4 x 7 D 6 x 5 B 2 D 0 6 2 6 4

2 4 2017 11 10 A C x 3 2 43 10 2 25 6 2 3 28 9 5 2 B D 4 14 9a 14 13 209 A 6 2 C 0 43 24 B 0 D T 18 15 0

2 9 3 98 lity 27 7 10 B 2 D 0 6 2 4 6 S al 4 14 9a 14 A 6 2 c 0 28 C 0 9 D 13 209 B 0 D 6 75 p 4 10 A 4 p 6 B 3 p 7 C p 2 or p 6 D p 3 or p 7 18

1 Solve each equation 1 x 6 10 A 4 16 C 4 B 8 26 D 20 0

14 15 16 17 18 19 20 21 Temperature C 22 Warm Up The dot plot shows a town s daily low temperature in degrees Celsius for 24 days Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown