ALLIED MAT110 FULL COURSE [ ALL DISCUSSIONS ALL HOMEWORK ASSIGNMENT AND ALL CHECK UNDERSTANDING ]

MODULE 2 DISS1. Kahn Academy is a website that provides free videos, instruction, and practice for a variety of topics, including math. I want you to read a little more about this website, then use it to find a video or practice exercises that would help you with this week’s concepts..khanacademy.org/about”>http://www.khanacademy.org/aboutPost the link that you find, and tell me your thoughts on this website. Do you think this will be a resource that you will use in future Modules?2. Think of a problem in your life or area of study that you could use an equation or inequality to find the solution. Describe this problem and state whether you typically write the equation down to solve it or if you usually solve it in your mind using short cuts.Do you ever solve equations (like the ones in the homework) by just guessing? What’s the upside to solving an equation by guessing? What’s the downside?MODULE 3This is the required discussion board. Remember, there is a 3 post minimum in the discussions.Do the variables of a polynomial ever have negative exponents? What is the smallest exponent that a variable can have in a polynomial?Find two applications of polynomials in the real world. Are polynomials used in your area of study?MODULE 4This is the required discussion board. Remember, there is a 3 post minimum in the discussions.Why do we cover Factoring Trinomials and simplifying Rational Expressions in the same Module? How are the two concepts connected?Unlike Polynomials, Rational Expressions have variables in the denominator. This means that Rational Expressions can be used to describe situations that Polynomials cannot. Find one example of how Rational Expressions are used in the real world.MODULE 5This is the required discussion board. Remember, there is a 3 post minimum in the discussions.Identify and discuss a real world application of graphing and the rectangular coordinate system. You may need to search the web for references. Cite any website that you use.MODULE 6.allied.edu/Images/1×1.gif”>Posted by Christina Holdiness at 04/24/13 12:19 PMThis is the required discussion board. Remember, there is a 3 post minimum in the discussions.One of the most common places that I have used concepts related to linear inequalities is in Economics, namely in relation to supply and demand or cost and revenue. The main relation between these concepts is related to the shading that we use when graphing linear inequalities.How is graphing a linear inequality similar to graphing a linear equation? How can you determine if you should shade above or below the line?Find of an example in your life or area of study that could be described by using a linear inequality.MODULE 7This is the required discussion board. Remember, there is a 3 post minimum in the discussions.Why is it okay to take the cube root of a negative number but not okay to take the square root of a negative number? You can use examples to explain your answer.Find an application that uses square roots.Find an application that uses cube roots.MODULE 8.allied.edu/Images/1×1.gif”>Posted by Christina Holdiness at 04/24/13 12:22 PMThis is the required discussion board. Remember, there is a 3 post minimum in the discussions.Do you have any suggestions to me to make this course a better experience for future students? Are there any suggestions you would give future students? Is there anything that you wish you would have known in the first Week of this course that I should add to the Announcement or Welcome email?Homework Assignment IntroductionWelcome to the Module 1 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. List all the factors of 88.2. List all the prime numbers between 25 and 60.3. Find the GCF for 16 and 17.4. Find the LCM for 13 and 39.5. Write the fraction in simplest form. .png”>6. Multiply. Be sure to simplify the product. .png”>7. Divide. Write the result in simplest form. .png”>8. Add. .png”>9. Perform the indicated operation. Write the result in simplest form. .png”>– .png”>10. Perform the indicated operation. Write the result in simplest form. .png”>÷.png”>11. Find the decimal equivalent of .png”> rounded to the hundredths place.12. Write 0.12 as a fraction and simplify.13. Perform the indicated operation. 8.50 – 1.7214. Divide. .png”>15. Write 255% as a decimal.16. Write 0.037 as a percent.17. Evaluate. 56 ÷ 7 – 28 ÷ 718. Evaluate. 9· 4219. Multiply: (-1/4)(8/13)20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 522. Identify the property that is illustrated by the following statement.(6 · 13)· 10 = 6 · (13 · 10)23. Identify the property that is illustrated by the following statement.10· (3 + 11) = 10· 3 + 10· 1124. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)25. Add. 14 + (–6)26. Subtract. –17 – 627. Evaluate. 3 – (–3) – 13 – (–5)28. Multiply. .png”>29. Divide. .png”>30. Evaluate. (–6)2 – 5231. Evaluate. (–9)(0) + 1332. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?33. Write the following phrase using symbols: 2 times the sum of v and p34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 435. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?36. Write the following geometric expression using the given symbols..png”> times the Area of the base (A) times the height(h)37. Evaluate .png”> if x = 12, y = .png”>, and z = .png”>.38. A formula that relates Fahrenheit and Celsius temperature is .png”>. If the current temperature is 59°F, what is the Celsius temperature?39. If the circumference of a circle whose radius is r is given by C = 2?r, in which ? ? 3.14, find the circumference when r = 15 meters (m).40. Combine like terms: 9v + 6w + 4v41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.43. Use the distributive property to remove the parentheses, then simplify by combining like terms: 7(4s – 5) + 944. Multiply: 8u6· 3u345. Simplify the expression, if possible: .png”>Welcome to the Module 2 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Is 12 a solution to the equation 7 – x = 5?2. Is –9 a solution to the equation 9 – 8x = 81?3. Solve -2x+7>=94. Solve 3(x-5)<2(2x-1)5. Solve. 8x + 2 = 7x6. Solve. 7x – 0.96 = 6(x – 0.67)7. Solve for x. 4x = –88. A company estimates that 5% of the parts they manufacture are defective. If 8 defective parts are found one week by the quality assurance testers, how many parts were manufactured that week?9. Solve for x. 35 – 7x = 3510. Solve for x. .png"> – 5 = 511. Solve for x. 4(x – 2) + 4x = 5x + 412. Solve for x. 7x – 3 + 3x = 10x – 313. Solve for x. –10x + 1 – 7x = –17x + 714. Solve the literal equation for y. x + 5y = 2515. A rectangular solid has a base with length 5 cm and width 2 cm. If the volume of the solid is 100 cm3, find the height of the solid. [Hint: The volume of a rectangular solid is given by V = LWH.]16. Translate the following statement into an algebraic equation. Let x represent the number. 1 less than 15 times a number is 9 times that same number.17. The sum of three consecutive odd integers is 201. Find the integers.18. At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mi/hr. Two hours later, a second truck leaves along the same route, traveling at 70 mi/hr. When will the second truck catch up to the first?19. The base of an isosceles triangle is 1 in. less than the length of one of the equal sides. If the perimeter of the triangle is 20 in., find the length of each of the sides.20. Identify the amount in the statement “318 is 53% of 600.”21. Elaine was charged $126 interest for 1 month on a $1800 credit card balance. What was the monthly interest rate?22. A broach was marked up $150 from cost, which amounts to a 50% increase. Find the original cost of the broach.23. Solve the solution set. 8x + 3 < 4x – 1324. Solve the solution set. 5x + 12 > 10x – 825. An arithmetic student needs an average of 70 or more to receive credit for the course. She scored 76, 69, and 84 on the first three exams. Write a simplified inequality representing the score she must get on the last test to receive credit for the course.26. The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 28 in., find the width of the rectangle.27. Solve and check: 6x=4(x-5)28. Solve 1/4x<=3/829. Solve 8x-7<=7x-530. Solve -5x>23.5Welcome to the Module 3 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Simplify. (a6b7)62. Simplify. .png”>3. Classify the following as a monomial, binomial or trinomial, where possible. .png”>4. Classify the following as a monomial, binomial or trinomial, where possible.4×2 – 3xy + y25. Classify the following as a monomial, binomial or trinomial, where possible.y7 + y6 + 8y5+ 26. Write in descending order and give the degree. 7×3 + 10×4 + 107. Evaluate –x2 – 10x– 6 for x = 3.8. True or False? The degree of a trinomial is never 4.9. Evaluate (assume x does not equal 0). 8×010. Write using positive exponents and simplify, if possible. 5–311. Simplify and write your answer with only positive exponents. .png”>12. Simplify. Write your answer with only positive exponents. .png”>13. Express the number in scientific notation. The diameter of Neptune: 49,600,000 m14. Perform the indicated calculations. Write your result in scientific notation..png”>15. The distance from a star to a planet is 7.4· 1018 m. How long does it take light, traveling at 1016 m/year, to travel from the star to the planet?16. Add 6m2 – 2m – 4 and 10m2 + 3m– 6.17. Remove the parentheses and simplify. 7y – (–10y – 9x)18. Subtract 4d2 + 9d – 10 from 10d2 – 3d+ 7.19. Perform the indicated operations. [(6y2 + 2y – 2) – (–y2 – 10y + 2)] – (–4y2 + 3y + 3)20. A census study shows that the population from 1990 to 1998 of the only large town in a certain county can be modeled by the formula 102t2 – 225t + 3090 where t= 0 represents the year 1990 and that over the same years, the population of the surrounding county (not including the town) can be modeled by the formula 125t2 + 72t + 4978 where t= 0 represents the year 1990. Find a model for the total population of the county during the years 1990 to 1997.21. Multiply. –6x(–4x – 7)22. Multiply. (5m – 3)(4m + 7)23. Multiply. (–4x – 2)224. Divide. .png”>25. Divide. .png”>26. Write 7.7×10^8 in standard notation.27. Evaluate 4x^0+528. Simplify and write using positive exponents. (-6)^-229. Simplify x^-7/y^-230. Multiply (x-9)(x+9)y problems with this assignment, please e-mail your instructor.Welcome to the Module 4 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Find the greatest common factor. 4, 6, 12.2. Factor. 24×3 + 30×23. Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n44. Factor completely by factoring out any common factors and then factoring by grouping.6×2– 5xy + 6x – 5y5. The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).6. The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.7. Factor the trinomial completely. x2 + 8x – 98. Factor the trinomial completely. 2×2 + 16x + 329. Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)10. State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x– 10)11. Factor completely. x2 + 11x + 2812. Factor completely. 15×2 + 23x + 413. Factor completely. 6z3 – 27z2 + 12z14. The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2– 19h + 24. Write this polynomial in factored form.15. Find a positive value for k for which the polynomial can be factored. x2 – kx + 2916. Factor completely. 9×2 + 417. Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 3618. Factor completely. 25×2 + 40xy + 16y219. Factor. s2(t– u) – 9t2(t – u)20. State which method should be applied as the first step for factoring the polynomial. 6×3 + 9×21. State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 1022. Solve the quadratic equation. 5×2 + 17x = –623. Solve the quadratic equation. 3x(2x – 15) = –8424. The sum of an integer and its square is 30. Find the integer.25. If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?26. Write in simplest form. .png”>27. Write in simplest form. .png”>28. Write the expression in simplest form. .png”>29. The area of the rectangle is represented by 5×2 + 19x + 12. What is the length?5x + 4.png”>30. Multiply. .png”>31. Multiply. .png”>32. Divide. .png”>33. Divide. .png”>34. Perform the indicated operations. .png”>35. Find the area of the rectangle shown..png”>36. Subtract. Express your answer in simplest form..png”>37. Subtract. Express your answer in simplest form..png”>38. Add. Express your answer in simplest form..png”>39. Add. Express your answer in simplest form..png”>40. Add or subtract as indicated. .png”>41. One number is 8 less than another. Let x represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers.42. Simplify. .png”>43. Simplify. .png”>44. What values for x, if any, must be excluded in the following algebraic fraction?.png”>45. What values for x, if any, must be excluded in the following algebraic fraction?.png”>46. Solve for x. .png”> + 6 = 147. Solve for x. .png”>48. Solve for x. .png”>49. One number is 3 times another. If the sum of their reciprocals is .png”>, find the two numbers.50. A 5-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 16 feet?Welcome to the Module 5 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Determine which of the ordered pairs (0, 1), (2, 0), (0, –1), (–8, 5) are solutions for the equation x + 2y = 2.2. Complete the ordered pairs so that each is a solution for the equation 2x + y = 10.(5,__?__), (__?__, 10), (__?__, –2), (7, __?__)3. Give the coordinates of the point graph:.png”>4. Give the coordinates of the point graphed below..png”>5. Find the slope of the line through the points (10, 7) and (8, –10).6. Find the slope of the line through the points (–3, –2) and (–3, 0).7. Find the slope of the line through the points (–6, 3) and (5, 3).8. Find the slope of the graphed line..png”>9. Find the slope of the graphed line..png”>(Gridlines are spaced one unit apart.)10. Find the slope of the graphed line..png”>11. Find the slope of the line that passes through (3, 2) and (8, 11).12. Find the slope of a line that passes through (3, 7) and (-2, 11).13. Find the slope of a line that passes through (3, -2) and (-1, -6).14. Graph 3x + 2y = 6.A).jpg”>(Gridlines are spaced one unit apart.)C).jpg”>(Gridlines are spaced one unit apart.)B).jpg”>(Gridlines are spaced one unit apart.)D).jpg”>(Gridlines are spaced one unit apart.)15 Determine whether (0, 5) is a solution for y=3x-5.16. Determine whether (-2, 3) is a solution fThis section prepares you to complete this assignment successfully. Please follow these instructions to complete and submit this assignment.You will create a document in either a .doc or .rtf format to record and save your work. If you have never created documents in an .rtf format, please visit the Academic Resource Center and click on Tutorials. You will then see a list of tutorials on the following page. Click on RTF Tutorial.Read the instructions carefully and review your work before you submit your assignment.Include a title page with this assignment. Your title page should follow standard APA formatting. Please view the .allied.edu/Pages/ViewPage.aspx?GroupID=189″>Title Page Example.When you are ready to submit the assignment, click the Start button at the bottom of the page to access the submission page and follow the instructions.If you have any problems with this assignment, please e-mail your instructor.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Solve the system by addition.x + 4y = 23x – 2y = –222. Solve the system by addition.x + y = 8x – y = 83. Solve the system by addition.5x – 3y = 134x – 3y = 114. The sum of two numbers is 33. Their difference is 7. What are the two numbers?5. Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.6. Adult tickets for a play cost $16 and child tickets cost $6. If there were 25 people at a performance and the theater collected $260 from ticket sales, how many adults and how many children attended the play?7. Solve the system by substitution.x + 3y = –42x + 2y = –88. The difference of two numbers is 36. The larger is 6 less than 4 times the smaller. What are the two numbers?9. The base of a ladder is 6 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.10. A company produces doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets.11. Evaluate .png”>, if possible.12. Evaluate .png”>, if possible.13. State whether .png”> is rational or irrational.14. State whether .png”> is rational or irrational.15. The area of a square is 83 cm2. Find the length of a side to the nearest hundredth.16. The time in seconds that it takes for an object to fall from rest is given by .png”>, in which s is the distance fallen (in feet). Find the time required for an object to fall from the ground from a building that is 800 feet high. Round your answer to the nearest hundredth of a second.17. Simplify. .png”>18. Simplify. Assume x represents a positive real number. .png”>19. Simplify. .png”>20. Decide whether the following is written in simplest form. .png”>21. Simplify by combining like terms. .png”>22. Simplify by combining like terms. .png”>23. Find the perimeter of the triangle shown in the figure. Write your answer in reduced radical form..png”>24. Perform the indicated multiplication. Then simplify. .png”>25. Perform the indicated multiplication. Then simplify the radical expression. .png”>26. Perform the indicated multiplication. Then simplify the radical expression. .png”>27. Perform the indicated division. Rationalize the denominator, if necessary. Then, simplify..png”>28. Solve. .png”>Welcome to the Module 8 Homework Assignment for MAT 110: Beginning Algebra.Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.1. Solve for x. x2 + 2 = 62. Solve for x. (x + 4)2 = 33. Solve for x. –9(x – 3)2 = –74. The base of a 19-ft ladder is 6 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth.5. Solve the equation for x. (2x – 1)2 – 9 = 06. The square of 3 more than a number is 36. Find the number.7. Determine whether the following19. Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2-12×20. Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+2×21. Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2-8×22. Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+x23. Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+9×24. Solve by completing the square. X^2+8x=-1525. Solve by completing the square. X^2+6x+2=026. Solve by completing the square. X^2+x-1=027. Solve by using the quadratic formula. X^2+11x-12=028. Solve by using the quadratic formula. X^2-6x+9=029. Solve by using the quadratic formula. 3x^2-7x=330. An entry in the Apple Festival Poster Contest must be rectangular and have an area of 1200 square inches. Also, its length must be 20 inches longer than its width. Find the dimensions each entry must have.CHECK UNDERSTANDINGQuestion Points1. A formula that relates Fahrenheit and Celsius temperature is C = 5/9 (F – 32). If the current temperature is 50°F, what is the Celsius temperature?a. –4°Cb. 10°Cc. 60°Cd. 46°12. Evaluate. 12 ÷ 2 – 6 ÷ 3a. 3b. 4c. 5d. 63. Divide. Write the result in simplest form. 9/10 ÷ 12/5a. 3/8b. 54/25c. 8/3d. 25/544. Evaluate. (–9)2 – 22a. –85b. –22c. 77d. 855. Identify the property that is illustrated by the following statement. 10 + 16 = 16 + 10a. Commutative property of additionb. Associative property of additionc. Distributive property16. Perform the indicated operation. Write the result in the simplest form. 3 1/5 + 2 2/3a. 8 8/15b. 5/6c. 5 13/15d. 1 1/617. Find the GCF for 7 and 26.a. 1b. 7c. 26d. 18218. Write the following geometric expression using the given symbols: Four times the radius (r) squared timesa. (4)2rb. (4r)2c. 4r2d. 4r219. Divide. –2 ÷ 0a. –2b. 0c. Undefinedd. 1110. Evaluate if m = -2, n = 4, and p = -1.a. –24b. 24c. –16d. 16111. Find the decimal equivalent of 5/9 rounded to the hundredths place.a. 0.55b. 0.56c. 0.57d. 0.581125. Multiply. Be sure to simplify the product. 2/9 4/5a. 8/45b. 4/7c. 3/7d. 5/18126. Add. 13 + (–9)a. 22b. 4c. –4d. –2227. Divide. 1.928 ÷ 1.6a. 0.995b. 0.905c. 1.205d. 1.325128. If the circumference of a circle whose radius is r is given by C = 2r, in which 3.14, find the circumference when r = 3 centimeters (cm).a. 18.84 cmb. 9.42 cmc. 4.71 cmd. 28.26 cm29. Write the following phrase using symbols: 7 times the sum of q and ta. 7q + tb. 7(q + t)c. 7 + (qt)d. 7 + (q + t)30. Write 860% as a decimal.a. 8.6b. 860c. 86,000d. 86MOD 2Upon returning to the U.S. from Canada, Burgette exchanged her remaining 150 Canadian Dollars for 134.53 U.S. Dollars. What exchange rate did she receive? [Hint: Use the equation 150x = 134.53 to solve this problem. Round to the nearest thousandth.]a. 0.896 U.S. Dollars for each Canadian Dollarb. 0.897 U.S. Dollars for each Canadian Dollarc. 1.114 U.S. Dollars for each Canadian Dollard. 1.115 U.S. Dollars for each Canadian Dollar12. Is 13 a solution to the equation 8 – x = 5?a. Yesb. No13. Solve. 4x – 0.76 = 3(x – 0.03)a. 0.81b. 0.67c. 0.46d. 1.0114. The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs.a. 4 cmb. 5 cmc. 11 cmd. 12 cm5. Solve for x. 10 – 5x = 25a. –3b. 5c. –15d. –7b.c.d.117. Elaine was charged $840 interest for 1 month on a $5600 credit card balance. What was the monthly interest rate?a. 15%b. 14.5%c. 16%d. 15.5%118. Solve for x. –2x = 6a. –3b. 3c. –12d. 12119. A necklace was marked up $225 from cost, which amounts to a 50% increase. Find the original cost of the necklace.a. $465b. $460c. $455d. $45020. Solve for x. x – 2 + 7x = 8x – 2a. 0b. 1c. Identityd. No solutionMOD 3Question Points1. Fill in the blank: A polynomial is ________ a binomial.a. neverb. sometimesc. always12. Add 5y – 4 and 2y2 – 8y.a. 2y2 – 3y – 4b. 2y2 + 3y – 4c. 7y2 – 12y – 4d. 2y2 + 13y – 413.Perform the indicated calculations. Write your result in scientific notation.a. 8 x 10–31b. 8 x 10–3c. 8 x 103d. 8 x 103114. Write in descending order and give the degree. 8 – xa. x – 8; 1b. x – 8; 0c. –x + 8; 1d. –x + 8; 015. Multiply. (–4×119. Subtract 6×2 – 2x + 8 from 10×2 – 10x + 3.a. 4×2 – 12x + 11b. 4×2 – 12x – 5c. 4×2 – 8x – 5d. 4×2 – 8x + 11120. Divide.a.b.c.d.MOD 4Question Points1. Solve the quadratic equation. 3x(2x – 5) = 75a. 0,b. 0, -c. 5, -d. –5,12. Subtract. Express your answer in simplest form.a.b.c. 2d.13. The GCF of 6y + 3 is 3. The GCF of 10y + 12 is 2. Find the GCF of the product (6y + 3)(10y + 12).a. 1b. 30c. 6d. 514. Determine whether the following trinomial is a perfect square. If it is, factor the binomial. x2 + 9x + 9a. Yes; (x + 3)2b. Yes; (x – 3)2c. Yes; (x + 9)2d. No15.State which method should be applied as the first step for factoring the polynomial.2×2 + 5xy + 2x + 5ya. Find the GCF.b. Group the terms.c. Factor the difference of squares.d. Use the ac m17. During rush hour, Fernando can drive 25 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Fernando’s rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.a. 36b. 38c. 45d. 4718. Factor completely. x2 + x – 42a. (x – 1)(x + 42)b. (x + 1)(x – 42)c. (x + 6)(x – 7)d. (x – 6)(x + 7)119. Solve the quadratic equation. x2 = –6xa. 0, –6b. 0, 6c. 6, –6d. 2, 6120. Solve for x.a. 8b.c. 32d.121. Multiply.a.b.c. –n2 + nd. 322. Factor completely. 9×2 + 30xy + 25y2a. (3x + 5y)2b. (3x – 5y)(3x + 5y)c. (9x + 5y)(x + 5y)d. (3x + y)(3x + 25y)123. Add or subtract as indicated.a.b.c.d.024. Write in simplest form.a.b.c. 4a4bd.125. What values for x, if any, must be excluded in the following algebraic fraction?a. 0b. –6c. 6d. None126. Factor the trinomial completely.. 6b4 – 18b3 – 60b2a. 6b2(b + 2)(b – 5)b. 6b2(b – 2)(b + 5)c. 6(b2 + 2)(b2 – 5)d. b2(2b + 5)(3b + 10)27. Write the expression in simplest form.a.b. -c. -d.28. Factor out the GCF with a negative coefficient. –40p2q5 + 24pq4 – 40q3a. –8(5p2q5 + 3pq4 – 5q3)b. –8(5p2q5 – 3pq4 + 5q3)c. –8q3(5p2q2 – 3pq + 5)d. –8q3(5p2q2 + 3pq – 5)129.Perform the indicated operations.a.b.c.d.130. Solve for x. + 7 = 7a. 0b. 35c. 49d. 84MOD 5Question Points1. Determine which of the ordered pairs is a solution for the equation 2x – 4y = 8.a. (0, 2)b. (–4, 0)c. (–4, –2)d. (0, –2)12.Find the slope of the graphed line.a. 0b. 1c. -2d. Undefined13.Give the coordinates of the point graphed below:a. (0, 4)Hint: An Introduction to GraphingSLO5:Identify how to graph linear equations and determine the slope of a line.LO5C:determine the slope of a line.115. Plot the point with coordinates (–4, 3).a.b.c.d.MOD 6Rewrite the equation 2x – 3y = –6 as a function of xa. f(x) = x + 2b. f(x) = x – 3c. f(x) = x – 6d. f(x) = x + 612. Find the slope of the following equation: y = 3x + 5a. 3b. 5c. 0d. 113. If f(x) = 5×2 – 3x + 1, find f(–2).a. -13b. 15c. -25d. 2714. Graph f(x) = 3x + 2.a.b.c.d.15.Determine which two equations represent parallel lines.(a) y = –7x + 2(b) y = 7x + 2(c) y = x + 2(d) y = –7x + 6a. (a) and (b)b. (b) and (c)c. (a) and (c)d. (a) and (d)16. Given f(x) = –5x + 3, find f(a – 3).a. –5a + 18b. –5c. a – 5d. a + 187. Graph the inequality. 3(x – y) + 2x < 3a.b.c.d.18. Find the slope of any line perpendicular to the line through points (5, 12) and (6, 2).a. -10b. 10119.Match the graph with one of the equations.a.b.c.d.120.Match the graph with one of the equations.a.b. y = 3xc.d. y = x + 3MOD 7Simplify .a. 54b.c.d.12. State whether is rational or irrational.a. Rationalb. Irrational13.PA manufacturer has two machines that produce dog toys. On Wednesday, machine A operates for 4 hours and machine B operates for 5 hours and 175 dog toys are produced. On Thursday, machine A operates for 6 hours and machine B operates for 5 hours and 225 dog toys are produced. Use the following system:4x + 5y = 1756x + 5y = 225where x is the number of dog toys produced by machine A in an hour and y is the number of dog toys produced by machine B in an hour. Solve the system graphically.a. A: 25 per hour, B: 15 per hourb. A: 15 per hour, B: 25 per hourc. A: 5 per hour, B: 15 per hourd. A: 15 per hour, B: 5 per hour5. State whether is rational or irrational.a. Rationalb. Irrational16. Adult tickets for a play cost $17 and child tickets cost $12. If there were 32 people at a performance and the theater collected $474 from ticket sales, how many children attended the play?a. 13 childrenb. 14 childrenc. 15 childrend. 18 children17.The forces (in pounds) on the arm of an industrial lift provide the equations.1.4x + 1.8y = 502.7x - 1.2y = 10Use the addition method to solve this system. Round your results to the nearest hundredth.a. x = 13.54 lb, y = 21.01 lbb. x = 21.01 lb, y = 13.54 lbc. x = 18.50 lb, y = 11.93 lbd. x = 11.93 lb, y = 18.50 lb18. A 82-ft rope is cut into two pieces so that one piece is 8 ft longer than the other. How long is each piece?a. 29 ft, 53 ftb. 37 ft, 45 ftc. 8 ft, 74 ftd. 41 ft, 41 ft19. The base of a ladder is 4 feet away from the wall. The top of the ladder is 5 feet from the floor. Find the length of the ladder to the nearest thousandth.a. 6.403 feetb. 4.271 feetc. 8.704 feetd. 5.382 feet10.Solve the following system by adding.-0.3x + 0.9y = -6.60.6x + 0.4y = -22a. (–26, –16)b. (–260, –160)c. (–16, –26)d. (–160, –260)011. Simplify. Assume x represents a positive real number.a.b.c.d.112. Solve.a. 1b. 0c. -1d. No solution113. Simplify. Assume all variables represent positive real numbers.a.b.c.d..1a. (–1, –8)b. (–8, –1)c. (1, 8)d. (8, 1)118. A chemist has a 35% and a 15% acid solution. How much o