MAT 1304 10

MAT1304

1.Findthe slope of the line through the following pair of points using theslope formula.(-2, -4) and (-11, -2) select the correct choicebelow, and if necessary, fill in the answer box to complete yourchoice.

Slope= change in Y/change in x

=(-2+4)/ (-11+2)

=-2/9a. The slope of the line is -2/92.Find theslope of the line if it is defined.Through (7, 9) and (7, -7)

Slope= (9+7)/7-7

17/0= ∞b. The slope is undefined.3. Find the slope,if it exists Select the correct choice below and fill in any answerboxes within your choice.3x-7y =14

Thisequation expressed in form of Y = mx + c will be as follows

7y= 3x -14

Y= 3/7x -2a. The slope is 3/74.Find the slope of thelineY=17This is the same rewriting the equation as y = 0x+ 17 the value of m = 0 implying the slope is 0a. The slope is0 (zero)5.Find an equation of the line having the givenslope and containing the given pointM = -7, (6, 9)Theequation of the line is y = (simplify your answer. Type your answerin slope-intercept form. Use integers or fractions for any numbers inthe expression.)

(Y– 9)/(x – 6) = -7

Y– 9 = -7(x – 6)

Y– 9 = -7x + 42

Y= -7x + 51

6.Find an equation of the line that contains the following pair ofpoints.The equation of the line is.(3, 2) and (1, 5)(simplify your answer. Type your answer in slope-intercept form. Donot factor)Slope = (5 – 2)/1-3

=-1.5

Equationof the line (y – 5)/(x – 1) = -1.5

Y– 5 = -1.5 (x – 1)

Y= -1.5x + 1.5 + 5

Y= -1.5x + 6.5

7.Find an equation for the given line in the form ax + by = c, where a,b, c are integers with no factor common to all three and a _>_0.Through (-8, 10) parallel to 5x + 4y = 17 The equationof the line in the form ax + by = c, passing through (-8, 10) andparallel to 5x + 4y = 17 is. (Simplify your answer.)

Slopeof the line 5x + 4y = 17 is -5/4 since the equation can be expressedas y = -5/4x + 17/4

Becausethe lines are parallel to each other, it implies they have the samegradient. Therefore, the equation of the line would be

(y– 10)/(x + 8) = -5/4

4(y-10)= -5 (x + 8)

4y– 40 = -5x – 40

Writtenin the form of ax + by = c it would be as follows

5x+ 4y = 0

9.Write an equation in standard form for the line describedThrough(7, 8), perpendicular to 8x + y = 2The equation of the line isx â + () y = ()

Thegradient of the given line is -8 since y = -8x + 2Because thelines are perpendicular, then the gradient of the other line is 1/8

Therefore,the equation of the line is as follows

(Y– 8)/ (x -7) = 1/8

8(y– 8) = x – 7

8y– 64 = x – 7

8y– x = 57

Instandard form -x + 8y = 5712. Graph the followingequation.7x + 4y = – 28Use the graphing tool to graph theequation.13.In 1999, there were 41,744 shopping centers in a certain country. In2009 there were 48,937.a. Write an equation expressingthe number y of shopping centers in terms of the number x of yearsafter 1999.

(48,937– 41,744)/ (2009 – 1999)

=7193/ 10

=719.3b.When will the number of shopping centers reach 80,000?(80,000 –48,937)/ x – 2009 = 719.3

31063= 719.3 (x – 2009)

31063= 719.3x – 1,445,073.7

719.3x= 1476136.7

X= 2052.2

Therefore,shopping centers will reach 80,000 in 2052

14.Let f(x) = 5 -3x. Find f (-5).F (-5) = 5 – 3 (-5)

=5 + 15=2015. Let g(x) = 6x -3. Find g (- ½)g(- ½) = Type an integer or a fraction.If g(x) = 6x –3, then g(-1/2) will be

6^-0.5– 3

=0.41– 3

=-2.59

16.Write a linear cost function for the following situation.A skiresort charges a snowboard rental fee of $20 plus $2.25 per hour.C(t) = (2.25) t+ 2017. Assume that the situation can beexpressed as a linear cost function. Find the cost function.Fixedcost is $100 50 items cost $2,100 to produce. The linear costfunction is C(x) = ().Variable cost = 2100 and fixed cost =100. In this case, X = 50

C(50)= 2100 + 100

C(50)= $220018. The dispatch tool works spends $32000 toproduce 140 parts, achieving a marginal cost of $210. Find the linearcost function.

Marginalcost implies producing one more part would cost $210 therefore,producing 140 parts would cost 140*210 = 29,400

Fixedcost = 32000 – 29400 = 2,600The linear cost function is C(x)= (210) x + 260019. Use the information listedbelow to solve parts a through h.Supposed that the demand andprice for a certain model of a youth wristwatch are related by thefollowing equation. P = D (q) = 24 – 1.25q.Where p is the price(in dollars) and q is the quantity demanded (in hundreds). Find theprice at each level of demand. Answer parts a through d.a.Findthe price when the demand is 0 watches.

Whenq = 0 P = 24 – 1.25 (0)

P= 24 dollarsThe price when the demand is 0 watches is $ 2421.Joan sells silk-screened T-shirts at community festivals and craftsfairs. Her marginal costs to produce one T-shirt is $2.50. Her totalcost to produce 40 T-shirts is $150, and she sells them for $6each.Find the linear cost function for Joanne’s T-shirtproduction.

Y– 150 = 2.50 (x – 40)

Y= 2.50x + 150 – 100

Y= 2.50x + 50

C(x)= 2.50x + 50

Howmany T-shirts must she produce and sell in order to break even?

Atbreak-even TR = TC

6x= 2.5x + 50

3.5x=50

X= 14.3

Howmany T-shirts must she produce and sell to make a profit of $700?

Profit= TR- TC

700= 6x – (2.50x + 50)

700= 6x – 2.5x -50

750= 3.5xx = 214.322. To produce xunits of a religious medal costs C(x) = 16x + 78. The revenue is R(x)= 29x. Both cost and revenue are in dollars.Find thebreak-even quantity.

TC=TR

16x+78 = 29x

13x= 78

X= 6

Break-evenquantity = 6 units

Findthe profit from 440 units.

Profit= TR – TC

29(440)– (16(440) + 78)

12760– 7040 – 78

=5642 dollarsFind the number of units that must be produced fora profit of $130.

Profitfunction = 29x – (16x +78)

=13x – 78130 = 13x -78

13x= 208

X= 16

=16 units23. A product has a production costfunction C(x) = 150x + 4350 and a revenue function R(x) = 200x. Findand analyze the break-even quantity, then find the profit function.Answer parts a and b below.

AtBreak-even, TR = TC 200x = 150x + 4350

50x= 4350

X= 87The break-even quantity is 87 units.Profitfunction = TR – TC

=200x – (150x + 4350)

=200x– 150x – 4350

=50x – 435024. Use the formula C=5/9(F -32) for conversionbetween Fahrenheit and Celsius to convert each temperature.a.75 degrees F to Celsius

C= 5/9 (75 -32)

C= 5/9 (47)

C= 26.11

=26.1degrees C

b.-30 degrees F to Celsius

C= 5/9 (-30 -32)

C= 5/9 (-62)

=-34.4 degrees Cc.30 degrees C to Fahrenheit

30= 5/9 (F – 32)

270= 5F – 160

5F= 430

F= 86

=86 degrees F

25.Use the echelon method to solve the following system of two equationsin two unknowns. Check your answersX + y = 135x + y= 17Select the correct choice below and, if necessary,fill in the answer box to complete your choice.a.The solutionis (1, 12)26.Use the echelon method to solve the given system of two equations intwo unknowns. Check your answers.3x – 2y = 06x – y= 9The solution of the system is (2, 3) 27.Use the echelon method to solve the given system of two equations intwo unknowns. Check your answers.16x -3y = 102x + 9y = 20The solution of the system is (25/26, 70/39) 28.Use the echelon method to solve the following system of two equationsin two unknowns. Check your answers.3x + 4y = 79x + 12y =6There is no solution.29. Use theechelon method to solve the following system of two equations in twounknowns. Check your answers.5x – 4y = – 3-10x + 8y =6There is no solution.30. Use theechelon method to solve the given system of two equations in twounknowns. Check your answers.X/2 + y = – 3/2X/7 + y =-38/7The solution of the system is (11, -7)

References

Lial,M. L., Greenwell, R. N., & Ritchey, N. P. (2012). *Finitemathematics (10th ed.)*.Boston, MA: Pearson Education.