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Tutors Answer Your Questions about Functions (FREE)
Question 85314: For the function y = x2 - 6x + 8, perform the following tasks:
Put the function in the form y = a(x - h)2 + k.
What is the equation for the line of symmetry for the graph of this function?
Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Show graph here.
Explanation of graphing.
describe how this graph compares to the graph of y = x2?
Click here to see answer by stanbon(75887)  |
Question 85647: I have a question that states: evaluate each the function and simplify the results for each of the following:
f(x)={1/2x if x<-3
{1-3x if x > or equal to -3
simplify:
a)f(-3)
b)f(0)
c)f(4)
d)f(-2.1)
PLease help, I have no clue how to do these 4 problems....
Click here to see answer by stanbon(75887) |
Question 86028: I have a question that states find the vertex of the graph of the function f(x)=(x+4)^2+2. I have no clue about this and its due tonight. Can anyone help? I can't even find the right steps to work it out.
Click here to see answer by Earlsdon(6294) |
Question 85947: What part of the general slope-intercept equation represents the slope?
What part of the general slope-intercept equation represents the y-intercept?
Define the y-intercept.
Define the x-intercept.
Identify the x-intercepts and y-intercepts of the equations for problems #6 and #7. Describe how to graph the line.
#6. 2x + y = 13
#7. -16x + y = -4
Describe how you found the x-intercepts and y-intercepts in problems #6 and #7.
Click here to see answer by checkley75(3666) |
Question 86105: I have a homework question that is due in 4 hours and I have tried to figure it out with nothing working. The question is: find the domain and range of the function f(x)=-5x^2+3 I have no clue what I am doing or supposed to do. Can someone walk me thru this? Please.
Click here to see answer by tutor_paul(519)  |
Question 86219:
7. Michael is shopping for a new CD player with a built-in alarm clock. Electronics City has a special coupon for $30 off any CD player and is also having a sale with a 25% discount on any alarm clock.
a. Write a function rule to model a 25%-off sale, and a function rule to model a $30-off coupon.
b. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies the discount first and then the coupon.
c. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies the coupon first and then the discount.
d. Michael selects a CD alarm clock with a regular price of $150. How much more will the item cost if the clerk applies the coupon first?
e. Why does the CD alarm clock cost less if the discount is applied after the coupon?
8. The radius of a balloon is given by r = 0.3t, where t is the time it takes to blow up the
balloon. The volume of a sphere is given by V=4/3IIr^3
a) Find an equation for the composite function V(r(t)).
b) What is the input and output of the composite function?
c) Find the Volume of a balloon 5 seconds after blowing it up.
Click here to see answer by scianci(186) |
Question 86446: Hello,
I am having an issue with solving this problem.
I have gotten this answer and don't think that it is right.
3x^3-x^2-10x
The problem
let f(x)=3x+5, g(x)=x^2-2x
(g*f)(x)
Thank you so much for your help.
Click here to see answer by scianci(186) |
Question 86577: 7.3
5. A farmer has 90 acres available for planting millet and alfalfa. Seed costs $4 per acre for millet and $6 per acre for alfalfa. Labor costs are $20 per acre for millet and $10 per acre for alfalfa. The expected income is $110 per acre for millet and $150 per acre for alfalfa. The farmer intends to spend no more than $480 for seed and $1400 for labor.
a. Write a system of linear inequalities to represent the constraints.
b. Graph the feasible region
c. Write the objective function that maximizes the income, and find the
maximum income for the given constraints.
6. The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can product, at most, 200 units of paper a day. At least 10 units of notebook paper and 80 units of newsprint are required daily by regular customers. The profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350.
a. Write a system of linear inequalities to represent the constraints.
b. Graph the feasible region.
c. Write the objective function that maximizes the income, and find the
maximum income for the given constraints.
6. Jerry works no more than 20 hours a week during the school year. He is paid $10 an hour for tutoring geometry students and $7 an hour for delivering pizzas for Pizza King. He wants to spend at least 3 hours, but no more than 8 hours, a week tutoring. Find Jerry’s maximum weekly earnings.
7. A theater where a drug abuse program is being presented seats 150 people. The proceeds will be donated to a local drug information center. Admission is $2.00 for adults and $1.00 for students. Every two adults must bring at least one student. How many adults and students should attend in order to raise the maximum amount of money?
8. The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space and a bus requires 30 square meters of space. The attendant can handle no more than 60 vehicles.
a. Let c be the number of cars and let b be the number of buses. Write a system of inequalities to represent the amount of space available and the total number of vehicles allowed.
b. If a car is charged $2.50 to park and a bus is charged $7.50, how many of each should the attendant accept to maximize income?
c. The parking lot prices for special events are $4.00 for cars and $8.00 for buses. How many of each vehicle should the attendant accept during a special event?
7.4
1. A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color B requires 1 unit of yellow dye and 6 units of green dye. Find the constraints, graph the feasible region, and find the maximum number of gallons possible.
2. A delicatessen has 10 pounds of garlic-flavored sausage and 10 pounds of plain sausage. The deli wants to make as many pounds of bratwurst as possible. Each pound of bratwurst requires ˝ pound of garlic-flavored sausage and ˝ pound of plain sausage. Find the maximum number of pounds of bratwurst that can be made.
3. Machine A can produce 30 steering wheels per hour at a cost of $16 per hour. Machine B can produce 40 steering wheels per hour at a cost of $22 per hour. At least 360 steering wheels must be made in each 8-hour shift. What is the least cost involved in making 360 steering wheels, if maintenance of the machines limits their use to no more than 8 consecutive hours?
4. The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each should be accepted to maximize income?
5. The cost to run Machine 1 for an hour is $2. During that hour, Machine 1 produces 240 bolts and 100 nuts. The cost to run Machine 2 for an hour is $2.40. During that hour, Machine 2 produces 160 bolts and 160 nuts. With a combined running time of no more than 30 hours, how long should each machine run to produce an order of at least 2080 bolts and 1520 nuts at the minimum operating cost?
6. The Oklahoma City division of SuperSport, Inc produces footballs and basketballs. It takes 4 hours on machine A and 2 hours on machine B to make a football. Producing a basketball requires 6 hours on machine A, 5 hours on machine B and 1 hour on machine C. Machine A is available 120 hours a week, machine B is available 72 hours a week, and machine C is available 10 hours per week. If the company makes $3 profit on each football and $2 profit on each basketball, how many of each should they make to maximize their profit?
Click here to see answer by Flake(45) |
Question 86569: 6.1
I. Solve each system by graphing, and classify the system as dependent or independent,
consistent or inconsistent.
1. {2x+3y=-7
{3x-4y=2
2. {3x-2y=10
{4x+y=6
3. {x-9=3y
{x+2y=-1
4. {2x+3y=2
{3x-4y=-14
5. {2x+4y=6
{5x-3y=2
6. {y=3x
{x+21=-2y
7. {x+y=6
{3x-4y=4
8. {12x-9y=27
{8x-6y=18
9. {a+b=8
{1.5a+2b=13.5
10. {5x-y=3
{y=5x-3
11. {2x-3y=7
{2x+3y=7
12. {4/3x+1/5y=3
{2/3x-3/5y=5
II. Use a calculator to solve each system of equations to the nearest hundredth.
13. {y=3x-2 14. {y=1/4x+3 15. {y=-x+7
{y=-0.5x+5 {y=-2x+21 {8=2x-y
16. {y=0.125x-3.005 17. {12y=4x-16 18. {1/2x+1/3y=1
{y=-2.58 {9y-3x=3 {3x+2y=6
19. The perimeter of a rectangular picture is 36 inches. Twice the width exceeds the length by 2 inches. What are the dimensions of the picture?
20. Find a and b so that and are consistent and dependent equations.
6.2
Part I. Solve each system by substitution.
1. {3x+y=7
{4x+2y=16
2. {2x+3y=4
{x-2y=16
3. {2x+y=5
{3x-3y=3
4. {2x+2y=4
{x-2y=0
5. {y=x+3
{y=2x-4
6. {4x+5y=-7
{3x-6y=24
7. {2s-5t=22
{2s-3t=6
8. {4x+2y=20
{y=x-2
9. {2x=5+4y
{2y=8+x
10. {4y+30=10x
{5x-2y=15
11. {s=10+5t
{2s=40+4t
12. {12y-5z=19
{12y+16z=40
Part II. Solve each system .
13.{x-2y+z=-9 14. {2a+b=2 15. {x+y+z=-1
{2y+3z=16 {5a=15 {3x-2y-4z=16
{2y=4 {a+b+c=-1 {2x-y+z=19
16. The sum of three numbers is 20. The first number is the sum of the second and the third. The third number is three times the first. What are the three numbers?
17. Melissa works at Angela’s Pizza. Her last three orders were 5 slices of pizza, 2 salads and 2 sodas for $9.75; 3 slices of pizza, 2 salads, and 1 soda for $7.15; and 2 slices of pizza, 1 salad, and 1 soda for a total of $4.35. What are the individual prices for pizza, salad, and soda at Angela’s?
6.3
Part I. Review: Solve each system by substitution.
1. {2x+y=4 2. {x-9=3y 3 {c+3d=8
{3x+2y=1 {x+2y=-1 {1/3c+d=9
Part II. Solve each system by elimination
4. {2x+y=11 5. {6x+3y=6 6.{4x-2y=5
{3x+2y=1 {8x+5y=12 {2x=y-1
7. {4p+5p=7 8. {7b-5c=11 9.{1/3x+1/2y=7
{3p-2q=34 {-4c-2b=-14 {2/3x-y=-2
10. {5m+2n=-8 11. {2y-4x=18 12.{3x-5y=17
{4m+3n=2 {-5x+3y=23 {4x+5y=46
Part III. Solve each system
13. {3x-6y+3z=33 14. {6a-2b=18 15.{1/x-1/y=5/8
{2x-4y+2z=22 {3b+5c=-34 {3/x+2/y=5/8
{4x+2y-z=-6 {a+bc=-28
hint: eliminate x in the first two equations.
hint: let m=1/x
and n=1/y
6.4
Part I. Use two variables and two equations to set up each problem. Do not solve.
1. One integer is twice another and their sum is 96. Find the integers.
2. The sum of two integers is 38 and their difference is 12. Find the integers.
3. Three times one integer plus another integer is 29. If the first integer plus twice the
second is 18, find the integers.
4. Twice one integer plus another integer is 21. If the first integer plus 3 times the
second is 33, find the integers.
Part II. Use two variables and two equations for each problem. Solve the systems by any method you choose, and write the answer in the appropriate form.
5. A rancher raises five times as many cows as horses. If he has 168 animals, how
many cows does he have?
6. A landscaper used 100 pounds of grass seed containing twice as much bluegrass
as rye. He added 15 more pounds of bluegrass to the mixture before seeding a
lawn. How many pounds of bluegrass did he use?
7. A youth group with 26 members is going skiing. Each of the five chaperones will
drive a van or a sedan. The vans can seat seven people, and the sedans can seat five
people. How many of each type of vehicle could transport all 31 people to the ski
area in one trip?
8. In a mayoral election, the incumbent received 25% more votes than the opponent.
Altogether, 5175 votes were cast for the two candidates. How many votes did the
incumbent mayor receive?
9. The drama club at Lincoln High School sells hot chocolate, and coffee at the
school’s football games to make money for a special trip. At one game, they sold
$200 worth of hot drinks. They need to report how many of each type of drink
they sold for their club records. Macha knows that they used 295 cups that night.
If hot chocolate sells for $0.75 and coffee sells for $0.50, how many of each type
of hot drinks did they sell?
Click here to see answer by Flake(45) |
Question 86748: 6.4
Part I. Use two variables and two equations to set up each problem. Do not solve.
1. One integer is twice another and their sum is 96. Find the integers.
2. The sum of two integers is 38 and their difference is 12. Find the integers.
3. Three times one integer plus another integer is 29. If the first integer plus twice the
second is 18, find the integers.
4. Twice one integer plus another integer is 21. If the first integer plus 3 times the
second is 33, find the integers.
Part II. Use two variables and two equations for each problem. Solve the systems by any method you choose, and write the answer in the appropriate form.
5. A rancher raises five times as many cows as horses. If he has 168 animals, how
many cows does he have?
6. A landscaper used 100 pounds of grass seed containing twice as much bluegrass
as rye. He added 15 more pounds of bluegrass to the mixture before seeding a
lawn. How many pounds of bluegrass did he use?
7. A youth group with 26 members is going skiing. Each of the five chaperones will
drive a van or a sedan. The vans can seat seven people, and the sedans can seat five
people. How many of each type of vehicle could transport all 31 people to the ski
area in one trip?
8. In a mayoral election, the incumbent received 25% more votes than the opponent.
Altogether, 5175 votes were cast for the two candidates. How many votes did the
incumbent mayor receive?
9. The drama club at Lincoln High School sells hot chocolate, and coffee at the
school’s football games to make money for a special trip. At one game, they sold
$200 worth of hot drinks. They need to report how many of each type of drink
they sold for their club records. Macha knows that they used 295 cups that night.
If hot chocolate sells for $0.75 and coffee sells for $0.50, how many of each type
of hot drinks did they sell?
Click here to see answer by Edwin McCravy(20056)  |
Question 87115: Can you help me?
I am working on a problem. The problem is :
From a 12cm by12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box. Express the volume of the box as a function of the length, x, in centimeters, of a cut-out- square and determine a reasonable domain for this function.
So far I have a table that looks like : ( the lines separate the columns
length - volume
20 - 0
10 - 100
8 - 128
6 - 108
4 - 64
2 -20
0 -0
The instructor says that I am on the right track, but I need to find out how the length and the volume relate to each other. I know that the domain is {10,8, 6, 4,2}. If you could help me figure out the equation it would be helpful, I don't see patterns well.
THANK YOU
Amanda
PS I need to turn it in by tomorrow thank you again
Click here to see answer by scott8148(6628)  |
Question 87115: Can you help me?
I am working on a problem. The problem is :
From a 12cm by12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box. Express the volume of the box as a function of the length, x, in centimeters, of a cut-out- square and determine a reasonable domain for this function.
So far I have a table that looks like : ( the lines separate the columns
length - volume
20 - 0
10 - 100
8 - 128
6 - 108
4 - 64
2 -20
0 -0
The instructor says that I am on the right track, but I need to find out how the length and the volume relate to each other. I know that the domain is {10,8, 6, 4,2}. If you could help me figure out the equation it would be helpful, I don't see patterns well.
THANK YOU
Amanda
PS I need to turn it in by tomorrow thank you again
Click here to see answer by stanbon(75887) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660
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