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Tutors Answer Your Questions about Functions (FREE)
Question 88740: Not sure how to explain this: - completely confused
f(x)=[x3 x<1
[-1/2x2 +1.5 x>=1
Okay need to capture the equation from the [y=] then using graphing calculator make visual graphs for each compound function!!! - I havae no clue what this is talking about - OMG
HELP!!
Click here to see answer by bucky(2189)  |
Question 86433: 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?
10. Suppose Rent-A-Truck’s rates are $50 a day plus $0.50 per mile and Sam’s U-Drive’s
are $70 a day plus $0.45 a mile.
a. Find the mileage at which the cost for the two would be the same.
b. What is the cost?
c. Under what conditions should one rent from Rent-A-Truck?
11. To earn money for college, Susan is making and selling earrings. Her weekly costs
for advertising and phone calls are $36, and each pair of earrings costs $1.50 to
produce. If Susan sells the earrings for $6 per pair, how many pairs must she sell
per week to break even?
12. Rebecca is the star forward on her high-school basketball team. In one game, her
field-goal total was 23 points, made up of 2-point and 3-point baskets. If she made
4 more 2-point baskets than 3-point baskets, how many of each type of basket did
she make?
13. When Dale baby-sat for 8 hours and worked at a restaurant for 3 hours, he made a
total of $58. When he baby-sat for 2 hours and worked at a restaurant for 5 hours,
he made a total of $40. How much does Dale get paid for each type of work?
14. Beth has saved $4500. She would like to earn $250 per year by investing her money.
She received advice about two different investments; a low-risk investment that
pays a 5% annual interest and a high-risk investment that pays a 9% annual interest.
a. How much should Beth invest in each type of investment to earn her annual
goal?
b. How much should Beth invest in each type of investment if she wishes to
earn $325 per year?
15. The perimeter of a rectangular picture is 86 inches. Twice the width exceeds the
length by 2 inches. What are the dimensions of the picture?
16. The steel braces for a new bridge are in the shape of a right triangle. The hypotenuse
is 75 meters. The length of one leg is four times one-third of the length of the other
leg. Find the lengths of the legs.
17. Maggie is 12 years old and Dwayne is 16. How many years ago was Dwayne five
times as old as Maggie? How old were they at that time?
18. The sum of three numbers is -4. The second number decreased by the third is equal
to the first. The sum of the first and second number is -5. Find the numbers.
6.2
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?
Click here to see answer by ordy(1) |
Question 89379: 3. In captivity, the average life span of a grizzly bear is 9 years more than that of a tiger. The sum of the two average life spans is 41 years. Find the average life span of a tiger in captivity.
a. Define the variables.
b. Write the expression for the life span of a grizzly bear in terms of the life span of a tiger.
c. Write an equation for the sum of their life spans in term of one variable.
d. Solve the equation for the life span of a tiger.
4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now?
a. Define the variables.
b. Write an expression for the age of George in terms of Jeannie's age.
c. Write an equation for the sum of their ages in 5 years from now.
d. Solve the equation for the age of Jeannie now.
5. Mandy begins bicycling west at 20mph. Liz leaves from the same point 1 hour later bicycling west at 30mph. When will she catch up with Mandy?
a. Define the variables.
b. Make a chart.
distance=rate x time Rate Time Distance
Mandy 20 t 20t
Liz 30 t -1 30(t-1)
c. Set the distances equal to one another (they travel the same distance) and solve the equation for t.
d. What does t represent?
Click here to see answer by stanbon(75887) |
Question 89505: A. Find the function of the circle's center.
B. Find the radius of the cirle.
C. Use your answer from part (a) and (b) to write the standard form of the cirle's equation. y
|
|(3,6)
| *
| *(5,4)
|_____________x
Click here to see answer by stanbon(75887) |
Question 89530: This is a question from a packet i am supposed to do over the summer.
A prince packed a basket of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half of the apples, plus two more. The prince gave him the apples and set off again. A little further on, he was stopped by a second troll guard. This troll demanded payment of one-half the apples, plus two more. The prince paid him and set off again. A third troll stopped him and demanded one-half of the apples plus two more. The prince now has two apples left. How many apples did he pick?
Click here to see answer by scott8148(6628)  |
Question 89530: This is a question from a packet i am supposed to do over the summer.
A prince packed a basket of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half of the apples, plus two more. The prince gave him the apples and set off again. A little further on, he was stopped by a second troll guard. This troll demanded payment of one-half the apples, plus two more. The prince paid him and set off again. A third troll stopped him and demanded one-half of the apples plus two more. The prince now has two apples left. How many apples did he pick?
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 89883: 1. In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?
2. There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points:
Fahrenheit Celsius
Freezing point of water 32 0
Boiling point of water 212 100
1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.
2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.
3. How do the graphs of these two functions differ?
Do not just list the functions. You must show all of the steps you used to derive the functions.
Click here to see answer by stanbon(75887) |
Question 89921: It has been a long time since I have done any algebra. A friend of mine is taking an algebra course and I could help him if I could just get started by recalling a simple equation. Once this is explained to me, the ball will start rolling.
Thank you.
f(x)=2x(3)^-7 find f(1)^x
Click here to see answer by scott8148(6628) |
Question 90043: Please help me write and equation and figure out if the following word problem is a function:
Jake works as a car salesman. To determine his weekly salary, Jake earns a base rate of $850.00 per week plus a 3% commission of the sale price of the car. Does this real life example represent a function? Explain your answer.
Click here to see answer by stanbon(75887) |
Question 90407: 7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height.
a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.
b) How high is the rock after 0.5 seconds?
c) After how many seconds will the rock reach maximum height?
d) What is the maximum height?
Click here to see answer by stanbon(75887) |
Question 91049: It seems easy to answer but just want to know if my answer I did was right.
Question: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
Click here to see answer by stanbon(75887) |
Question 91371: The function h(x) was used to generate the following code:
21,30,45,30,60,27,18,15,63,18,60,63
Decode this message if h(x)=(f+g)(x) and f(x)= 2x+1 g(x)= x+2
I'm lost, how do I solve this?
Click here to see answer by Earlsdon(6294) |
Question 91997: Can someone check my work. You can't imagine how grateful I am to this site and to all of the tutors. I am able to see step by step my mistakes. thank you.
state the domain...I think I have it...maybe
f(x) = sq rt x+4
x + 4 = 0 - 4
x = -4 is the domain???
g(x) = 2x+1/x-3
x-3= 0
x - 3 = 0 + 3
x = 3
h(x)= 3x^2 + 5x - 3
all of the numbers are real, correct?
or
9x + 5x -3
14x-3 = 0
that's not right
l(x) = 2x + 3
D = all real numbers
m(x) = 3/x^2 + 7
x + 7 = 0
x + 7 = 0 - 7
x = -7
Click here to see answer by stanbon(75887) |
Question 91997: Can someone check my work. You can't imagine how grateful I am to this site and to all of the tutors. I am able to see step by step my mistakes. thank you.
state the domain...I think I have it...maybe
f(x) = sq rt x+4
x + 4 = 0 - 4
x = -4 is the domain???
g(x) = 2x+1/x-3
x-3= 0
x - 3 = 0 + 3
x = 3
h(x)= 3x^2 + 5x - 3
all of the numbers are real, correct?
or
9x + 5x -3
14x-3 = 0
that's not right
l(x) = 2x + 3
D = all real numbers
m(x) = 3/x^2 + 7
x + 7 = 0
x + 7 = 0 - 7
x = -7
Click here to see answer by jim_thompson5910(35256) |
Question 92007: I am lost
I'm not sure what this is asking? To plot my points help. my brain is mush right now.
Consider the function f(x)= x^2+4x+1
Find h, the x-coordinate of the vertex of this parabola.
Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
x __|_y_
____|___
____|___
h=__|___
____|___
____|___
Click here to see answer by mathispowerful(115) |
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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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