Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 1203907: a norman windo with a perimeter of 20 units has the shape of rectangle surmounted by a semi-circle. If its base is x units long and the height of the rectangle is y units long, write a mathematical model for its area in terms of x.

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Question 1203920: The model y=120x+55 represents the total cost a plumber charges per hour. What represents the domain of the function, if the plumber does not work more than 6 hours on a job?

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Question 1203920: The model y=120x+55 represents the total cost a plumber charges per hour. What represents the domain of the function, if the plumber does not work more than 6 hours on a job?

Click here to see answer by mananth(16946) About Me 

Question 1203919: Dario has an arcade debit card with a $75 prepaid balance to use for the
summer. Each time he plays a game he is charged 48 cents. The
function b(g) = 75 − 0.48g models the amount of money Dario has on
his debit card after playing g games.
Select all of the constraints for this context.
Ⓐ b(g) ≥ 0
Ⓑ b(g) ≤ 75
Ⓒ b(g) ≤ 156
Ⓓ g ≥ 0
Ⓔ g ≤ 75
Ⓕ g ≤ 156

Click here to see answer by josgarithmetic(39618) About Me 
Question 1203919: Dario has an arcade debit card with a $75 prepaid balance to use for the
summer. Each time he plays a game he is charged 48 cents. The
function b(g) = 75 − 0.48g models the amount of money Dario has on
his debit card after playing g games.
Select all of the constraints for this context.
Ⓐ b(g) ≥ 0
Ⓑ b(g) ≤ 75
Ⓒ b(g) ≤ 156
Ⓓ g ≥ 0
Ⓔ g ≤ 75
Ⓕ g ≤ 156

Click here to see answer by math_tutor2020(3817) About Me 

Question 1203953: What is the average rate of change of the function g(x)=3-2/3x on the interval -2 ≤ x ≤ 6?
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Question 1203954: A speed versus time graph is shown below. What is the average rate of change in the speed from 8 seconds to 10 seconds? Please let me know the steps you took to arrive at your answer.
Graph link: https://gyazo.com/0c25dcc85dd8dd5590ea989e1ea608b3

Click here to see answer by Alan3354(69443) About Me 
Question 1203954: A speed versus time graph is shown below. What is the average rate of change in the speed from 8 seconds to 10 seconds? Please let me know the steps you took to arrive at your answer.
Graph link: https://gyazo.com/0c25dcc85dd8dd5590ea989e1ea608b3

Click here to see answer by MathLover1(20850) About Me 

Question 1203952: Estimate the instantaneous rate of change in the area of a circle when the radius is 3 cm. The formula for the area of a circle is A=πr^2
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Question 1203952: Estimate the instantaneous rate of change in the area of a circle when the radius is 3 cm. The formula for the area of a circle is A=πr^2
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Question 1203971: What is the average rate of change of the function g(x)=3-2/3x on the interval -2 ≤ x ≤ 6?
Please provide full steps toward the answer. Thank you

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Question 1203970: An object travelling in a straight line away from a motion sensor at a constant rate moves from 4 m away to 16 m away between t = 1 s and t = 6 s. Describe the segment corresponding to this walk on the speed versus time graph.
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Question 1203974: Determine all possible values of a such that the average rate of change of the function h(x)=x^2+3x+2 on the interval -3 ≤x ≤a is -1.
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Question 1203974: Determine all possible values of a such that the average rate of change of the function h(x)=x^2+3x+2 on the interval -3 ≤x ≤a is -1.
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Question 1203974: Determine all possible values of a such that the average rate of change of the function h(x)=x^2+3x+2 on the interval -3 ≤x ≤a is -1.
Click here to see answer by ikleyn(52794) About Me 

Question 1204034: Express the rule in function nota-
tion. (For example, the rule “square, then subtract 5” is expressed
as the function f1x2  x2  5.)
7. Multiply by 3, then subtract 5
8. Square, then add 2

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Question 1204160: An amusement park charges a cost per ride plus an entrance fee. The total cost, f(x), in dollars, of riding x rides is modeled by the function shown.


y=0.50x+6.99
which part of the function represents the cost per ride?

A. X
B.6.99
C. 0.50
D. 0.50x

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Question 1204305: Determine whether the binomial (3x - 2) is a factor of the polynomial 3x%5E3-14x%5E2%2B26x-12




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Question 1204305: Determine whether the binomial (3x - 2) is a factor of the polynomial 3x%5E3-14x%5E2%2B26x-12




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Question 1204305: Determine whether the binomial (3x - 2) is a factor of the polynomial 3x%5E3-14x%5E2%2B26x-12




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Question 1204305: Determine whether the binomial (3x - 2) is a factor of the polynomial 3x%5E3-14x%5E2%2B26x-12




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Question 1204303: Identify the end behaviour of g%28x%29=-3x%5E4%2Bx%5E3-9x%5E2%2B2x-3
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Question 1204299: What two parts of a polynomial function indicate the end behaviours of the graph?
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Question 1204299: What two parts of a polynomial function indicate the end behaviours of the graph?
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Question 1204302: State the end behaviours of the polynomial function g(x)=x(3x-4)(-2x+1)(x-5)?
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Question 1204304: Write an equation and sketch an example of a quartic function with the zeros at - 4, - 1, 2 (order 2). Be sure to include an image of your solution.

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Question 1204304: Write an equation and sketch an example of a quartic function with the zeros at - 4, - 1, 2 (order 2). Be sure to include an image of your solution.

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Question 1204304: Write an equation and sketch an example of a quartic function with the zeros at - 4, - 1, 2 (order 2). Be sure to include an image of your solution.

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Question 1204343: Factor the polynomial -2x%5E3%2B12x%5E2%2B8x-48 using the factor theorem.
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Question 1204344: When ax%5E3-x%5E2%2B3x%2Bb is divided by x - 2, the remainder is 59. When it is divided by x + 1, the remainder is - 1. Find the values of a and b.
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Question 1204342: Hi, can you help me to factor f%28x%29=x%5E4-2x%5E3-13x%5E2%2B38x-24 fully?
Click here to see answer by MathLover1(20850) About Me 
Question 1204342: Hi, can you help me to factor f%28x%29=x%5E4-2x%5E3-13x%5E2%2B38x-24 fully?
Click here to see answer by math_tutor2020(3817) About Me 

Question 1204359: Dario has an arcade debit card with a $75
prepaid balance to use for the summer. Each time he plays a game he is charged 48
cents. The function b(g)=75−0.48g
models the amount of money Dario has on his debit card after playing g
games.

Select all of the constraints for this context.

Click here to see answer by mananth(16946) About Me 
Question 1204359: Dario has an arcade debit card with a $75
prepaid balance to use for the summer. Each time he plays a game he is charged 48
cents. The function b(g)=75−0.48g
models the amount of money Dario has on his debit card after playing g
games.

Select all of the constraints for this context.

Click here to see answer by ikleyn(52794) About Me 

Question 1204492: Which illustrate a polynomial equation?
a. 2x^-3 + 5x^2 = 0
b. sqrt6x^5 + sqrt7x^3 = 0
c. 9/(x^2) = 0
d. 3x^7 - 5x^4 = 0

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Question 1204492: Which illustrate a polynomial equation?
a. 2x^-3 + 5x^2 = 0
b. sqrt6x^5 + sqrt7x^3 = 0
c. 9/(x^2) = 0
d. 3x^7 - 5x^4 = 0

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Question 1204562: Ms. R wants to construct a house for her pet bunny out of a cardboard box. To make the house she is going to cut squares of side length x cm from each corner of a rectangular box (see diagram below). The original dimensions of the uncut box are 51 cm by 45 cm. She wants the volume of the house to be 7175 cm^3.
Here is the link to the image: https://gyazo.com/b09d71efd4ffcfcc851e1ad3c3821622
a) Determine an equation that models this situation.
b) Find all possible dimensions of the box.

Click here to see answer by josgarithmetic(39618) About Me 
Question 1204562: Ms. R wants to construct a house for her pet bunny out of a cardboard box. To make the house she is going to cut squares of side length x cm from each corner of a rectangular box (see diagram below). The original dimensions of the uncut box are 51 cm by 45 cm. She wants the volume of the house to be 7175 cm^3.
Here is the link to the image: https://gyazo.com/b09d71efd4ffcfcc851e1ad3c3821622
a) Determine an equation that models this situation.
b) Find all possible dimensions of the box.

Click here to see answer by greenestamps(13200) About Me 

Question 1204560: Determine the solution to the double inequality 28≤2(4x+9)<5(x+7)≤64
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Question 1204559: Determine the intervals you would check to see when f%28x%29=7x%5E3%2B10x%5E2-11x-6%3C0
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Question 1204573: Write a function rule for the area of a rectangle whose length is 7ft more than its width. What is the area of the rectangle when its width is 12ft?

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Question 1204561: You are asked to factor a quintic polynomial g(x). Argue whether or not g(x) could be factored completely by using only the factor theorem. Give examples to support your argument(s). Make sure to discuss all possibilities (real solutions, no real solutions, rational solutions, etc.).
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Question 1204759: How does the graph of g(x) = (x-4)² + 3 compare to the parent function f(x) = x²?
A. g(x) is shifted 4 units to the left and 3 units up.
B. g(x) is shifted 3 units to the right and 4 units down.
C. g(x) is shifted 4 units to the right and 3 units up.
D. g(x) is shifted 3 units to the left and 4 units up.

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Question 1204759: How does the graph of g(x) = (x-4)² + 3 compare to the parent function f(x) = x²?
A. g(x) is shifted 4 units to the left and 3 units up.
B. g(x) is shifted 3 units to the right and 4 units down.
C. g(x) is shifted 4 units to the right and 3 units up.
D. g(x) is shifted 3 units to the left and 4 units up.

Click here to see answer by josgarithmetic(39618) About Me 

Question 1204826: Solve 7%2F3+=+5%2Fx+%2B4 for x.
Click here to see answer by mananth(16946) About Me 

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