Questions on Algebra: Graphs, graphing equations and inequalities answered by real tutors!

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Question 149847: what is the slope of the line that passes through the following pairs...
(-2/3, 6) (3, 9)
I know the problem is M = 9-6/3-(-2/3) Im stuck after M = 3/3-(-2/3)....can someone help me find the slope
Click here to see answer by josmiceli(19441)

Question 149740: a. For the polynomial P(x) =3x^3 + 13x^2 - 16
, what does Descartes' Rules of Signs tell you about the number of possible positive real zeros ? Choose one of the following
1. 0
2. 1
3. 2 or 0
4. 3 or 1

b. Use synthetic division to divide the polynomial 2x3 + 7x2 - 5 by 3 + x
write the quotient and the remainder.

c. let f(x)=x^2-4x-5/3x^2+2

(1) Find the domain.

(2) Determine the horizontal asymptote or oblique asymptote.

(3) Determine the vertical asymptotes
(4) Find the y-intercept.
(5) Find the intercepts

Click here to see answer by sandae(1)

Question 150018: 12. Solve. Find the exact solution(s). Show work. 5x^2 + 8x + 5 = 0
Click here to see answer by jim_thompson5910(35256)

Question 150020: 13. (8 pts) If a projectile is launched from a platform 40 feet high with an initial velocity of 96 feet per second, then the height of the projectile at t seconds is given by
s(t) = �16t^2 + 96t + 40 feet.
(i) At what time does the projectile attain its maximum height? Show some work.

(ii) What is the maximum height attained by the projectile? Show some work.

Click here to see answer by jim_thompson5910(35256)

Question 150021: 14. (7 pts) Casey is a salesperson who must decide between two monthly income options:
Option A: Salary of $1950 per month, plus 10% of monthly sales
or Option B: Salary of $2420 per month, plus 6% of monthly sales
For what amount of monthly sales is Option A a better choice for Casey than Option B?
Show work. Write an appropriate inequality and solve it. Be sure to state the answer to the question.

Click here to see answer by jim_thompson5910(35256)

Question 150022: A contagious disease is infecting residents of a town of 7,300 residents.
The number of residents infected t days after the disease has begun is given by the function

How many residents are infected with the disease after 6 days?

Click here to see answer by jim_thompson5910(35256)

Question 150023: ) Consider the polynomial f(x) = x3 + 6x2 � 25x + 18.
Find all of the zeros of the given polynomial. Be sure to show work.

Click here to see answer by jim_thompson5910(35256)

Question 150025: Let

(i) State the domain.

(ii) State the vertical asymptote(s).

(iii) State the horizontal asymptote.

(iv) Find the inverse function of f. Show work.

Click here to see answer by jim_thompson5910(35256)

Question 150026: Solve and check all proposed solutions.
Click here to see answer by jim_thompson5910(35256)

Question 150031: How to I calculate the data?
Plotting Points, Interpreting Data
The South Carolina Statistical Abstract reports the rate of Aggravated Assault (per 10,000 residents) as follows:
YEAR 1985 1986 1987 1988 1989 1990

IV. Assume that the population of South Carolina was 3.1 million in 1980, and grew at a steady 2.5% rate throughout the 80's. (a) Find the S.C. population for the years starting 1985 and ending in 1990, and (b) use those population values to calculate the numbers of aggravated assaults in S.C. during those years. Organize your information in a meaningful format in Excel, and construct a plot of your new data.
Click here to see answer by stanbon(75887)

Question 150052: Write the equation y = 4/3 x-1 in standard form using only integers and a positive coefficient for x. Match your result to the correct answer below.
A) 4x + 3y = �1
B) 4x � 3y = 1
C) 4x � 3y = �3
D) 4x � 3y = 3
Click here to see answer by nerdybill(7384)

Question 150076: Two planes leave O'Hare Airport Chicago at the came time. One flies directly east at 540 miles per hour. the other flies directly west at 720 miles per hour. How long will it take them to be 1890 miles apart?
Click here to see answer by nerdybill(7384)

Question 150044: Solve: 3 ( x- 1/3) = 7(x-1/7)
Click here to see answer by Alan3354(69443)

Question 150096: I need to, "Sketch the graph the feasible region"
x+y is greater than or equal to 7
I can't figure out how to do that. Any help would be greatly appreciated.
Click here to see answer by stanbon(75887)

Question 150146: i need help with this problem any help on how to do it is greatly appreciated. Also on whats it talking about im not sure either thank you for the help.
Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of line AB?
Click here to see answer by Fombitz(32388)

Question 148851: Use the rational roots theorem to solve:
p(x)=x^4-5x^3+5x^2+5x-6
Click here to see answer by Edwin McCravy(20054)

Question 150239: I need help graphing a line that goes through (2,3) and haas a slope of 1/2 on a rectangular coordinate system. I have been trying and trying this one for a while. I am using m=y2-y1/x2-x1. Is this correct.
My next question is writing 2 linear equations written in the slope intercept form that are 1 parallel and perpendicular. I know that parallel forms a 90 degree angle.
My last question is to find the slope of the line that goes through the points (-1,3),(5,-2) It would be greatly appreciated if you could help..
Click here to see answer by stanbon(75887)

Question 150225: Could someone help me with this problem? I know how to graph, but when the function deals with fractions I get a bit confused. I have indicated the answers and want to know if my answers are correct. I would appreciate help to see if I solved the problem correctly.
The problem states:
Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.
f(x)=1/2(x+6)^2+4
The vertex is: (-6,4)
The line of symmetry is x= -6
What is the maximum/minimum value of f(x)? 4
Is the value, f(-6)=4, a maximum or minimum? Maximum
Note: The 1/2 means one half, not 1 divided by 2, just to clarify the problem.
Did I solve this problem correctly? Thank you for your help.

Click here to see answer by Fombitz(32388)

Question 150369: If you can help me figure the points to plot, I can plot the points without any problem.
Plot the graphs of the following functions. Scan the graphs and post them to the Facilitator along with your response.
1. f(x)=7x
2. f(x)=4x - 3
3. f(x)=(1/5)x
4. f(x)= log3x

Click here to see answer by jim_thompson5910(35256)

Question 150341: Find the equation of a line passing through (-1,2) and (3,4)
Click here to see answer by jim_thompson5910(35256)

Question 150347: You are planning to spend no less than $6000 and no more than $10,000 on your landscaping project.
1. Write an inequality that demonstrates how much money you will be willing to spend on the project.
2. Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
3. Would 5 trees be a solution to the inequality in number 2? Justify your answer.
Click here to see answer by mangopeeler07(462)

Question 150402: Hope someone can help me with these

a. Marika is a salesperson who must decide between two monthly income options:
Option 1: Salary of $1412 per month, plus 10% of monthly sales
or Option 2: Salary of $2000 per month, plus 6% of monthly sales
What must the monthly sales amount be so that Option 1 is a better choice for Marika than Option 2?
Show all your calculations. (this is an example of linear inequality)

b. Solve and check the solutions.
2/x+2/x+1=3x-1/x^2-1

Click here to see answer by stanbon(75887)

Question 150340: Write the equation of a line, in slope-intercept form, passing through (2,3) and perpendicular to a line with an equation x-2y=2
Click here to see answer by mgmoeab(37)

Question 150435: Plot the graph of the following function.
f(x) =7^x
Click here to see answer by jim_thompson5910(35256)

Question 150436: Plot the graph of the following function
f(x) = 4^x-3
Click here to see answer by jim_thompson5910(35256)

Question 150438: Plot the graph of the following function
f(x) = log3^x
Click here to see answer by jim_thompson5910(35256)

Question 150339: Write the equation of a line in standard form, passing through (-2,-3) and parallel to a line with the equation 3x-y=2
Click here to see answer by ankor@dixie-net.com(22740)

Question 150454: Perform the indicated operation

(2b +3)(5b-1)-(b + 2)^2
Click here to see answer by jim_thompson5910(35256)

Question 150332: y=2/9x-3/4 in standard form
Click here to see answer by checkley77(12844)

Question 150481: For the following set of numbers,find the average, the median and the mode.
19,13,20,40,22,22
Average round to nearest ten
Median type and interger or decimal
Mode is/are if there is more than one mode use a comma to separate the numbers.
Click here to see answer by stanbon(75887)

Question 150480: Solve using the addition and multiplication principles.
9-9y-8y<162
The solution set is { y | y > __}.

Click here to see answer by stanbon(75887)

Question 150372: 1. Graph the following quadratic functions
F(x)= -x^2-2x+2
F(x)= -x^2+3x+2
F(x)= x^2+2x+2
F(x)= x^2-2x-2

2. Solve the equation and check the proposed solutions 2/x+2/x+1 = 3x-1/x^2-1. Show all work

Click here to see answer by Alan3354(69443)

Question 150542: Find the vertex and intercepts for each parabola. Sketch the graph.
G(x) = x� + x � 6

Click here to see answer by jim_thompson5910(35256)

Question 150437: Plot the graph of the following function
f(x) - (1/5)^x
Click here to see answer by josmiceli(19441)

Question 150478: Solve using the addition and multiplication principles.
5+2x<23
The solution set is {x, x__and __}
Type and inequality symbol, and then an integer or fraction.
Click here to see answer by Edwin McCravy(20054)

Question 150671: Find the x- and y-intercepts of 7x � 2y = �5
I think I suppose to solve this equation using the substitution method....
Click here to see answer by jim_thompson5910(35256)

Question 150676: Hi
Please help me and show me how to calculate the values for e^x, and e^2x and plot their values on a graph. Please help, How do I write this to get a value.
Click here to see answer by Earlsdon(6294)

Question 150691: x+y=13
x-y=-3
Click here to see answer by Fombitz(32388)

Question 150765: y<3x
Click here to see answer by jim_thompson5910(35256)

Question 150802: Which graph below correctly indicates the solution set of the linear inequality
y>3x-2?
ok....I am not understanding how to solve and graph inequalities.. please explain thanks
Click here to see answer by mangopeeler07(462)

Question 150811: Graph y=5x.
NOTE-the x after the 5 is an exponent.
Thanks,
Pat
Click here to see answer by jim_thompson5910(35256)

Question 150840: find the slope of a line parallel to the line -x = 2y + 5
Click here to see answer by Fombitz(32388)

Question 150842: choose the equation of the line parallel to the line 5 = -10x - 10y that passes through the point (-2, 1).
Click here to see answer by nerdybill(7384)

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, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975