Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 206329: Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height "t" seconds after it is tossed is - 16t^2 + 96t feet. The green ball is given an initial velocity of 80 feet per second and its height "t" seconds after it is tossed is - 16t^2 + 80 feet.
a) Find a polynomial D(t) that represents the difference in the heights of the two balls?
b) How much higher is the red ball 2 seconds after the balls are tossed?
c) In reality, when does the difference in the heights stop increasing?
I am not even sure how to find any of these solutions and am not even sure how to set up the problems to solve them. Please share the formulas using applications so I may solve.
Click here to see answer by scott8148(6628)

Question 206335: Solve for the indicated variable:
A = 2pi r^2 + 2 pi r h for positive r
or A = 2 Πr^2 + 2Πrh
Thank you! You are great!
Click here to see answer by Alan3354(31518)

Question 206304: Please help me solve this problem
Click here to see answer by mickclns(59)

Question 206336: This weekend, while my fiance and daughter were out of town, I decided to paint my living room. I am a horrible painter, but my mom Mary, is excellent. It takes me 4 more hours to paint room the same size of my living room than it takes my mom. We painted the room in 5 hours together. If we worked independently, how long would it take to finish painting the room?

Click here to see answer by Alan3354(31518)

Question 206352: how to do you find all values of y satisfying this equation?
7/y-2= -8 -3/y-1
Click here to see answer by stanbon(57962)

Question 206352: how to do you find all values of y satisfying this equation?
7/y-2= -8 -3/y-1
Click here to see answer by vleith(2825)

Question 206375: The problem I am trying to figure out really has me stumped.I have to "factor completely" 185x^2 + 9x -2. I have tried grouping, GCF, FOIL, trial and error and I can't come up with anything any better than x(185x + 9)-2. Can you help me?
Click here to see answer by scott8148(6628)

Question 206417: How is this problem simplified?
10x^2 - 5x
___________ <-----(divided by)
5x
Click here to see answer by nerdybill(7003)

Question 206444: This question is from an Appendix for an assignment I need to turn in. Can you please help me with the steps to complete the answer? (The question has copied and pasted into this box.)
a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).
Thank you,
Snoopyg
Click here to see answer by stanbon(57962)

Question 206449: I am studying for the compass exam and I see that others have posted the same question: What is the rational expression when r is not equal to plus or minus 2, r^2-5r+6 / r^2-4. What I don't understand is why r^2-5r+6 factors to [(r-3)(r-2)]...please help!
Click here to see answer by stanbon(57962)

Question 206464: If f(x)=1-3x and g(x)=1/x2+1,find f(g(0)) and g(f(1)).
(by 1/x2+1 i mean 1 over x squared plus 1) PLEASE HELP!!!

Click here to see answer by stanbon(57962)

Question 206536: Simplify each complex fraction. Reduce each answer to lowest terms.
ab + b^2/4ab^5/a + b/6a^2b^4
Click here to see answer by stanbon(57962)

Question 206551: Please help me factor this equation. Thank you.

Click here to see answer by Alan3354(31518)

Question 206551: Please help me factor this equation. Thank you.

Click here to see answer by stanbon(57962)

Question 206554: Please help me factor this equation:
Thank you.

Click here to see answer by Alan3354(31518)

Question 206554: Please help me factor this equation:
Thank you.

Click here to see answer by jim_thompson5910(28708)

Question 206554: Please help me factor this equation:
Thank you.

Click here to see answer by stanbon(57962)

Question 206533: Perform the indicated operation. Reduce each answer to lowest terms.
y/4 + 2y
Click here to see answer by HyperBrain(694)

Question 206534: Simplify each complex fraction. Reduce each answer to lowest terms.
1/9+1/3x and all of this is over x/9-1/x
Click here to see answer by profemmanuel2q@yahoo.com(15)

Question 206598: This questions comes from a Checkpoint I am currently taking in Algebra 117. This is the second Algebra class I have had within a year, the first being Algebra 116. Will you please help convert the following expression to a decimal notation and simplify the answer?
All your help has been stupendous! Don't know what I would do without your tutoring.
Thank you,
Snoopyg
Click here to see answer by nerdybill(7003)

Question 206640: I need to simplify x^-1+2/x+2x^2
I know that x^-1 is equal to 1/x. I get a little confused on what to do next. Do I add or multiply the 1/x to what is left--which would be 2/x+2x^2. Any help you can provide would be greatly appreciated.
Click here to see answer by ichudov(499)

Question 206639: Please help me factor this trinomail:

Thank You.
Click here to see answer by jim_thompson5910(28708)

Question 206660: Please help me factor completely:

Thank you.
Click here to see answer by Marth(57)

Question 206660: Please help me factor completely:

Thank you.
Click here to see answer by jim_thompson5910(28708)

Question 206665: This questions comes from a Checkpoint I am currently taking in Algebra 117. This is the second Algebra class I have had within a year, the first being Algebra 116. Will you please help convert the following expression to a decimal notation and simplify the answer? 10^-2
All your help has been stupendous! Don't know what I would do without your tutoring.
Thank you,
Snoopyg

Click here to see answer by Alan3354(31518)

Question 206666: Please help me solve:

Thank you.
Click here to see answer by jim_thompson5910(28708)

Question 206549: I cannot find an example of this problem worked in my textbook. I even tried my various MathZone learning tools but still could not find an example. This is from Chapter 6.1 Reducing Rational Expressions - Will someone please provide an example of how to work this type problem with step by step instructions?
Toxic pollutants. The cost, in million of dollars, to remove p% of toxic chemicals from a town's water supply is given by the formula
C= 6,000/200-2x. Answer the following questions:

a. What is the cost to remove 75% of the pollutants?
b. Describe what happens to the cost as the percentage of pollutions removed increased from 75% and moves toward 100%.
c. According to this model, is it possible to remove 100% of the pollution? Why or why not?
Click here to see answer by stanbon(57962)

Question 206703: 2x^4-162 and then there is 3x^3-3x
The directions say to factor completely, or state that the polynomial is prime.
Click here to see answer by edjones(7569)

Question 206750: show me the steps to figure this out.
what is the value of the expression
when and
Click here to see answer by Edwin McCravy(8999)

Question 206757: factor this and tell me step by step how you get every answer..
9x^3+18x^2-x-2
Click here to see answer by stanbon(57962)

Question 206764: Find the vertex of the parabola y=-2xto the second power+ 12x-13=?
Click here to see answer by jim_thompson5910(28708)

Question 206776: Filing a tank. A water tank has an inlet pipe and a drain pipe. A full tank came be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidently opened when the tank is full, then how long will it take to empty the tank? Ok, drain pipe=30 minutes while the inlet pipe=45 minutes. So would it take 30d/45i=30 to 45 ratio. I am lost after this. Help!!
Click here to see answer by Alan3354(31518)

Question 206775: The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangel was one for which the ratio of the length to the width was approximately 8 to 5, the golden ratio. If the length of a rectangle painting is 2 feet longer than its width, then for what dimensions would the length and the width have to the golden ratio? Ok, the ratio is L=8 to W=5. However, the length is 2 feet more, so is the L=8+2 and W=5. Would the golden ratio be 10 to 5? I am lost.
Click here to see answer by stanbon(57962)

Question 206778: Hi can someone please help with this one;
Solve for w
1 = w x 0.6 + (1 - w) x 2
Click here to see answer by Alan3354(31518)

Question 206791: How do I divide polynomials? I need help solving using long division.
8t^3 - 22t^2 - 5t + 12 / 4t + 3
Click here to see answer by vleith(2825)

Question 206806: ``Filing a tank. A water tank has an inlet pipe and a drain pipe. A full tank came be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidently opened when the tank is full, then how long will it take to empty the tank? Ok, drain pipe=30 minutes while the inlet pipe=45 minutes. So would it take 30d/45i=2/3. I am lost. Could you explain to me step by step so I can understand. I did receive an earlier answer of 90 minutes but I need a second opinion. If it takes 30 minutes for the tank to empty and 45 minutes to fill. wouldn't the tank continue to fill because the inlet is open? Please explain to me !!
Click here to see answer by Alan3354(31518)

Question 206873: I need the answer to this equation and also the steps to get the answer
x^2+3x-10
--------- =
x=5
Click here to see answer by jim_thompson5910(28708)

Question 206909: Simplify:
2(8x^2y-7xy+3xy^2)-(3x^2y-2xy-9xy^2).

Click here to see answer by jim_thompson5910(28708)

Question 206920: why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression?

Click here to see answer by stanbon(57962)

Question 206961: (3y^8)(2zy^2)^4

Click here to see answer by stanbon(57962)

Question 206983: Please help...
An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50in^2. Find the depth of the gutter.
Click here to see answer by checkley77(12569)

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, 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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, 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