Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 569574: Find Y in the following equation:

Click here to see answer by JBarnum(2044)

Question 569602: 1/a+1/b+1/x=1/a+b+x ,a#0,b#0,x#0,x#-(a+b).
Click here to see answer by Alan3354(31537)

Question 570434: the value of d in this equation: d-34.8=5.3
Click here to see answer by solver91311(17077)

Question 570512: please help me solve this problem 2x to the second power -3=1
Click here to see answer by jillfired(3)

Question 570645: Solve the equation by factoring.
(2x/x+3)+(5/x)-4=(18/x^2+3x)
--------------------------------
I have gotten this far with the problem....
LCM = X(x+3) thus I have 2x^2+5x+15-4x^2-12=18--->-2x^2+5x+3=18--->-2x^2+5x-15=0

I think my problem is the (-2x^2) which I got from 2x^2-4x^2 and the (-4x^2) is from multiplying the LCM (x(x+3))to -4.
Could you show me where my error is?
Thank you
Kenneth
Click here to see answer by Earlsdon(6294)

Question 570705: I need to solve : f(x)=(1)/(3) (x+4)^(2)+3 for the vertex, and the line of symmetry..Have been working on this one problem for about 20 minutes now.
Click here to see answer by scott8148(6628)

Question 570835: I am having a hard time solving this equation quadratic in form:
9x(to the 4th power)=85x(squared)-196.
I know it then becomes 9x(to the 4th power)-85x(squared)+196=0.
Then u = x squared. So then it becomes 9u squared-85u+196=0
Now I'm stuck on how to solve the equation from here because I don't think I factor here???
Click here to see answer by mananth(12270)

Question 570939: x^2-6x-28=0
Click here to see answer by jim_thompson5910(28717)

Question 571016: my homework question reads:
an object is thrown upward from the top of a 256ft tower at a velocity of 96ft/sec. Find the height after 3 seconds.
I know I need to use the quadratic equation, but I don't know what to do next.
3t=-16t^2+96t+256
16t^2-93t-256=0
Thanks for your help!
Click here to see answer by KMST(1936)

Question 570883: Ticket Sales
Living in or by a metropolitan area has certain advantages. Entertainment opportunities are almost boundless in a major city. Events occur almost every night, from sporting events to the ballet. Tickets to these events are not available long; and quantity of tickets demanded can often be modeled by quadratic equations.
Application Practice
Answer the following questions. You must use Equation Editor or MathType when writing mathematical expressions or equations. Working in a new MS Word file, provide solutions and answers to all problems, clearly labeling your work. You must show your steps or provide verbal explanations (where appropriate) to receive full credit. Use textbook examples as your guide as to what level of detail is expected.
1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day n. ( is the day tickets go on sale, Day 1).

[Note: Function f(n) “maps” the days (dates) when tickets are sold to the corresponding number of tickets sold on each specific day (date), so f(15) would denote the number of tickets sold on the 15th day of ticket sales]
a. Does the graph of this equation open up or down? How did you determine this?

b. Describe what happens to the tickets sales as time passes.
c. Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.

d. Will tickets peak or be at a low during the middle of the sale? How do you know? After how many days will the peak or low occur?

e. How many tickets would be sold on Day 4? On Day 13? On Day 32?

f. How many tickets will be sold on the day when the peak or low occurs?

g. What is the point of the vertex? How does this number relate to your answers in parts d. and f?

h. How many solutions are there to the equation ? How do you know?

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
j. (Optional – advanced) How many tickets in total will be sold during the entire period when tickets are sold?
[Hint: One can, of course, take this problem “heads on”, calculating the number of tickets sold on each day that tickets are sold (e.g. for all n when f(n)>0). However, this will involve way too much work, as you probably have seen in e. We need to “speed up” the process. How? Well, if a constant number of tickets (e.g. 100 tickets) were sold on days 1 through k, we know that the total number of tickets sold would be 100*k. You should use your answer to c. above as your actual k.
What if ticket sales were proportional to the day number, e.g. 1 ticket sold on Day 1 and k tickets sold on Day k? Formula for the sum of an arithmetic progression (specific to this case) would yield the number of tickets to be . Now if the proportionality coefficient were to be not 1 but some “b”, then the formula would simply be: (do you see why?)

The most challenging is probably the formula for the total number of tickets sold if ticket sales were directly proportional to the square of the day number: . Try this formula to see if it works for the first few sums of squares (e.g. 1+4+9, here k would be 3).
Of course, if there was a proportionality coefficient different from 1, say “a”, then the formula would simply be:
Now, all you have to do would be to understand that the quadratic function’s three separate elements may be evaluated separately using the above formulas for the entire domain of days when tickets are sold, and the total can be arrived at much quicker than taking the problem “head on”]
I am totally confused on this problem and not matter what I did I cannot figure it out. Please help.
Click here to see answer by richard1234(5390)

Question 571908: I am ridiculously confused on these problems. I don't even know where to start with them.
x²+41 =8x and the answer has to be in the form of a+bi
The second one is:
x²+13/2x=3
and then the last one is:
The width of a rectangle is 1 ft less than the length. The area is 2ft²
width=
length=
Click here to see answer by stanbon(57982)

Question 572106: What is the curve in a quadratic equation called
Click here to see answer by scott8148(6628)

Question 571239: x^2-x=72
Click here to see answer by jim_thompson5910(28717)

Question 572378: 9x^2+21x-8=0
Click here to see answer by Maths68(1474)

Question 572330: find a quadratic equation having 5/3 and 1/3 as roots
Click here to see answer by ankor@dixie-net.com(15746)

Question 572487: how to solve: Write a quadratic function in standard form whose graph passes through the given points. "(1,-2) (-2,1) (3,6)" please show work so i know how to do it
Click here to see answer by richard1234(5390)

Question 572446: The product of two positive integers is 45. One number is 4 more than the other. Find the numbers.
Click here to see answer by richard1234(5390)

Question 573125: how do i solve (f+g)(x)

Click here to see answer by solver91311(17077)

Question 573139: The length of a rectangle is twice the width. The area is 32yds squared . Find the length and the width
Click here to see answer by solver91311(17077)

Question 573163: Solve for x. 4x^2=-13x-10
Click here to see answer by mathsmiles(68)

Question 573158: m^2+m-62=-6
Click here to see answer by mathsmiles(68)

Question 573394: to go over a tree, a golfer uses a 7 iron to hit the ball with an intial upward velocity of 80 feet per second write a quadratic function that gives the height of the ball t seconds after it is hit
Click here to see answer by stanbon(57982)

Question 573534: I need help on this math question m squared-7m-8=0
Click here to see answer by scott8148(6628)

Question 573801: Showing all the steps, solve the following:
3x^3+x^2=4x

Can the below equation be solved? If yes, show how.
3x^2+4x=7
Click here to see answer by htmentor(809)

Question 574220: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standered form, ax^2+bx+c=0. Solution: 5, only solution
The equation is _______=0
Click here to see answer by nerdybill(7009)

Question 574248: solve x in 6(x^+1)=13x
Click here to see answer by nerdybill(7009)

Question 574249: please solve and graph f(x)=(x-3)^2+4
Click here to see answer by ankor@dixie-net.com(15746)

Question 574602: How do you rewrite a function in the form of f(x)=a(x-h)^2+k then complete the square of f(x)=2x^2-20x+3
Click here to see answer by nerdybill(7009)

Question 574633: Find the constant that must be added to each binomial expression to form a perfect-square trinomial.
x^2 + 10x
Click here to see answer by josmiceli(9817)

Question 574550: what is exact value of the only real root of the equation x^3 + 6x^2 + 12x + 24 = 0
Click here to see answer by KMST(1936)

Question 574533: The product of digit of two digit number is 24.If 18 is added to the number digits are reversed.find the number.

Click here to see answer by ankor@dixie-net.com(15746)

Question 574673: How would I use the quadratic formula to solve 3x^2-6x-7=0?
Click here to see answer by Earlsdon(6294)

Question 574681: Solve. x²-5x+1=0
I`m stuck on this problem. I don`t even know how to start this problem.
Click here to see answer by g1000000(5)

Question 574827: Compute the discriminant of the quadratic equation 3x^2+x+2=0
Then write a brief sentence describing the number and type of solutions for this
equation. How do I solve this?
Click here to see answer by jerryguo41(162)

Question 574851: Solve the quadratic equation 2x^2-3x-2=0 in quadratic "form" . How so i solve this problem. If you can please show me step from step.
Click here to see answer by ankor@dixie-net.com(15746)

Question 574729: Please help me solve this problem
A person on the edge of a cliff throws a stone so that it hits the ground near the base of the cliff. The stone's height (in feet above the base) h(t) after t seconds is given by the function h(t)= -16t^2+30t+200
a. Find the vertex. What does it mean in this situation?
b. Estimate the height of the cliff
c. Did the person throw the stone upward or downward? Explain.

Click here to see answer by ankor@dixie-net.com(15746)

Question 575141: How to solve this for x
x(x+5)=0
Click here to see answer by jim_thompson5910(28717)

Question 575219: The width of a garage is five feet less than twice the length. What is the length of the garage if the area is 700 square feet?
Click here to see answer by chana(69)

Question 575668: 52. A rectangular painting has dimensions x and x + 10. The painting is in a
frame 2 in. wide. The total area of the picture and the frame is 900 in.

Click here to see answer by JBarnum(2044)

Question 575837: Hercomer charges $.50 per minute to tutor calculus students. Mergatroid charges $12 base rate plus $.25 per minute on top of that. For what interval of time does it cost less to hire Hercomer?
Click here to see answer by reviewermath(604)

Question 575890: A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees.
I have developed the formula for the cross sectional area by letting x define the unknown quantity of depth that is to be the independent value.
my formula is f(x)= 2x^2 + 10x

My question is, what happens to the cross sectional area as depth size increases?
What x and y values make sense for this problem? (restricted domain and range)
Click here to see answer by ankor@dixie-net.com(15746)

Question 576132: find a formula ( in the form f(x)=ax2+bx+c) for aquadratic function with roots 1/2 and 6, and where the point (2,-56) is on the graph of the function
Click here to see answer by josmiceli(9817)

Question 576318: How do i solve this problem? 1/5r^2-2=5/6
The book says its 510/6, but i keep getting 85/6. What am I doing wrong?
Click here to see answer by vleith(2825)

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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