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7x^2-7x^2y-28x+28xy
1 solutions
Answer 367987 by KMST(574)   on 2012-02-11 06:42:52 (Show Source):
You can put this solution on YOUR website!We can find common factors in groups of terms, and see what we end up with:
If both factors in brackets were exactly the same, we would be finding a common factor again. We can fix that, because
So
and we can write that in more elegant ways, and even factor out a 
Because  , it can be factored too, to get to the full factorization.
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test/570984: 1.) A citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Find the total number of trees the grower should plant to maximize yield.
2.) A person is standing 3 ft away from a street light that is 15.6 ft tall. How long is his shadow if he is 5.2 ft tall?
1 solutions
Answer 367986 by KMST(574) on 2012-02-11 06:24:23 (Show Source):
You can put this solution on YOUR website!CITRUS GROWER PROBLEM
The yield per tree,  can be expressed as  with  being the number of trees.
The total yield,  will be  .
We need to express as a function of .
-->  --> 
So 
The total yield function,
 , is a quadratic function, which would graph as a parabola.
Because the leading coefficient is negative, the function has a maximum, corresponding to the vertex of the parabola, where the parabola crosses its axis of symmetry.
We need to find the axis of symmetry, which will give us the x-coordinate for the maximum.
The equation for axis of symmetry/x-coordinate of the maximum is
 --> 
The number of trees for maximum total yield in the same acreage is  .
SHADOW PROBLEM
 <--- This sketch illustrates the situation.
Consider two similar right triangles. The legs of the smaller right triangle are the height of the person (p) and the length of the person’s shadow. The legs of the larger right triangle are the height of the street light (sl) , and the distance from its base to the end of the person’s shadow. The hypotenuse of the larger triangle is the light beam coming from the light bulb, grazing the person's head, and touching the ground just at the end of the person's shadow.
Let x be the length of the person’s shadow. Because those right triangles are similar, there is a proportion for the ratio of horizontal leg to vertical leg:
 -->  -->  -->  -->  -->  --> 
The length of the shadow is  feet.
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Polynomials-and-rational-expressions/570916: What is the difference in these two questions and how do I do them?
Describe the mathematic process of canceling like factors when working with rational expressions. Demonstrate this with an example. And explain in your own words how factoring is used to solve quadratic equations. Demonstrate the process with an example. Please help this is late and I am so lost
2 solutions
Answer 367985 by harsh.9119(1)  on 2012-02-11 05:05:39 (Show Source):
Answer 367975 by richard1234(4783)  on 2012-02-11 00:16:21 (Show Source):
You can put this solution on YOUR website!Canceling like factors is similar to canceling common factors in a fraction such as 15/24. Pretty straightforward, as long as you cancel the factors correctly.
Factoring helps solve quadratics, as you don't have to use the quadratic formula. If x^2 + bx + c = 0 factors to (x-p)(x-q) = 0, then right away you know that the roots are p and q. However, not all quadratics factor nicely, and you almost have to "recognize" instantly if a quadratic is factorable (by being able to factor the constant term), otherwise the method is useless.
For example, consider the quadratic  . Since 35 = 5*7 and 5+7 = 12, you could factor it like
(x+7) = 0) (check to make sure the coefficients are the same upon expanding). By the zero-product rule, the roots are -5 and -7.
Factoring quadratics with a leading term other than 1 uses a slightly different method; look in your textbook or online for examples.
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Percentage-and-ratio-word-problems/571116: The resistance (in ohms) of a circular conductor varies directly with the length of the conductor and inversely with the square of the radius of the conduction. If 50ft of wire with a radius of 6 x 10^-3 inch has a resistance of 10ohms, what would be the resistance of 100ft of the same wire if the radius is increased to 7 x 10^13 inch?
1 solutions
Answer 367984 by lwsshak3(2900)  on 2012-02-11 02:51:48 (Show Source):
You can put this solution on YOUR website!he resistance (in ohms) of a circular conductor varies directly with the length of the conductor and inversely with the square of the radius of the conduction. If 50ft of wire with a radius of 6 x 10^-3 inch has a resistance of 10ohms, what would be the resistance of 100ft of the same wire if the radius is increased to 7 x 10^13 inch?
**
Resistance=10(100/50)[(6*10^-3)/(7*10^13)]^2
=20(6*10^-16)/7)=(120/7)*10^-16≈17.14*10^-16 ohms
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Systems-of-equations/571157: A two- digit is such that the sum of the digits is 11. When the number with the same digits reversed is subtracted from this number, the difference is 9. What is the number?
1 solutions
Answer 367983 by lwsshak3(2900) on 2012-02-11 02:35:17 (Show Source):
You can put this solution on YOUR website!A two- digit is such that the sum of the digits is 11. When the number with the same digits reversed is subtracted from this number, the difference is 9. What is the number?
**
let u=units digit
let t=tens digit
u+t=11
t=11-u
original number=10t+u
reversed number=10u+t
10t+u-10u-t=9
10(11-u)+u-10u-(11-u)=9
110-10u+u-10u-11+u=9
18u=90
u=5
t=11-u=6
ans:
original number=65
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Rate-of-work-word-problems/571158: Susan delivers 108 newspapers in 90 minutes. Stan delivers the same number of newspaper 120 minutes. which of the following formula would allow you to determine the time required to deliver the newspapers by both Susan and Stan working together
1 solutions
Answer 367981 by lwsshak3(2900) on 2012-02-11 02:15:11 (Show Source):
You can put this solution on YOUR website!Susan delivers 108 newspapers in 90 minutes. Stan delivers the same number of newspaper 120 minutes. which of the following formula would allow you to determine the time required to deliver the newspapers by both Susan and Stan working together
**
let x=minutes required by Susan and Stan working together to deliver the newspapers
Susan's work rate=108/90
Stan's work rate=108/120
working together Susan and Stan can deliver 108 newspapers in x minutes
108x/90+108x/120=108
LCD: 90*120
120*108x+90*108x=90*120*108
12960x+9720x=116640
x≈51 minutes
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Numbers_Word_Problems/571120: Center City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1225 cars, find the capacity for each garage.
1 solutions
Answer 367980 by josmiceli(6766)  on 2012-02-11 00:33:31 (Show Source):
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Volume/571149: I need to know how to estimate the volume of a box (approximately 100 - 500 cm3) in cubic centimeters.
1 solutions
Answer 367978 by richard1234(4783) on 2012-02-11 00:26:10 (Show Source):
You can put this solution on YOUR website!Volume of a box = length*width*height.
Also, I would think that "approximately 100 - 500 cm3" is an estimate for the volume of a box in cubic centimeters.
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test/570611: I sent u a question this is supposed to be free so why couldn't u answer the question
1 solutions
Answer 367977 by richard1234(4783) on 2012-02-11 00:24:49 (Show Source):
You can put this solution on YOUR website!The way algebra.com works is, tutors see a long list of questions posted by users. They will usually answer questions to their liking (e.g. algebra questions, calculus questions, easy/hard questions) or whichever they can answer right away, but it all depends. They have to locate your question and answer it. Since questions are uploaded at a faster rate than tutors can solve it, some questions will go unnoticed.
Best advice would be to repost the question. The site is completely free to use; you can hire certain tutors but that's up to you and them. However, make sure that a tutor can be willing to answer your question. If your question violates the guidelines for posting (e.g. too many questions in one post, too long, ambiguous, poor grammar, etc.), tutors may reply with a negative response, or simply gloss over the question.
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Money_Word_Problems/571145: Henry invest money in two plans. He invest three-fifths of the money in an account at a return rate of 7%. He invests the remainder of the money in an account with a return rate of 3%. I f the total intrest earned in one year for the investments is $54.00, how much was invested in each plan. i made a chart that says account, rate, principal, and intrest
under account i have first account and second account. under rate i have 0.07 and 0.03. and under principal i have 3/5p but my problem is i dont know how to find 0.03's principal. so for 0.07 in the intrest box i have 0.07*3/5p.
1 solutions
Answer 367976 by josmiceli(6766) on 2012-02-11 00:24:48 (Show Source):
You can put this solution on YOUR website!If  = principle
 is invested @ 7%
 is invested @ 3%
Note that 
as it should
given:
 ( I used decimals instead of fractions )
$600 was invested @ 7%
$400 was invested @ 3%
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Probability-and-statistics/570976: Suppose k identical boxes contained n balls numbered one through n. One ball is drawn from
each box. What is the probability that m is the largest number drawn?
1 solutions
Answer 367974 by richard1234(4783) on 2012-02-11 00:09:21 (Show Source):
You can put this solution on YOUR website!For this problem we will assume that  .
The best way is probably to try small cases (for m). Let P(m) be the probability that m is the largest number drawn. If m = 1, then every number drawn must be a 1, and
 = (\frac{1}{n})^k)
If m = 2, every number must be a 1 or a 2, and we would try to claim something like
 = (\frac{2}{n})^k)
However, this is incorrect, because this includes the case where every number is a 1 (which violates the constraint that at least one number must be a 2). To fix this, we subtract P(1):
 = (\frac{2}{n})^k - P(1) = (\frac{2}{n})^k - (\frac{1}{n})^k)
Finding P(3) is similar to finding P(2), except that we subtract P(2):
 = (\frac{3}{n})^k - P(2) = (\frac{3}{n})^k - (\frac{2}{n})^k +(\frac{1}{n})^k)
This generalizes to
 = (\frac{m}{n})^k - P(m-1)) , or
 = (\frac{m}{n})^k - (\frac{m-1}{n})^k + (\frac{m-2}{n})^k ... \pm (\frac{1}{n})^k)
where the plus/minus of (1/n)^k depends on the parity of m (i.e. if m is odd, +; if m is even, -).
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Quadratic_Equations/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.
1 solutions
Answer 367973 by richard1234(4783) on 2012-02-10 23:48:47 (Show Source):
You can put this solution on YOUR website!Try to limit your post to one or two questions; here, you posted two questions that have 10 or 12 parts and most tutors won't solve all of them for you. Plus, you didn't provide a quadratic for #1.
For #2, you can approximate it by adding up each f(n), 0 <= n <= d, where f(n) is the function and d is the last day tickets are sold. However, unless you have a graphing calculator that can do summations, this will be quite a task. Another way to approximate it is to take the integral of f(n):
 dn)
Note the "approximately equal," as the integral assumes f(n) is continuous instead of day-to-day. Only use this method if you know calculus.
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Polygons/571070: What is the height and radius of a cube with a volume of 113.1, with an answer in centimeters preferably??
Thank you, I apreciate your help
1 solutions
Answer 367970 by rfer(10417) on 2012-02-10 23:26:45 (Show Source):
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percentage/571135: If the population of a town is 25000, an increase of 70% from its population 5 years ago, what was its polulation 5 years ago?
How do you figure this out?
1 solutions
Answer 367966 by rfer(10417) on 2012-02-10 23:13:40 (Show Source):
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Linear-equations/571138: I need help solving this word problem...I have been trying for 2 hours.
In 1920, the record for a certain race was 45.4 sec. In 1970, it was 44.4 sec.
Let R(t)=the record in the race and t=the number of years since 1920.
Find a linear function that fits the data
R(t)=
Round to nearest hundredth
What is the predicted record for 2003____sec
What is the predicted record for 2006?
In what year will the predicted record be 43.50 seconds?
Thanks so much!
1 solutions
Answer 367965 by mananth(10539)  on 2012-02-10 22:50:38 (Show Source):
You can put this solution on YOUR website!year Record time
1920 45.4 seconds
1970 44.4 seconds
Difference
50 -1
rate of reduction per year =-1 /50 = -0.02
R(t)= 45.4-0.020t
2003 t=83
R(t)= 45.4 + -0.020 * 83
R (83)= 43.74 seconds
------------
R(t)= 45.4-0.02t
43.5=45.4-0.02t
45.4-43.5=0.02t
1.9=0.02t
t= 1.9/0.02
t=95 years
1920 +95 = 2015
year 2015 it will bve 43.5 seconds
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Pythagorean-theorem/571131: The hypotenuse of angle XYZ is 10 and length of one of its legs is 8. Find the length of the other leg. Show diagram and calculation.
1 solutions
Answer 367962 by mananth(10539) on 2012-02-10 22:37:15 (Show Source):
You can put this solution on YOUR website!Pythagoras theorem
Hypotenuse ^2 = leg1^2+leg2^2
Leg1^2= Hypotenuse^2-leg2^2
Hypotenuse = 10 ft
leg1= 8 ft
leg2= ? ft
Leg1^2= Hypotenuse^2-leg2^2
leg1^2= 10 ^2 - 8 ^2
leg1= 
leg1= 6 ft
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Functions/571130: Sorry I forgot to write out the pair of lines
3x+8=y
2y=6x-3
are these lines parallel?
2 solutions
Answer 367961 by Maths68(1140)  on 2012-02-10 22:30:12 (Show Source):
You can put this solution on YOUR website!3x+8=y............(1)
y=3x+8
Compare above equation with the standard equation of the line
y=mx+b
slope =m=3 and y-intercept =b=8
2y=6x-3...........(2)
Divide above equation by 2
2y/2=(6x-3)/2
y=6x/2-3/2
y=3x-3/2
Compare above equation with the standard equation of the line
y=mx+b
slope =m=3 and y-intercept =b=-3/2
Both lines are parallel because their slopes are same.
Answer 367959 by mananth(10539) on 2012-02-10 22:26:49 (Show Source):
You can put this solution on YOUR website!3x+8=y
y=3x+8
2y=6x-3
/2
y=3x-(3/2)
compare both the lines with y= mx+b
m the slope of both lines are 3 so the lines are parallel
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Pythagorean-theorem/571125: Name three(3) sets of Pythagorean triplets and prove that they are indeed Pythagorean triplets.
1 solutions
Answer 367957 by mananth(10539) on 2012-02-10 22:19:56 (Show Source):
You can put this solution on YOUR website!There are many many triplets
PYthagoras theorem states
the sum of squares of the adjacent sides = hypotenuse^2
leg1^2+leg2^2=hypotenuse^2
In a right triangle the largest side is aways the hypotenuse.
First the basic one
3,4,5
3^2+4^2=5^2
(+16=25
25=25
----
5,12,13
5^2+12^2=13^2
25+144=169
169=169
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Third one you can find
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Money_Word_Problems/571100: Suppose you invest money in two accounts. One of the accounts pays 8% annual interest, whereas the other pays 9% annual interest. If you have $2000 more invested at 9% than you have invested at 8%, how much do you have invested in each account if the total amount of interest you earn in a year is $860?
1 solutions
Answer 367955 by mananth(10539) on 2012-02-10 22:08:16 (Show Source):
You can put this solution on YOUR website!8%---------------x
9%= x+2000
sum of idividual interests = total interest
0.08x+0.09*(x+2000)=860
0.08x+0.09x+180=860
0.17x=860-180
0.17x=680
/0.17
x= 680/0.17
x= 4000
Amount invested @8% = $4000
Amount invested @ 9% = $4000+2000 = $6000
m.ananth@hotmail.ca
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