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Functions/519109: Express f(x)= -4x^2+40x-13 into f(x)=a(x-h)^2 + k and find the vertex of this quadratic function. I'm at a loss on where to begin and what to do, could someone more intelligent than I am, please give me an example to follow?
Thanks so much!!! :)
1 solutions
Answer 345420 by scott8148(6628)   on 2011-10-21 18:31:01 (Show Source):
You can put this solution on YOUR website!this ain't rocket science ___ make the equation look like the general form
separate the constant term ___ f(x) = -4x^2 + 40x .... -13
factor ___ f(x) = -4(x^2 + 10) .... -13 ____ starting to look like something?
now the "tricky" part - complete the square ___ f(x) = -4(x^2 + 10x + 25) + 100 .... -13
___ you complete the square by taking half of the x-term coefficient, squaring it and adding it
___ the "trick" is that the square you are completing is being multiplied by a value (-4)
___ to avoid changing the overall value of f(x), you have to balance the extra -100 (the -4 times 25) by adding 100
writing in vertex form ___ -4 (x + 5)^2 + 87
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Expressions-with-variables/518996: Solve for Y: (2)/(3)+3y=5y-(2)/(15)
Your supposed to eliminate the fractions first. I keep coming up with 5/2 even though I know the answer is 2/5. I just cant see what I'm doing wrong
I first eliminate 2/3 by multiplying both sides by 3/2. This gives me:
3y=5y-1/5
Move the 5y over and get -2y
multiply by the recip -1/2
that gives me 5/2! Grrr
1 solutions
Answer 345331 by scott8148(6628) on 2011-10-21 11:15:58 (Show Source):
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Divisibility_and_Prime_Numbers/518776: I am trying to find a starting point to help my daughter with the following math problem (right now we are working through it manually with boxes and check marks):
Following recess, the 400 students in a school lined up and entered the school as follows: the first student opened all the 400 lockers in the school. The second student closed all the even numbered lockers. The third student "changed" all the lockers that were numbered with a multiple of 3 by closing those lockers that were opened and opening those lockers that were closed. The fourth student changed all the lockers that were numbered with a multiple of 4 in the same way, and so on. After all 400 students had entered the building in this fashion, which lockers were left open?
1 solutions
Answer 345267 by scott8148(6628) on 2011-10-20 21:59:09 (Show Source):
You can put this solution on YOUR website!1___ o1
2__ o1, c2
3__ o1, c3
4__ o1, c2, o4
5__ o1, c5
6__ o1, c2, o3, c6
7__ o1, c7
8__ o1, c2, o4, c8
9__ o1, c3, o9
10__ o1, c2, 05, c10
11__ o1, c11
12__ o1, c2, o3, c4, o6, c12
13__ o1, c13
14__ o1, c2, o7, c14
15__ o1, c3, o5, c15
16__ o1, c2, o4, c8, o16
25__ o1, c5, o25
36__ o1, c2, o3, c4, o6, c9, o12, c18, o36
I don't know why, but the perfect squares are the ones left open
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Quadratic_Equations/518194: A basketball is shot with an initial vertical velocity of 24 ft/s from 6 ft. above the ground. At what time will the basketball reach its maximum height?
1 solutions
Answer 345083 by scott8148(6628) on 2011-10-19 22:03:07 (Show Source):
You can put this solution on YOUR website!gravitational acceleration is 32 ft/s^2
it takes .75 sec (24 ft/s / 32 ft/s^2) for the vertical velocity to go to zero (max height)
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Money_Word_Problems/518126: How much interest is earned in 2 years on $4000 deposited in an account thats pays 6% interest, compounded quarterly?
I've come close to the answer but haven't reached the correct one.
It would help to be shown a step by step process! Thank you!
1 solutions
Answer 345081 by scott8148(6628) on 2011-10-19 21:56:28 (Show Source):
You can put this solution on YOUR website!A = P (1 + r)^t
quarterly compounding means that there are 8 compoundings in 2 yr and the interest per period is 1.5% (6% / 4)
a = 4000 (1 + .015)^8 ___ this will give the accrued amount
___ just subtract the 4000 to find the interest
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Linear-systems/517538: I have a word problem which needs to be translated into an equation:
Two motorcyclists start at the same point and travel in opposite directions. One travels 6 mph faster than the other. In 4 hours, they are 336 miles apart. How fast is each traveling?
Speed of slower motorcyclist _____ mph
Speed of faster motorcyclist _____ mph
1 solutions
Answer 344833 by scott8148(6628) on 2011-10-18 22:53:41 (Show Source):
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Probability-and-statistics/517547: In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 24 prospective jurors?
1 solutions
Answer 344831 by scott8148(6628) on 2011-10-18 22:51:35 (Show Source):
You can put this solution on YOUR website!ways of choosing 14 from 24 ___ 24C14
ways of choosing 12 (or 2) from 14 ___ 14C12
the number of ways to choose a panel is the product ___ (24C14)(14C12)
OR
ways of choosing 12 from 24 ___ 24C12
ways of choosing 2 from remaining 12 ___ 12C2
product is the same
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Functions/517520: Okay, so my friend needs help and I haven't taken this class in awhile so this is kind of a refreshment.
Find the range for each equation if the domain is { -3,-1,0,2,3 }. Plug each number of the range into the equation - the answer will be the corresponding number in the domain "
This is one of the equeations
VVV
y=5x+1
1 solutions
Answer 344816 by scott8148(6628) on 2011-10-18 22:31:34 (Show Source):
You can put this solution on YOUR website!"Plug each number of the range into the equation - the answer will be the corresponding number in the domain "
___ it is usually the other way around
___ especially since you are given the domain values
plug the domain (x) values into the equation (one at a time) and find (solve for) the corresponding range (y) values
___ list the range (y) values just like the domain (x) values are listed
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Polynomials-and-rational-expressions/517523: I need to find the excluded variables for this expression= (y^2+5y-6)/(y^2-8y+7) I've already simplified it into (y+6)/(y-7) but i'm having trouble finding the excluded variables
1 solutions
Answer 344811 by scott8148(6628) on 2011-10-18 22:16:02 (Show Source):
You can put this solution on YOUR website!excluded values are those which result in undefined results (usually, division by zero)
if y = 7, then your simplified denominator is zero ___ this is excluded
even though you canceled the y-1 factors, y = 1 is an excluded value because there is a "hole" in the graph there
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Graphs/516182: I am trying to solve the system of equations for the following set:
{ 4/5x + y = 14/5 and -1/8x - 1/4y = -1 }
I cannot get the right answer because I keep factoring incorrectly when I multiply by the LCM.
Please provide the ordered pair.
Thanks.
1 solutions
Answer 344272 by scott8148(6628) on 2011-10-16 23:02:58 (Show Source):
You can put this solution on YOUR website!multiplying 2nd eqn by 4 ___ -1/2 x - y = -4
adding 1st eqn (to eliminate y) ___ 3/10 x = -6/5 ___ x = -4
-1/2 (-4) - y = -4 ___ 2 - y = -4 ___ y = 6
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Travel_Word_Problems/516178: Two riders depart from city a to city b. One rider rides at 12 mph and other rider at 18 mph. Slower rider takes 1.5 hours longer to ride the distance.
How long did it take both riders to reach the destination
How far is city a to city b?
HELP!!!! How am I supposed to figure out how far the cities are from each other without any information on one or the other? And 1.5 hours to ride the distance??? AARRRGGGHHHH!!!!
1 solutions
Answer 344270 by scott8148(6628) on 2011-10-16 22:55:20 (Show Source):
You can put this solution on YOUR website!...calm...take deep breaths...
d = r * t ___ they ride the same (equal) distance
18t = 12(t + 1.5) ___ 18t = 12t + 18 ___ 6t = 18 ___ t = 3 ___ t + 1.5 = 4.5
d = 18 * 3 = 54
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Probability-and-statistics/516114: A bag contains 5 red marbles, 10 white marbles, and 6 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?
The probability that all the marbles are red is:
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is:
What is the probability that none of the marbles are red?
The probability of picking no red marbles is
1 solutions
Answer 344269 by scott8148(6628) on 2011-10-16 22:48:50 (Show Source):
You can put this solution on YOUR website!ways to pick 5 out of 21 ___ 21C5
there is one way to select 5 out of 5 (red), so the probability of 5 red is ___ 1 / 21C5
ways to pick 2 out of 5 (red) ___ 5C2
ways to pick 3 out of 16 (non-red) ___ 16C3
___ so the probability of 2 red is ___ [(5C2)(16C3)] / 21C5
ways to pick no red ___ 16C5
___ probability of no red ___ 16C5 / 21C5
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logarithm/516126: log(base 16) x + log(base 4 x + log(base 2) x = 7
the answer is 16, but i want to know how they got it because i keep getting 16^1/3
1 solutions
Answer 344264 by scott8148(6628) on 2011-10-16 22:22:31 (Show Source):
You can put this solution on YOUR website!16 = 2^4 ___ log2(x) = 4[log16(x)]
16 = 4^2 ___ log4(x) = 2[log16(x)]
log16(x) + 2[log16(x)] + 4[log16(x)] = 7
7[log16(x)] = 7
log16(x) = 1
x = 16
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Travel_Word_Problems/515176: Kathy bicycles 4/km/h faster than Robert. In the same time it takes Robert to bicycle 57 km, Kathy can bicycle 69km. How fast does each bicyclist travel?
Robert -
Kathy -
Thank you,
Diane
1 solutions
Answer 343818 by scott8148(6628) on 2011-10-14 20:48:59 (Show Source):
You can put this solution on YOUR website!"Kathy bicycles 4/km/h faster than Robert" ___ K = R + 4
"In the same time it takes Robert to bicycle 57 km, Kathy can bicycle 69km" ___ t = d / r
___ the times are the same (equal) ___ (57 / R) = (69 / K)
"cross" multiplying ___ 57K = 69R
substituting ___ 57R + 228 = 69R
solve for R and substitute back to find K
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Linear_Algebra/515166: I am having trouble with elimination, is it possible you could explain it to me through this problem
Solve Each system by elimination
-3x+2y-5z=-3
3x-y+3z=4
3x+5y-8z=6
Answers:
one third,9,4
two third, 7,3
3,-7,-4
no solutions
1 solutions
Answer 343809 by scott8148(6628) on 2011-10-14 20:37:06 (Show Source):
You can put this solution on YOUR website!add the 1st and 2nd eqns to eliminate x ___ y - 2z = 1 (A)
add the 1st and 3rd eqns to eliminate x ___ 7y - 13z = 3 (B)
multiply eqn (A) by -7 and add to eqn (B) to eliminate y ___ z = -4
substitute back to find x and y
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test/515208: If Sam can do the job in 6 days.. carla can do it in 4 days... John can do it in 2 days. How many days do they need .. if they do it together..
1 solutions
Answer 343799 by scott8148(6628) on 2011-10-14 20:21:18 (Show Source):
You can put this solution on YOUR website!they each do a fraction of the task based on their individual rates; the fractions sum to one, the whole task
(x/6) + (x/4) + (x/2) = 1
2x + 3x + 6x = 12
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Probability-and-statistics/515083: Find the probability of the given value of x
mean = 28 standard deviation = 6.5 and x equal or less than 20
I need simple steps I know the formula is z= x-u/o and plus or minus .5 but I do not seem to come out right we are using the standard normal distribution chart
1 solutions
Answer 343740 by scott8148(6628) on 2011-10-14 15:20:37 (Show Source):
You can put this solution on YOUR website!20 is (8/6.5) or 1.231 (approx) standard deviations below the mean of 28
so the z-score you are looking for is -1.231
the probability is the fraction of the distribution at or below this score
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Angles/515060: Can you please Help me answer this question: Angles A and B are complementary angles. Determine the measure of angles A and B if angle B is 2 less than three times the size of angle A
1 solutions
Answer 343736 by scott8148(6628) on 2011-10-14 15:12:10 (Show Source):
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Graphs/514119: can u help me with my homework i dont get it at all and its really confusing to me. i have algebra 1 and i am learning about compound inequalities with absolute value.
the one i cant get is 2=|g+1|
1 solutions
Answer 343304 by scott8148(6628) on 2011-10-12 22:22:46 (Show Source):
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