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would you please help me with this problem, i have been racking my brain for two days to figure it out...ok this is how it goes: There is a sailboat which must have a 110 ft mast and a combined mainsain and jibsail area of 3000 sq ft. The design calls for the mainsail to be 60% of the combined sail area,and the jibsail area to be 40%(of course). If the height of the triangular mainsail is 28ft more than twice the length of the boom, find the length of the boom and the height of the mainsail.
I've figured out this much so far... the mainsail=1800sq ft, and the jibsail =1200sq ft. Height=(2(boom)+28sq ft). and i know that the area of a triangle is A=1/2(base)(heigth). that is about it, i've played around with the numbers but haven't gotten it correct yet. Any help you can offer would be tramendous!Thanks
1 solutions
Answer 139416 by scott8148(6628)   on 2009-03-09 20:26:03 (Show Source):
You can put this solution on YOUR website!you do know that the boom is the base, right?
1800 = 1/2 * boom * (2(boom)+28)
1800 = b^2+14b ___ 0 = b^2+14b-1800
factoring ___ 0 = (b-36)(b+50)
so b=36
and h=100
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Expressions-with-variables/185920: This question is from textbook Integrated Algebra I
During your summer vacation, you are offered a job at which you can work as many days as you choose. If you work 1 day, you will be paid $0,01. If you work 2 days you will be paid a total of $0.02. If you work 3 days you will be paid a total of $0.04. If you continue to work, your total pay will continue to double each day.
a) Would you accept this job if you planned to work 10 days? Explain why or why not.
b) Would you accept this job if you planned to work 25 days? Explain why or why not.
I know the answer to a is no, because you would only make $5.12 and
the answer to b is yes because you would make $167,772.16
what I don't know is how to get those amounts without entering it individually into the calculator for each day.
I think the formula should be A = P (1 + r)ⁿ
1 solutions
Answer 139414 by scott8148(6628) on 2009-03-09 20:02:18 (Show Source):
You can put this solution on YOUR website!for 1 day ___ 2^0
for 2 days ___ 2^1
for 3 days ___ 2^2
etc.
the pattern is: pay (in cents) equals 2 to the n-1 power (where n equals days worked)
pay=2^(n-1)
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Polynomials-and-rational-expressions/185923: could you please help me in solving this problem?I have to factor each trinomial
the problem is x2+8x+12
1 solutions
Answer 139412 by scott8148(6628) on 2009-03-09 19:48:52 (Show Source):
You can put this solution on YOUR website!which factors of 12 can "combine" to give 8??
2*6=12 ___ 2+6=8
so the trinomial factors into (x+2)(x+6)
******************************************************************
I have two questions i have tried
to solve and just can not get the solution. I would appreciate it if
you would please help me with the following problems:
6x^2-4x+3x-2 and 12x^2+3x-8x-2
the reason these have more than one x term is that they are set up to solve by grouping
(6x^2-4x) + (3x-2) ___ 2x(3x-2) + 1(3x-2) ___ (2x+1)(3x-2)
(12x^2+3x) - (8x+2) ___ 3x(4x+1) - 2(4x+1) ___ (3x-2)(4x+1)
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Quadratic_Equations/185678: Solve Problems Using Linear Systems
17. Ian flew his airplane at best cruise speed for 2 h, then at economy cruise speed for 3 h, covering a total of 850 km. On the following day, he flew a tbest cruise speed for 3 h and at economy cruise speed for 2 h, covering a total of 900 km. Find the best cruise speed and the economy cruise speed for Ian's airplane.
(The answer is: best cruise speed 200 km/h, economy cruise speed 150 km/h, but i dont know how to solve this problem?) Thank you very much!!!
1 solutions
Answer 139268 by scott8148(6628) on 2009-03-08 16:41:01 (Show Source):
You can put this solution on YOUR website!"Ian flew his airplane at best cruise speed for 2 h, then at economy cruise speed for 3 h, covering a total of 850 km"
___ 2b+3c=850
"he flew a tbest cruise speed for 3 h and at economy cruise speed for 2 h, covering a total of 900 km"
___ 3b+2c=900
multiplying the 1st equation by -2 and the 2nd equation by 3 will allow you to ELIMINATE the c variable by addition
-2(2b+3c=850) ___ -4b-6c=-1700
3(3b+2c=900) ___ 9b+6c=2700
adding equations ___ 5b=1000 ___ b=200
substituting ___ 2(200)+3b=850 ___ 3b=450 ___ b=150
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Quadratic_Equations/185664: Solve Problems Using Linear Systems
2. James looks in his TV cabinet and finds some old Beta and VHS tapes. He has 17 tapes in all. He finds that he has three more Beta tapes than VHS tapes. How much many of each type does he have?
(The answer is: 10 Beta tapes and 7 VHS tapes, but i dont know how solve this problem?) Thank you very much!!!
1 solutions
Answer 139267 by scott8148(6628) on 2009-03-08 16:24:00 (Show Source):
You can put this solution on YOUR website!"He has 17 tapes in all" ___ B+V=17
"He finds that he has three more Beta tapes than VHS tapes" ___ B=V+3
substituting ___ (V+3)+V=17 ___ 2V+3=17 ___ 2V=14 ___ V=7
substituting ___ B+(7)=17 ___ B=10
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Graphs/185662: Find an equation of the line that is parallel to the line y = 4x - 2 and that passes through the point (8,6).
Thanks for the help.
1 solutions
Answer 139266 by scott8148(6628) on 2009-03-08 16:17:14 (Show Source):
You can put this solution on YOUR website!parallel means that the slope is the same
the given line is already in slope-intercept form (y=mx+b), and the slope is 4
to find the intercept for the new line, just substitute the given point
y=4x+b ___ 6=4(8)+b ___ 6-32=b ___ -26=b
so the equation of the new line is y=4x-26
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Quadratic_Equations/184813: Solve Problems Using Linear Systems
15. A motor boat took 5h to travel a distance of 60 km up a river, against the current. The return trip took 3h. Find the average speed of the boat in still water and the speed of the current.
Thank you sooooooo much!!!!
1 solutions
Answer 138707 by scott8148(6628) on 2009-03-03 19:57:34 (Show Source):
You can put this solution on YOUR website!"A motor boat took 5h to travel a distance of 60 km up a river" ___ so b-c=60/5 or 12
"The return trip took 3h" ___ so b+c=60/3 or 20
adding equations ___ (b-c)+(b+c) = 12+20 ___ 2b = 32 ___ b=16
substituting __ (16)+c = 20 ___ c = 4
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Quadratic_Equations/184816: Solve Problems Using Linear Systems
17. Fran and Winston have a combined income of $80 000. One quarter of Winston's income is the same as one-sixth of Fran's income. How much does each person earn?
Thankssssssssss
1 solutions
Answer 138698 by scott8148(6628) on 2009-03-03 19:41:22 (Show Source):
You can put this solution on YOUR website!"Fran and Winston have a combined income of $80 000" ___ F + W = 80000 ___ W = 80000-F
"One quarter of Winston's income is the same as one-sixth of Fran's income" ___ W/4 = F/6
substituting ___ (80000-F)/4 = F/6 ___ 20000 - (F/4) = F/6
adding F/4 ___ 20000 = 5F/12
multiplying by 12/5 ___ 48000 = F
substituting ___ W = 80000 - (48000) ___ W = 32000
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Quadratic_Equations/184593: I'm can't figure out how to create a quadratic equation out of the vertex and a point that it must pass through. All i've managed so far is some trial and error and come up with this.
y=2(x+2)²+4
From the vertex of (-2,4) and passing through (-1,8).
I have been fiddling around with it and have two ideas how to proceed.
I could change (x+2) to something else to move it along the x axis or change the first part of it to change the fatness or whichever you want to call it of the parabola. Regardless i figure there is a better way to do it other then trial and error, if it has been answered before i'm sorry I didn't see it. I'm self taught and this is the first time I really have had any problem.
-Thanks
1 solutions
Answer 138554 by scott8148(6628) on 2009-03-02 19:38:53 (Show Source):
You can put this solution on YOUR website!the general vertex form of a quadratic is y = a(x-h)^2 + k
(h,k) is the vertex, and "a" controls what you call the "fatness"
your question is basically solving for "a" __ algebra, not trial and error
y = a(x+2)^2 + 4
substituting (-1,8) ___ 8 = a(-1+2)^2 + 4
subtracting 4 ___ 4 = a
so the equation is ___ y = 4(x+2)^2 + 4
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Linear_Equations_And_Systems_Word_Problems/184327: A man will be three times as old as his son will be in nine years. If he is six times as old as his son is now, how old is the SON? .
What I have come up with is as follows.
3n+9 = 6n
But I am not positvie this equations even works, thanks for the help.
1 solutions
Answer 138368 by scott8148(6628) on 2009-03-01 13:05:56 (Show Source):
You can put this solution on YOUR website!let m="man now" and s="son now"
"A man will be three times as old as his son will be in nine years" ___ m+9=3(s+9)
"he is six times as old as his son is now" ___ m=6s
"how old is the SON?" ___ substituting ___ (6s)+9=3(s+9)
expanding ___ 6s+9=3s+27
subtracting 3s+9 ___ 3s=18
dividing by 3 ___ s=6
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Miscellaneous_Word_Problems/184330: A man is carrying rice on a journey. He passes through three custom stations. At the first he gives up 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; at the second he is allowed to keep 1/3 of what is left; and at the third. After passing through all three customs stations, he has 6 pounds less than he started with. How much rice did he have when he started?
I have been struggling with this problem for over a week now and still can't even figure out where to start. Thanks for the help
1 solutions
Answer 138367 by scott8148(6628) on 2009-03-01 12:52:20 (Show Source):
You can put this solution on YOUR website!let x=starting amount
"At the first he gives up 1/3 of his rice" ___ x-(1/3)x=(2/3)x remaining
"at the second he is allowed to keep 1/3 of what is left" ___ (1/3)*(2x/3)=2x/9 remaining
"at the third, he gives up 1/4 of what remains" ___ (2x/9)-(1/4)*(2x/9)=x/6 remaining
"After passing through all three customs stations, he has 6 pounds less than he started with"
___ x/6 = x-6
multiplying by 6 ___ x=6x-36
adding 36-x ___ 36=5x
dividing by 5 ___ 7.2=x
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Linear-systems/184212: During a work-out session, Mark either ran at a speed of 7MPH or walked at a speed of 3MPH. He completed 20 miles in 3 hours. Please help me.
1. Let r represent the number of miles Mark ran and w respresent the number of miles Mark walked. Write a system of equations that represents the situation.
2.Solve the system of equations to find how much time Mark spent running.
1 solutions
Answer 138261 by scott8148(6628) on 2009-02-28 16:33:37 (Show Source):
You can put this solution on YOUR website!the total distance is 20 mi, so r+w=20 ... and w=20-r
the total time is 3 hr ... since rate times time equals distance, time equals distance divided by rate
(r/7)+(w/3)=3
substituting ... (r/7)+((20-r)/3)=3
subtracting 20/3 ... (r/7)-(r/3)=-11/3
multiplying by 21 (LCD) ... 3r-7r=-77 ... -4r=-77
dividing by -4 ... r=77/4
since time equals distance divided by rate, Mark's running time is (77/4)/7 or 11/4 hr (2hr45min)
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Volume/184223: This question is from textbook
If you cut a 1-inch square out of each corner of an 8.5-by-11-inch piece of paper and forld it into a box without a lid, what is the volume of the container?
My Work: Since it is a 1 inch square I subtracted 2 inches from each side which would leave me with 6.5 and 9 inches and then I multiplied those together and got 58.5 and I need the top number of the cube to multiply 58.5 by but Im not sure what it would be, I think it is 6.5 which would make the answer V=380.25cm3
1 solutions
Answer 138258 by scott8148(6628) on 2009-02-28 16:12:48 (Show Source):
You can put this solution on YOUR website!you are cutting a 1-inch square from each corner...so when you fold up the box, how DEEP is it?
volume is length times width times DEPTH
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Travel_Word_Problems/182931: I need help with this problem: buses from carbondale to bllomington leave every hour on the hour. Buses from bloomington to carbonfale leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming that the buses travel on the same highway how many bloomington buses does a carbondale bound. Bus meet on the highway(not counting in the station.)
1 solutions
Answer 137472 by scott8148(6628) on 2009-02-21 22:29:28 (Show Source):
You can put this solution on YOUR website!when a C. bus leaves the B. station;
there is a B. bus 1/2 hr from the B. station,
and another B. bus 1 hr behind the first,
and another B. bus 2 hr behind the first,
and another B. bus 3 hr behind the first,
and finally a 5th B. bus 4 hr behind the first
the C. bus will meet all 5 of these B. busses
PLUS
during the 5 hr trip, 5 more B. busses will leave the C. station and meet the C. bus
this means that the C. bus will meet 10 B. busses
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Money_Word_Problems/182937: Please help me: a candy company is going to test market 1 kg packages each containing 3 kinds of candy the company plans to prepare 10,000 packages each will contain mints that sell for $2.20 per kg caramels that sell for $3.00 per kg and toffee that sells for $3.20 per kg marketing says that they must use twice as many caramels as toffee in each package the cost will be $2.72 per kg to break even how many total kg of mints will they need for the 10,000 packages
1 solutions
Answer 137463 by scott8148(6628) on 2009-02-21 21:49:56 (Show Source):
You can put this solution on YOUR website!let x="kg of toffee", so 2x="kg of caramels" and 1-3x="kg of mints"
x(3.20) + 2x(3.00) + (1-3x)(2.20) = 2.72
expanding __ 3.2x + 6x + 2.2 - 6.6x = 2.72
subtracting 2.2 and combining terms __ 2.6x = .52
dividing by 2.6 __ x = .2
substituting __ 1-3(.2) = .4 __ this is the kg of mints in one package
so they will need .4(10000) or 4000kg of mints in total
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Miscellaneous_Word_Problems/183085: This question is from textbook Precalculus
Page 132 (problem 95): A length of wire 16 inches is to be cut into two pieces, and then each piece will be bent to form a square. Find the length of the two pieces if the sum of the areas of the two squares is 10 square inches.
(x/4)^2 + ((16-x)/4)^2 = 10
I've gotten this far but can't figure out the next steps to solve it.
Thank you, Lynn Scott
1 solutions
Answer 137459 by scott8148(6628) on 2009-02-21 21:30:23 (Show Source):
You can put this solution on YOUR website!expanding __ (x^2)/16 + (256-32x+x^2)/16 = 10
multiplying by 16 and rearranging __ 2x^2-32x+256 = 160
subtracting 160 and dividing by 2 __ x^2-16x+48 = 0
factoring __ (x-12)(x-4) = 0
x equals 12 or 4 (which sum to 16)
one square is 9in^2 and the other is 1in^2
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Probability-and-statistics/182417: This question is from textbook discrete mathematical structures
Suppose that two cards are selected at random from a standard 52 card deck. What is the probability that both cards are less than 10 and neither of them is red?
Total no of outcomes = 52 C 2 = 1326
there are 26 black and 26 red cards .
After that i don't know how to proceed please help me.
Thanks
1 solutions
Answer 136905 by scott8148(6628) on 2009-02-17 17:31:24 (Show Source):
You can put this solution on YOUR website!how many cards are less than 10?
32
how many of those are not red?
16
so 16C2 is the number of possible desired outcomes
probability is (16C2)/(52C2)
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Angles/181440: Segment JK=2x + 5
Segment KL=5x + 3
Segment JL=x^2
Find x.
So far, we have x^2=2x+5+5x+3
x^2=7x+8
We don't know how to solve for x by showing our work. We can figure out that the answer is x=8, but can't work it out.
Thanks for any assistance!
1 solutions
Answer 136046 by scott8148(6628) on 2009-02-10 21:39:07 (Show Source):
You can put this solution on YOUR website!x^2=7x+8
subtracting 7x+8 .... x^2-7x-8 = 0
factoring .... (x+1)(x-8) = 0
x+1 = 0 .... x = -1 .... negative lengths not realistic
x-8 = 0 .... x = 8
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Age_Word_Problems/181435: Five years ago, Tom was one third as old as his father was then. In 5 years, Tom will be half as old as his father will be then. Find their ages now.
1 solutions
Answer 136043 by scott8148(6628) on 2009-02-10 21:31:16 (Show Source):
You can put this solution on YOUR website!let t="Tom now", and f="father now"
"Five years ago, Tom was one third as old as his father was then"
... 3(t-5) = f-5
distributing ... 3t-15 = f-5
adding 5 ... 3t-10 = f
"In 5 years, Tom will be half as old as his father will be then"
... 2(t+5) = f+5
distributing ... 2t+10 = f+5
subtracting 5 ... 2t+5 = f
substituting ... 3t-10 = 2t+5
adding 10-2t ... t = 15
substituting ... 2(15)+5 = f ... 35 = f
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Equations/181184: This question is from textbook PRE-ALGEBRA
My son & I cannot find an answer to a problem posed by his teacher for this
chapter. She wants to know the arithmetic sequence for "t=a+(n-1)d".
Thank you.
1 solutions
Answer 135859 by scott8148(6628) on 2009-02-09 21:06:34 (Show Source):
You can put this solution on YOUR website!"t" is the value of the term
"a" is the starting point (a constant)
"n" is the number of the term
"d" is the difference between successive terms -- arithmetic sequence
to generate the sequence, start with n=1 and go as far as you wish; using the formula (t=a+(n-1)d) as a "template"
t1=a; t2=a+d; t3=a+2d; t4=a+3d ...
a, a+d, a+2d, a+3d, a+4d ...
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Equations/180041: I know the answer to my question, because I kept multiplying, but I don't know howto show my work as a stratey. The question is. In a math class of 26 students, each girl drew a triangle and each boy drew a rectangle. There were 92 slides in all. How may girls and how many boys were in the class. The answer I came up with was 16 girls and 11 boys.
1 solutions
Answer 134907 by scott8148(6628) on 2009-02-03 20:26:31 (Show Source):
You can put this solution on YOUR website!16 + 11 = 27 ... not 26
let g=girls and b=boys
"a math class of 26 students" __ g + b = 26 __ g = 26 - b
"each girl drew a triangle and each boy drew a rectangle. There were 92 slides in all"
__ I'm thinking "sides", not slides...
__ 3g + 4b = 92
substituting __ 3(26-b) + 4b = 92 __ 78 - 3b + 4b = 92
subtracting 78 __ b = 14
substituting __ g + (14) = 26
subtracting 14 __ g = 12
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Proportions/179230: I have to use two different types of milk (eg. Milk A & B)which have two different protein to fat ratios - in percents per 100 litre of milk.
In milk A, the protein to fat ratio is 3.3/ 3.85. = .857
In milk B, the protein to fat ratio is 4.3/ 2.50 = 1.72
What quantities of milk A and B should be used to get 6000 L of mix at a ratio of (protein/fat) = 1.05
If possible let me know the equation used for this
thanks
1 solutions
Answer 134406 by scott8148(6628) on 2009-01-31 12:11:41 (Show Source):
You can put this solution on YOUR website!let A=liters of A, and B=liters of B
A+B = 6000, so A = 6000-B
A(.857) + B(1.72) = 6000(1.05)
substituting from 1st eqn. to 2nd eqn. __ (6000-B)(.857) + B(1.72)=6000(1.05)
5142 - .857B + 1.72B = 6300
subtracting 5142 __ .863B = 1158
dividing by .863 __ B = 1342L (approx)
A = 6000 - 1342 = 4658L (approx)
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Unit_Conversion_Word_Problems/179468: A graduated cylinder contains 21.0 of water. What is the new water level after 30.0 of silver metal with a density of 10.5 is submerged in the water?
I used the formula d=m/v but my answer comes out to 21.35ml and the program says this is wrong. I am not sure if i am doing it wrong or have the wrong # of sig figs.
1 solutions
Answer 134404 by scott8148(6628) on 2009-01-31 11:56:12 (Show Source):
You can put this solution on YOUR website!guessing that the units are grams and milliliters/cubic centimeters
ml and cm^3 are equivalent
if the density of the metal is 10.5g/cm^3,
then 30.0g has a volume of 30.0/10.5 or 2.86cm^3
this, added to the original 21.0ml, gives 23.9ml
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Divisibility_and_Prime_Numbers/179424: You are asked to arrange the towels in a locker room is stacks of equal size. In stacks of 4, 1 is left over. Stacks of 5, one is left over. The same is true for stacks of 6. You can arrange in stacks of 7 each. What is the smallest possible number of towels.
I did the LCM of 4, 5, and 6 and added one and got 121. Now I don't know how to work the 7 in there. Please help
1 solutions
Answer 134356 by scott8148(6628) on 2009-01-30 21:27:52 (Show Source):
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Unit_Conversion_Word_Problems/179275: A porous catalyst for chemical reactions has an internal surface area (800m^2)/(cm^3) of bulk material . Fifty percent of the bulk volume consist of the pores-[holes] , while the other 50% is made up of the solid substance . Assume that the pores are all cylindrical tubules of uniform diameter d and length L , and that the measured internal surface area is the total area of the curved surfaces of the tubules . What is the diameter of each pore . Hint-[find the number of tubules per bulk cm^3, n , in terms of L and d , by using the formula for the volume of a cylinder V=.25(pi)d^2L . Then apply the surface area formula S=(pi)dL , to the cylindrical surfaces to the n tubules ] Please explain in detail , step by step , I have been working on this for three days , and I am not sure how to aproach question . The answer to this is 25 Angstroms , signed Michael
1 solutions
Answer 134353 by scott8148(6628) on 2009-01-30 21:18:53 (Show Source):
You can put this solution on YOUR website!the hint is a good one
look at one cm^3 of bulk material
50% is pores, or .5cm^3
__ so .5cm^3 = n * .25 * π * d^2 * L
__ rearranging (commutative principle) __ .5cm^3 = .25 * d * n * π * d * L
the internal surface area is 800m^2
__ so 800m^2 = n * π * d * L
__ or 8x10^6cm^2 = n * π * d * L
substituting the 2nd equation into the 1st
__ .5cm^3 = .25 * d * 8x10^6cm^2
dividing by .25 * 8x10^6 gives 2.5x10^(-7)cm = d
__ or 25 angstroms
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Linear-equations/178646: This question concerns using the slope intercept form.
The problem is this,
write an equation of the line that has the given slope and passes through the given point.
m= -5, (-3,6)
how do i do this problem and please explain how to do it in slope intercept form
1 solutions
Answer 133618 by scott8148(6628) on 2009-01-26 20:04:44 (Show Source):
You can put this solution on YOUR website!the slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept
just substitute the values you have and find the missing value (b)
6=-5(-3)+b __ 6=15+b __ -9=b
so the equation is y=-5x-9
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Quadratic-relations-and-conic-sections/178427: I am in over my head here, so please use very simple explanations. Find b and c so that the parabola y=20x^2+bx+c has vertex (10,-3)
1 solutions
Answer 133395 by scott8148(6628) on 2009-01-25 17:19:49 (Show Source):
You can put this solution on YOUR website!the vertex is on the axis of symmetry
the general equation for the axis of symmetry is x = -b/(2a)
in this case, 10=-b/(2*20)
multiplying by 40 __ 400=-b __ -400=b
the value of c can be found by substituting the vertex coordinates
-3=20(10^2)-400(10)+c __ -3=2000-4000+c
adding 2000 __ 1997=c
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Equations/178349: I cannot remeber how to solve equation with 3 variables. the problems are 6x+3y=12z
(2x+y)/4=z. I just had this last semester but didn't keep any of my work. This is for an astronomy paper that is due monday. will you help me please?
1 solutions
Answer 133332 by scott8148(6628) on 2009-01-25 11:27:49 (Show Source):
You can put this solution on YOUR website!in general; to solve for three variables, you need three independent equations
substitution and/or elimination are the most straight forward methods
it can also be done with matrices, using Cramer's Rule
the two equations you have are NOT independent
__ multiplying the 2nd equation by 12 gives the 1st equation
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Parallelograms/178364: Solve for the variables usin algebra.
I have a parallelogram..the left hand angle is d degrees, the upper righht angle is c degrees, the bottom left angle is (b-10) degrees and the lower right angle is (b+10) degress, and I have to solve for variable b, c, and d.
1 solutions
Answer 133331 by scott8148(6628) on 2009-01-25 11:18:44 (Show Source):
You can put this solution on YOUR website!opposite angles are equal and consecutive angles are supplementary
(b+10)+(b-10)=180 __ 2b=180 __ b=90
c=b-10 __ c=80
d=b+10 __ d=100
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