See tutors' answers!

Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On


   
By Tutor
 | By Problem Number | 

Tutor:
New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'richwmiller'

richwmiller answered: 9124 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149, >>Next

Radicals/283373: Simplifying radicals 7 sq root 3 - 3 sq root 3. Thanks
1 solutions

Answer 205693 by richwmiller(9135) About Me  on 2010-03-21 09:04:04 (Show Source):
You can put this solution on YOUR website!

Think of it as 7a-3a=(7-3)a=4a
7sqrt(3)-3sqrt(3)
So we get 4sqrt(3)


Triangles/283369: a right triangle has legs lengths of 9 and 12: The altitude of the hypotenuse has lenght of ?
1 solutions

Answer 205692 by richwmiller(9135) About Me  on 2010-03-21 08:56:48 (Show Source):
You can put this solution on YOUR website!
Are you looking for the length of the hypotenuse? It is 15
this is a triple multiple of the 3,4,5 right triangle
3*3=9
3*4=12
3*5=15


Linear-equations/283370: how do i solve this.. y=x+1 i need to set of coordinates but i don't know how to get the second set of corrdinates from this problem.
1 solutions

Answer 205691 by richwmiller(9135) About Me  on 2010-03-21 08:50:55 (Show Source):
You can put this solution on YOUR website!
How did you get the first set of coordinates?
Was it given ?
Did you give us the whole problem?
plug in zero for x and find y
plug in zero for y and find x
Now you have two sets of coordinates.


Triangles/282676: In ΔABC, m∠A = 3x + 40, m∠B = 8x + 35, and m∠C = 10x. Which is the longest side of the triangle?
1 solutions

Answer 205690 by richwmiller(9135) About Me  on 2010-03-21 08:48:17 (Show Source):
You can put this solution on YOUR website!
3x+40+8x+35+10x=180
x=5
so we have angles
3x+40=55
8x+35=40+35=85
10x=50
the side opposite the largest angle B is the longest


Triangles/283371: If they hypotenuse of a 30-60-90 degree triangle has a lenght of x, then (a) the shorter leg has length? and (b) the longer leg has length ?
1 solutions

Answer 205689 by richwmiller(9135) About Me  on 2010-03-21 08:40:56 (Show Source):
You can put this solution on YOUR website!
a 30-60-90 degree triangle has special known proportions
the shorter leg will be x/2 if the hypotenuse is x
and the longer leg will be sqrt(3)*x/2
the hypotenuse is twice the shorter leg.
and the longer leg is sqrt(3) times the shorter leg


test/283344: Question 1: I start with 8.I add -2 then take away -6. What do I get?
Question 2: What do you get if you add 3*-6 and -7*-10?
Answer clear and readable please.
1 solutions

Answer 205688 by richwmiller(9135) About Me  on 2010-03-21 08:33:56 (Show Source):
You can put this solution on YOUR website!

You said , "Answer clear and readable please."
Is this clear and readable?
Some website rules that you won't like.
one problem per submission (No more than one problem at a time)
No similar problems (only different kinds of problems)
Limit four submissions daily (that is 4 questions a day)


Probability-and-statistics/283364: If a coin is tossed 100 times, the greatest number of times a head could possibly occur is
a) 50 b) 60 c) 75 d) 80 e) 100
1 solutions

Answer 205685 by richwmiller(9135) About Me  on 2010-03-21 08:18:50 (Show Source):


Travel_Word_Problems/283319: A six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?


Do I times 180 mph with 7 miles, and the same with the 5 miles?
Please help. I appreciate it.
1 solutions

Answer 205661 by richwmiller(9135) About Me  on 2010-03-20 23:27:43 (Show Source):
You can put this solution on YOUR website!
r*t=d
(180+w)*t=7
(180-w)*t=5

t=7/(180+w)
t=5/(180-w)
set them equal to each other
7/(180+w)=5/(180-w)
w=30 mph


Travel_Word_Problems/283318: I am having problems figuring this problem out,
Juniors boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?
can you please help me, and explain the steps. thank you.
1 solutions

Answer 205660 by richwmiller(9135) About Me  on 2010-03-20 23:22:23 (Show Source):
You can put this solution on YOUR website!
r*t=d
(15+c)*t=12
(15-c)*t=9

t=12/(15+c)
t=9/(15-c)
12/(15+c)=9/(15-c)
4/(15+c)=3/(15-c)
4*(15-c)=3*(15+c)
60-4c=45+3c
15=7c
c = 15/7=2 1/7 mph
t = 7/10*60=42 minutes


Polynomials-and-rational-expressions/283311: Susan can do a certain job in 5 hours. Kim can do the same job in 3 hours. Working together, how many hours would they need to do the job?
1 solutions

Answer 205655 by richwmiller(9135) About Me  on 2010-03-20 22:49:43 (Show Source):
You can put this solution on YOUR website!
x/5+x/3=1
3x+5x=15
8x=15
x=15/8
x=1 7/8 hours
x/5=15/8/5=3/8 of the job
x/3=15/8/3=5/8 of the job
Sue does 3/8 and Kim does 5/8 of the job


Quadratic_Equations/283306: 2y^(2/3)+17y^(1/3)+30=0

I don't understand how to do this problem!
1 solutions

Answer 205654 by richwmiller(9135) About Me  on 2010-03-20 22:45:37 (Show Source):
You can put this solution on YOUR website!
2y^(2/3)+17y^(1/3)+30=0
let y^(1/3)=u
2u^2+17u+30=0
(u+6) (2 u+5) = 0
plug y^(1/3) back in for u
(y^(1/3)+6)*(2y^(1/3)+5)=0
(y^(1/3)+6)=0
y^(1/3)=-6
y=(-6)^3
(2y^(1/3)+5)=0
2y^(2/3)=-5
y^(2/3)=-5/2
y^2=(-5/2)^3
y^2 = -125/8
y=sqrt(-125/8)
y=-sqrt(-125/8)



Polynomials-and-rational-expressions/283303: two cars leave an intersection, one car travels north the other east. When the car traveling north had gone 12 miles the distance between the cars was 8 miles more than the distance traveled by the car heading east. how far had the eastbound car traveled?
1 solutions

Answer 205652 by richwmiller(9135) About Me  on 2010-03-20 22:25:46 (Show Source):
You can put this solution on YOUR website!
12^2+b^2=(b+8)^2
144+b^2=b^2+16x+64
144=16x+64
80=16x
5=x
a classic 5,12,13 right triangle triplet


Quadratic-relations-and-conic-sections/283259:
1 solutions

Answer 205650 by richwmiller(9135) About Me  on 2010-03-20 22:20:35 (Show Source):
You can put this solution on YOUR website!
x^2+2x+y^2-4y-4=0
x^2+2x+y^2-4y=4
we are going to complete the square once for x and once for y. That will give us the center and the radius
we want to complete the square for x^2+2x
take 2/2and square it 1^2=1
add 1 to both sides
next we want to complete the square for y^2-4y
take 4/2and square it 2^2=4
add four to both sides
so we have added 5 to both sides
x^2+2x+1+y^2-4y+4=9
(x+1)^2+(y-2)^2=9
the center is (-1,2) and the radius is 3 (sqrt(9)


Polynomials-and-rational-expressions/283296: frank can type a report in 4 hours and james takes 7 hours. how long will it take the two of them typing together?
1 solutions

Answer 205648 by richwmiller(9135) About Me  on 2010-03-20 22:11:27 (Show Source):
You can put this solution on YOUR website!
This problem might make math sense but practically how do you divide up the job of typing a report?
x/4+x/7=1
7x+4x=28
11x=28
x=28/11
x=2 6/11


Numbers_Word_Problems/283295: 1. the product of two consecutive integers is 600.find the integers.(show working out)
2. the product of two consecutive even integers is 1848.find the integers.(show working out)
3.two positive integers differ by 12 and their product is 405.find the integers.(show working out)
topic is quadratic equations
1 solutions

Answer 205644 by richwmiller(9135) About Me  on 2010-03-20 22:00:30 (Show Source):
You can put this solution on YOUR website!
Some website rules that you won't like.
one problem per submission (Tutors are busy)
No similar problems (different kinds of problems)
Limit four submissions daily (4 questions a day)
Don't try to get us to do your homework for you. We are here to teach you how to solve not do it for you.


expressions/283293: Multiply (3x+2)(-5x-6)answers could be -2x^2, -15x^2-28x-12, -2x^2-28x-12, -15x^2-28x-28

1 solutions

Answer 205642 by richwmiller(9135) About Me  on 2010-03-20 21:36:09 (Show Source):
You can put this solution on YOUR website!
since according to FOIL, the first term must be 3x*(-5x) we need a -15 in the expression
since the last term must be 2(-6) we need -12 in the expression
so that leaves only the second expression -15x^2-28x-12


Linear-equations/283287: x-y=3, -6+6y=17
I need help with this problem
1 solutions

Answer 205640 by richwmiller(9135) About Me  on 2010-03-20 21:31:45 (Show Source):
You can put this solution on YOUR website!
Something is wrong with the second equation.


Travel_Word_Problems/283290: hi, my question is following
A toy rocket is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. Using the function V(x)=-16t^2+vt+h, answer the following.
1. Give the function that describes the height of the rocket in terms of t?
2. Determine the time at which the rocket reaches its maximum height, and its maximum height in feet?
3. For what time interval will the rocket be more than 300 ft above the ground level?
4. After how many seconds will it hit the ground?
1 solutions

Answer 205639 by richwmiller(9135) About Me  on 2010-03-20 21:27:27 (Show Source):
You can put this solution on YOUR website!
Let me know when your question catches up to you. Is it following real close?
I see 4 questions from your teacher.


Complex_Numbers/283282: factoring completely
6x(3x-y)+ 5y(y-3x) where to start

1 solutions

Answer 205637 by richwmiller(9135) About Me  on 2010-03-20 21:19:48 (Show Source):
You can put this solution on YOUR website!
notice that -(y-3x)=(3x-y)
-6x*(y-3x)+5y*(y-3x)
(5y-6x)*(y-3x)


Quadratic_Equations/283270: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be?
1 solutions

Answer 205634 by richwmiller(9135) About Me  on 2010-03-20 21:12:03 (Show Source):
You can put this solution on YOUR website!
the pool has an area of
20*40=800
(20+2x)*(40+2x)=1500
positive answer only
x=5
the walkway will be 5 feet wide
check
30*50=1500
ok
why 2x? because the path is on both sides of the pool


Functions/283271: Graph this function on paper:
f(x)=x(squared)+4
the graph is a -10, 10 graph
1 solutions

Answer 205625 by richwmiller(9135) About Me  on 2010-03-20 20:45:15 (Show Source):
You can put this solution on YOUR website!
f(x)=x^2+4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A4=-16.

The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28-0%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-0%2B-+i%2A4%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B4+%29


Linear-systems/283268: I took Algebra 1 last year and will be taking Algebra 2 next year. I really have no knowledge as to what algebra is other than basic things like if you were to say 3X=9; I would know X=3. Only the most basic of Algebra do I understand and since it will be impossible to take an Algebra 2 class without the concepts of Algebra 1, I have decided I must learn them.
The teacher I had last year simply gave children grades based on behavior, and homework completion, etc.
I recall her doing a few Systems of equations on the board and assigning pages in a textbook that I nor any of my friends or classmates understood. I would appreciate it very much if you could solve a few. I don't have any examples; all I know is that there is a number with X +or- Y = a number.
Thank You very much!
1 solutions

Answer 205622 by richwmiller(9135) About Me  on 2010-03-20 20:41:27 (Show Source):
You can put this solution on YOUR website!
The website is here 24/7. So when you have a question, ask.
But we cannot teach you the whole algebra course. There are many lessons on many math topics.


Coordinate-system/283250: in a coordinate system, point a(-2,3) and b(6,-1) have a mid point of x. what is the midpoint between a and x
1 solutions

Answer 205614 by richwmiller(9135) About Me  on 2010-03-20 20:00:25 (Show Source):
You can put this solution on YOUR website!
x=(2,2)
midpoint between a and x is (0,2.5)


Polynomials-and-rational-expressions/283253: i need to know what is A=pi*r^2
1 solutions

Answer 205613 by richwmiller(9135) About Me  on 2010-03-20 19:51:38 (Show Source):
You can put this solution on YOUR website!
the area of a circle


Rational-functions/283243: if f(x)=x^2 - 7x, find f(a), f(a - 3), and f(a h)?
1 solutions

Answer 205612 by richwmiller(9135) About Me  on 2010-03-20 19:50:41 (Show Source):
You can put this solution on YOUR website!
substitute a for x and solve
next
substitute a-3 for x and solve


Permutations/283249: please help me solve this equation. what is the slope of line ((8x+12y+5=0 is))
1 solutions

Answer 205611 by richwmiller(9135) About Me  on 2010-03-20 19:47:59 (Show Source):


Linear-equations/283247: can u tell me wat 20x-5y=1.2 is caz i got an answer of 5 and i dont know if its right.
1 solutions

Answer 205608 by richwmiller(9135) About Me  on 2010-03-20 19:37:33 (Show Source):
You can put this solution on YOUR website!
You got 5 for what? Your answer makes no sense.


Human-and-algebraic-language/283244: Vern can shovel snow from his driveway in 45 minutes. Nina can do the same driveway in 60 minutes. How long will it take them to do the driveway if they work together?
1 solutions

Answer 205607 by richwmiller(9135) About Me  on 2010-03-20 19:34:13 (Show Source):
You can put this solution on YOUR website!
x/45+x/60=1
x/3+x/4=15
4x+3x=180
7x=180
x=25 5/7 minutes


Exponents-negative-and-fractional/283241: I saw a problem worked like this:
cubert(8^2) = 8^(2/3) = (8^2)^(1/3) or (8^1/3)^2
How do they work each step of this answer?

1 solutions

Answer 205605 by richwmiller(9135) About Me  on 2010-03-20 19:24:36 (Show Source):
You can put this solution on YOUR website!
root%283%2C8%5E2%29
Yes they are all equivalent.
And it does not matter whether you square first or find the cube root first
^2 means square
^!/3 means cube root
The denominator tells you it is a root.
The numerator tells you to square or cube.
It can be even more fun if there is a minus sign
The minus sign tells you to take the reciprocal.
2^(-1) means 1/2
2^(-1/2) take the square root of the reciprocal. sqrt(1/2)
You should have a lesson already or soon on fractional and negative exponents.


Signed-numbers/283232: how can i simplify 19 145/72
1 solutions

Answer 205604 by richwmiller(9135) About Me  on 2010-03-20 19:11:20 (Show Source):
You can put this solution on YOUR website!
19 145/72=19 +2 1/72=21 1/72


Quadratic_Equations/283235: Factor completely.
a^5 - 625a
1 solutions

Answer 205603 by richwmiller(9135) About Me  on 2010-03-20 19:06:59 (Show Source):
You can put this solution on YOUR website!
a*(a^4-625)=
a*(a^2-25)*(a^2+25)=
a*(a-5)(a+5)(a^2+25)