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Recent problems solved by 'stanbon'
stanbon answered: 57894 problems
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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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next
Mixture_Word_Problems/393357: A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?
1 solutions
Answer 279169 by stanbon(57967)   on 2011-01-11 17:26:54 (Show Source):
You can put this solution on YOUR website!A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?
------------
Equation:
gold + gold = gold
0.70x + 0.60(100-x) = 0.66*100
---
Multiply thru by 100 to get:
70x + 60*100 - 60x = 66*100
10x = 6*100
x = 60 oz (amt. of 70% alloy needed in the mix)
---
100-x = 40 oz (amt of 60% alloy needed in the mix)
==============
Cheers,
Stan H.
|
Graphs/393353: write the slope-intercept form of the equation of the line passing through the points (-6,-2) and parallel to this line y=-3x-4
1 solutions
Answer 279168 by stanbon(57967) on 2011-01-11 17:19:17 (Show Source):
You can put this solution on YOUR website!write the slope-intercept form of the equation of the line passing through the points (-6,-2) and parallel to this line y=-3x-4
-----------------------------
The given line has a slope of -3.
----
Any line parallel to it must have a slope of -3.
----
Equation Form:
y = mx + b
---
You know x = -6 when y = -2 and you know m = -3 ; solve for "b":
----
-2 + -3(-6)+b
b = -2-18 = -20
----
Equation:
y = -3x-20
|
Linear-equations/393347: PLEASE HELP! (:
my teacher JUST informed us that there is a test on slope tomorrow, and we only spent two days learning about the topic! I really need help on things like finding the difference between slopes,writing equations of slopes, and how to write an equation in slope-intercept form . PLEASE HELP!
1 solutions
Answer 279167 by stanbon(57967) on 2011-01-11 17:14:17 (Show Source):
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test/393344: If f(x) = -4x +5 and g(x) = |x-6| then what is f(g)(-2))
1 solutions
Answer 279164 by stanbon(57967) on 2011-01-11 17:06:17 (Show Source):
You can put this solution on YOUR website!If f(x) = -4x +5 and g(x) = |x-6| then what is f(g)(-2))
------
f[g(-2)] = f[-2-6|] = f(8) = -4*8+5 = -27
============================
Cheers,
Stan H.
=======
|
Quadratic_Equations/393329: What is the solution to the factoring problem 2x^2-24x^3+14x^2? I tried it this way: 2x^2(x^-12x+7), but was not able to simplify beyond this point.
Thanks
1 solutions
Answer 279163 by stanbon(57967) on 2011-01-11 17:02:10 (Show Source):
You can put this solution on YOUR website!What is the solution to the factoring problem 2x^2-24x^3+14x^2?
----
It is not an equation, so it does not have a "solution".
-------------
2x^2-24x^3+14x^2
Simplify:
-24x^3+16x^2
It can be factored:
-8x^2(3x-2)
============
Cheers,
Stan H.
|
Angles/393327: what is the measure of an angle that is supplement to angle b when b is 35?
1 solutions
Answer 279157 by stanbon(57967) on 2011-01-11 16:27:12 (Show Source):
You can put this solution on YOUR website!what is the measure of an angle that is supplement to angle b when b is 35?
----
The supplement of 35 degrees is 180-35 = 145 degrees
==============
Cheers,
Stan H.
|
Trigonometry-basics/393289: I'm having a very hard time with this question, can somebody please help me!
The question is:
Prove the identity of:
sinx + sinx cot^2x=cscx
Thankyou!
1 solutions
Answer 279140 by stanbon(57967) on 2011-01-11 15:48:03 (Show Source):
You can put this solution on YOUR website!Prove the identity of:
sinx + sinx cot^2x=cscx
---
factor the left side to get:
sin(x)[1+cot^2(x)] = csc(x)
---
Since 1+cot^2(x) = csc^2(x) you get:
---
sin(x)[csc^2(x)] = csc(x)
---
sin(x){1/sin^2(x)] = csc(x)
---
1/sin(x) = csc(x)
---
csc(x) = csc(x)
===================
Cheers,
Stan H.
|
test/393286: 60 - 20 = 20 + _______ what is the answer. I need to explain to my 8 year old.
1 solutions
Answer 279138 by stanbon(57967) on 2011-01-11 15:43:34 (Show Source):
You can put this solution on YOUR website! 60 - 20 = 20 + _______ what is the answer. I need to explain to my 8 year old.
---
The answer is 20.
If I had to do this with an eight yr. old I would get a bunch of dimes.
I would make a group of 6 for the 60 (the left side of the equation)
and I would make a group of 2 for the 20 (the right side of the equation.
---
I would form a "bank" of several dimes away from the two "groups".
---
I would ask the 8 yr old to remove 20 from the left side and
put it in the bank.
---
I would ask the 8 yr old to take enough from the bank so the group
on the right equaled the group on the left.
---
If that did not answer the question you have posted, I would run
through the whole process again till the answer was seen.
------------
If you are looking for an algebric method go through the following.
60 - 20 = 20 + _______ what is the answer
Explain the the right side must balance the left side of the equal side
Evaluate the left side to get 40.
Ask what needs to be added to the right side so it will balance the 40
on the left.
=================
Good luck.
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/393281: 1. 5+2logx=4
2. log(x-2)+log(2x-3)=2logx
3. 4^x+3=7^x
4. log2x + log2 (x+2)=log2 (x+6)
5. 5^(x/2)=123
1 solutions
Answer 279134 by stanbon(57967) on 2011-01-11 15:32:58 (Show Source):
You can put this solution on YOUR website!1. 5+2logx=4
2logx = -1
log(x) = -1/2
x = 10^-1/2
x = (1/10)sqrt(10)
==============================
2. log(x-2)+log(2x-3)=2logx
log[(x-2)(2x-3)] = log(x^2)
---
2x^2-7x+6 = x^2
x^2-7x+6 = 0
(x-6)(x-1) = 0
x = 6 is a usable answer; x = 1 is not.
==========
3. 4^(x+3)=7^x
(x+3)log(4) = xlog(7)
x[log(7)-log(4)] = 3log(4)
---
x = [3log(4)]/[log(7)-log(4)]
---
x = 7.4317
============
4. log2x + log2 (x+2)=log2 (x+6)
---
log2[x(x+2)] = log2(x+6)
----
x(x+2) = x+6
x^2+x-6= 0
(x+3)(x-2) = 0
-----
Positive solution:
x = 2
=======================
5. 5^(x/2)=123
(x+2)log(5) = log(123)
x+2 = log(123)/log(5)
---
x+2 = 2.99
x = 0.99
===============
Cheers,
Stan H.
|
Money_Word_Problems/393268: a model for the path of a toy rocket is given by h=68t-4.9t(t), where h is the altitude in meters and t is the time in seconds. Explain how to find both the maximum altitude of the rocket andhow long it takes to reach that altitude.
1 solutions
Answer 279131 by stanbon(57967) on 2011-01-11 15:14:50 (Show Source):
You can put this solution on YOUR website! a model for the path of a toy rocket is given by h=68t-4.9t(t), where h is the altitude in meters and t is the time in seconds. Explain how to find both the maximum altitude of the rocket and how long it takes to reach that altitude.
-------------------
There are several ways to find the max of min of a quadratic equation.
---
Max occurs when t = -b/2a
t = -b/2a = -68/(2*-4.9) = 6.93 seconds
---
Max altitude = h(6.93) = 68(6.93)-4.9(6.93^2) = 235.92 meters
--------------------------
Cheers,
Stan H.
|
Equations/393275: If sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
I need step by step please i have been out of high school for 5 years and am trying to get into college. thanks
1 solutions
Answer 279129 by stanbon(57967) on 2011-01-11 15:08:44 (Show Source):
You can put this solution on YOUR website!If sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
-------------------
Sally DATA:
time = 4 hrs/job ; rate = 1/4 job/hr
-----
John DATA:
time = 6 hrs/job ; rate = 1/6 job/hr
-----
Together DATA:
time = x hrs/job ; rate = 1/x job/hr
-----------------------------------------
Equation to solve for "x":
rate + rate = together rate
1/4 + 1/6 = 1/x
Multiply thru by 12x to get:
3x + 2x = 12
5x = 12
x = 12/5 = 2.8 hrs (time to do the job when they work together)
---
Note: 2.8 hrs = 2 hr + 0.8*60min = 2hr+48 minutes
==================================================
Cheers,
Stan H.
|
Linear_Algebra/393274: Set up equation for problem and solve
1) An object is thrown up in the air at a velocity of 20 ft/sec. The height of the object t seconds after it is thrown is given by the function h(t)= -16t^(2)+20t . How long will it take for the object to hit the ground?
1 solutions
Answer 279128 by stanbon(57967) on 2011-01-11 15:04:24 (Show Source):
You can put this solution on YOUR website!An object is thrown up in the air at a velocity of 20 ft/sec. The height of the object t seconds after it is thrown is given by the function h(t)= -16t^(2)+20t . How long will it take for the object to hit the ground?
-------------
Height is zero when the object hits the ground.
---
Solve:
-16t^2+20t = 0
-4t(4t-5) = 0
Positive solution:
t = 5/4 = 1 1/4 seconds
==========================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/393269: If one painter charges a base price of $250 plus $16/hr and another painter charges a base price of $210 plus $18/hr how many hours does it take for them to be the same? I know the answer is 20 hours but how would you set it up to come up with 20 hours?
1 solutions
Answer 279127 by stanbon(57967) on 2011-01-11 15:00:51 (Show Source):
You can put this solution on YOUR website! If one painter charges a base price of $250 plus $16/hr
A(x) = 250+16x
---------------------------
and another painter charges a base price of $210 plus $18/hr
B(x) = 210+18x
---------------------------
how many hours does it take for them to be the same?
---
Solve:
A(x)=B(x)
250+16x = 210+18x
2x = 40
x = 20 hrs
================
Cheers,
Stan H.
================
|
Rational-functions/393266: 3x-2y=0
x+y=-5
Solving Systems Using Substitution..
1 solutions
Answer 279126 by stanbon(57967) on 2011-01-11 14:57:40 (Show Source):
You can put this solution on YOUR website!3x-2y=0
x+y=-5
Solving Systems Using Substitution..
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Rearrange:
x = -5-y
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Substitute for "x" and solve for "Y":
3(-5-y)-2y = 0
-15-3y-2y = 0
-5y = 15
y = -3
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Solve for "x":
x = -5-y
x = -5+3
x = -2
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Cheers,
Stan H.
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Quadratic_Equations/393261: When one number is 2 more than twice another and their product is 2 more than twice their sum, what is the two number solution? I used x to represent one number and 2x + 2, which equals to x(2x + 2)= 2 + 2x + 2 = 2x^2 + 2x = 2x + 4, therefore, 2x^2 + 2x-2x = -4, 2x^2 = -4 = (2x-2)(x+2). Answer: 2 and -2?
1 solutions
Answer 279124 by stanbon(57967) on 2011-01-11 14:51:21 (Show Source):
You can put this solution on YOUR website!When one number is 2 more than twice another and their product is 2 more than twice their sum, what is the two number solution?
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Let one number be "x".
The other number is "2x+2"
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Equation:
x(2x+2) = 2(x+2x+2) + 2
2x^2 + 2x = 2x+4x+4 + 2
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2x^2 + 2x = 6x+6
2x^2-4x-6 = 0
Factor:
2x^2-6x+2x-6 = 0
2x(x-3)+2(x-3) = 0
(x-3)(2x+2) = 0
Positive solution:
x = 3
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1st number: x = 3
2nd number: 2x+2 = 2*3+2 = 8
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Cheers,
Stan H.
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logarithm/393174: How do you solve 2log[base 6](x)-2log[base 6] (x-4)= 1
1 solutions
Answer 279087 by stanbon(57967) on 2011-01-11 11:59:47 (Show Source):
You can put this solution on YOUR website!solve 2log[base 6](x)-2log[base 6] (x-4)= 1
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Divide thru by 2 to get:
log6(x)-log6(x-4) = 1/2
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log6[x(x-4)] = 1/2
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x(x-4) = 6^(1/2)
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x^2-4x-6^(1/2) = 0
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Use the Quadratic formula to find a positive solution
because x must be positive in the original problem statement:
x = [4 + sqrt(16-4*6^(1/2))]/2
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x = [4 + sqrt(6.202)]/2
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x = 3.245..
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That is not an acceptable answer because 3.234-4 is negative
and you cannot take a log of a negative number.
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Conclusion: No solution
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Cheers,
Stan H.
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Triangles/393023: Write a polynomial that represents the area of each triangle
Width is 2x+3 and length is 4x
1 solutions
Answer 278976 by stanbon(57967) on 2011-01-10 22:26:53 (Show Source):
You can put this solution on YOUR website!Write a polynomial that represents the area of each triangle
Width is 2x+3 and length is 4x
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A(x) = 4x(2x+3)
A(x) = 8x^2+12x
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Cheers,
Stan H.
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Quadratic_Equations/393021: write an equation for the horizontal line passing through the point (5, -3)
1 solutions
Answer 278974 by stanbon(57967) on 2011-01-10 22:23:38 (Show Source):
You can put this solution on YOUR website! write an equation for the horizontal line passing through the point (5, -3)
If the y-value of this point is -3, the y-value
of every point on the horizontal line thru (5,-3) is -3.
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Equation: y = -3
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cheers,
Stan H.
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Inequalities/393012: Ok solve this inequality please thanks
-3(2r-4) greater than or equal to 2(5-3r)
1 solutions
Answer 278962 by stanbon(57967) on 2011-01-10 22:08:10 (Show Source):
You can put this solution on YOUR website!-3(2r-4) greater than or equal to 2(5-3r)
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-6r+12 >= 10-6r
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12 >= 10
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The inequality is true for All Real Numbers.
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Cheers,
Stan H.
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Linear-equations/393008: is x= -5/2 a solution of the inequality 5x-4<_3 (x-7)?
1 solutions
Answer 278959 by stanbon(57967) on 2011-01-10 22:01:59 (Show Source):
You can put this solution on YOUR website!is x= -5/2 a solution of the inequality 5x-4<_3 (x-7)?
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Substitute to see if you get a true statement.
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5(-5/2) -4 <= 3(-5/2-7)
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-25/2 -4 <= 3(-19/2)
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-33/2 <= -57/2
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False
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So x=-5/2 is not a solution for the inequality.
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Cheers,
Stan H.
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Travel_Word_Problems/393006: two trains simultaneously left moscow and sverdlovsk, and traveled towards each other. the first traveled at 48 km per hour and the second at 54 km per hour. how far apart were the two trains 12 hours after departure if it is 1822 km from moscow to sverdlovsk?
1 solutions
Answer 278958 by stanbon(57967) on 2011-01-10 21:56:23 (Show Source):
You can put this solution on YOUR website!two trains simultaneously left moscow and sverdlovsk, and traveled towards each other. the first traveled at 48 km per hour and the second at 54 km per hour. how far apart were the two trains 12 hours after departure if it is 1822 km from moscow to sverdlovsk?
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Closing speed for the two trains is 48+54 = 102 km/hr
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After 12 hrs they had covered 12*102 = 1224 km
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They were 1822-1224 = 598 apart
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Cheers,
Stan H.
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Age_Word_Problems/392910: Melinda's father Lester is 3 times as old as Melinda. Seven years ago, he was 4 times as old as Melinda. How old is each now?
1 solutions
Answer 278935 by stanbon(57967) on 2011-01-10 20:29:24 (Show Source):
You can put this solution on YOUR website!Melinda's father Lester is 3 times as old as Melinda. Seven years ago, he was 4 times as old as Melinda. How old is each now?
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Equations:
f = 3m
(f-7) = 4(m-7)
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Substitute for "f" and solve for "m":
(3m-7) = 4m-28
m = 21 (Melinda's age now)
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Solve for "f":
f = 3m
f = 3*21 = 63 (Father's age now)
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cheers,
Stan H.
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