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Recent problems solved by 'stanbon'
stanbon answered: 57214 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextGraphs/155136: How would you graph the equation y=0.2x-0.5?
1 solutions
Answer 114219 by stanbon(57282)   on 2008-09-04 20:02:20 (Show Source):
You can put this solution on YOUR website!How would you graph the equation y=0.2x-0.5?
----------------------------------------------
Two methods are usually taught.
1st: Plot two points:
Let x = 0, then y = -0.5 giving you point (0,-0.5)
Let x = 1, then y = 0.2 - 0.5 = -0.3 giving you point (1,-0.3)
Plot the points and draw a line thru them.
-----------------------
2nd: slope, intercept method
Plot the y-intercept, which is -0.5, on the y-axis.
From that point move your pencil 1 to the right and then up 0.2
----------------
Draw a line thru those two points.
----------------------
Cheers,
Stan H.
|
Distributive-associative-commutative-properties/155137: This question is from textbook Pre-Algebra An Integrated transition to Algebra and Geometry
I am trying to find and unmderstand how to arrive at the answer of restating 2a+4b using the distributive property. I have other problems that need restating that is why it is important for me to understand how to get the answr as well. I hope you can help me.
1 solutions
Answer 114217 by stanbon(57282) on 2008-09-04 19:53:42 (Show Source):
You can put this solution on YOUR website!I am trying to find and understand how to arrive at the answer of restating 2a+4b using the distributive property.
--------------------------------------------
The distributive property is a(b+c) = ab + ac
But it can be read from left to right or from right to left.
-------------------------------------------------
Your problem has the right side as 2a+4b
The corresponding left side would be 2(a+2b)
--------------------------------------------------
Left to right it is called "distributive".
Right to left it is called "factoring".
--------------------------------------------
Cheers,
Stan H.
|
absolute-value/155132: 1. Solve:|x-1|+|x|+|x+1|=x+2
1 solutions
Answer 114215 by stanbon(57282) on 2008-09-04 19:49:38 (Show Source):
You can put this solution on YOUR website!1. Solve:|x-1|+|x|+|x+1|=x+2
----------------------------------
The absolute terms change meaning depending on whether the variable
expression is positive or negative.
---------------
So determine the "zeroes" of the expressions:
x = 1, or x=0, or x=-1,
-----------------------------
Draw a number line and mark -1, 0, and 1,
------------------------------------------
Solve the equation for each of the resulting four intervals.
-------------------------
If x < -1 you get: 1-x -x -x-1 = x+2 ; -4x = 2; x = -1/2
But x=-1/2 is not less than -1 so no solution.
---------------------------
If -1 < x <0 you get: 1-x -x +x+1 = x+2; -x+2 = x+2; x = 0
But x=0 is not in (-1,0) so no solution.
---------------------------
If 0 < x < 1 you get: 1-x + x + x + 1 = x + 2; x+2 = x+2
That is true for all x in (0,1)
-------------------------------------
If 1
But x=1 is not in (1,+inf) so no solution
-----------------------------------------------
Final Answer: 0 < x < 1
===========================
Cheers,
Stan H.
|
Sequences-and-series/155130: I need to know what number comes next in this sequence and why.
9,73,241,561,1081,1849,_?__
1 solutions
Answer 114214 by stanbon(57282) on 2008-09-04 19:32:27 (Show Source):
You can put this solution on YOUR website!I need to know what number comes next in this sequence and why.
9,73,241,561,1081,1849,_?__
-----------------------------
I matched 1,2,3,...,6 up with the numbers.
I tried a linear regression, a quadratic regression,
and a cubic regression on it. Best results were
with the cubic:
y = 8x^3 + 4x^2 -4x = 1
-----------------------------
The next term would be f(7) = 2913
========================================
Cheers,
Stan H.
|
Graphs/155129: How do you identify the slope, m, and the y-intercept, b, in 3/4x+2y=-3? Thank you.
1 solutions
Answer 114212 by stanbon(57282) on 2008-09-04 19:16:34 (Show Source):
You can put this solution on YOUR website!identify the slope, m, and the y-intercept, b, in (3/4)x+2y=-3
-------------------------
Solve for "y":
y = [(-3/4)/2] - (3/2)
y = [-(3/8)]x - (3/2)
-------------------
slope = -3/8
intercept = -3/2
============================
Cheers,
Stan H.
|
Geometric_formulas/155127: The state of colorado is almost perfectly rectangular with it's north border 111 miles longer than it's west border. If the state encompasses 104,000 square miles, estimate the dimensions of colorado. Round your anwser to the nearest mile.
I was thinking that the equation was x times (x+11)=104,000 but i couldn't figure it out.
1 solutions
Answer 114211 by stanbon(57282) on 2008-09-04 19:12:10 (Show Source):
You can put this solution on YOUR website!Yes, that's right.
Multiply out the left side so you have a quadratic.
Use the quadratic formula to solve for x = 317.037 miles
---------------------------------------------
Cheers,
Stan H.
|
Triangles/155122: How do I find the missing sides of the triangles when each trianlge measues 30,60,90 degrees and the leg is 8
Thank you
1 solutions
Answer 114209 by stanbon(57282) on 2008-09-04 19:05:30 (Show Source):
You can put this solution on YOUR website!How do I find the missing sides of the triangles when each trianlge measues 30,60,90 degrees and the leg is 8
----------------------------------
That depends on whether the 8 is opposite the 30 or the 60 degree angle.
--------------------
If it is opposite the 30 degree angle, it is half the hypotenuse, so
the hypotenuse would have to be 16 and the 3rd side would have to be
sqrt[16^2 - 8^2]
----------------------
If is is opposite the 60 degree angle, the side opposite the 30 is "x"
and the hypotenuse is 2x.
Then (2x)^2 = x^2 + 8^2
3x^2 = 64
x^2 = 64/3
x = 8/sqrt(3)
2x = 16/sqrt(3)
=====================
Cheers,
Stan H.
|
decimal-numbers/155123: Division can be used to show that 7 over 40 can be written as what kind of decimal?
1 solutions
Answer 114207 by stanbon(57282) on 2008-09-04 18:58:33 (Show Source):
You can put this solution on YOUR website!Ans: A repeating decimal.
Since there can be at most 39 different remainders when you divide
by 40, the decimal must repeat its pattern if your dividing takes
more than 39 steps.
---------------------------------
Cheers,
Stan H.
|
Trigonometry-basics/155107: Solve in radians(must work with left side)
1-2sin^2*x=cos^2*x
1 solutions
Answer 114202 by stanbon(57282) on 2008-09-04 17:30:28 (Show Source):
You can put this solution on YOUR website!Solve in radians(must work with left side)
1-2sin^2*x=cos(2x)
------------------
since sin^2 + cos^2 = 1
Substitute for "1" to get:
(sin^2 + cos^2) - 2sin^2 = cos(2x)
cos^2x - sin^2x = cos(2x)
cos(2x) = cos(2x)
==========================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/155110: The starned rate for tiping in a reatarunt is 15%percent of your Bill.
If you spend $120 dollar, how much would your tip be
1 solutions
Answer 114201 by stanbon(57282) on 2008-09-04 17:24:10 (Show Source):
You can put this solution on YOUR website!The standard rate for tipping in a reatarunt is 15% of your Bill.
If you spend $120 dollar, how much would your tip be?
-------------------------------------
EQUATION:
Let the price of the meal be "x:
x + 0.15x = 120
1.15x = 120
x = $104.35 (cost of the meal)
===============================
Cheers,
Stan H.
|
Quadratic_Equations/155098: find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
1 solutions
Answer 114200 by stanbon(57282) on 2008-09-04 17:20:16 (Show Source):
You can put this solution on YOUR website!find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
----------------------------------
Plot those points and you will see that f(-6) = 16 by symmetry about
the x-axis
-----------------
So you have three points: (-6,16),(-2,-16),(2,16)
----------------------------------------------------
Substitute these into ax^2 + bx + c = y
to get three equations with unknowns a,b, and c.
36a -6b + c = 16
4a -2b + c =-16
4a +2b + c = 16
-------------------------
Use any method to solve this system to get:
a = 2
b = 8
c =-8
---------------
EQUATION:
y = 2x^2 + 8x -8
==========================
Cheers,
Stan H.
|
Graphs/155100: find the vertex, intercepts (x and y), axis of symmetry and sketch of y=-3x^2-6x-2
1 solutions
Answer 114189 by stanbon(57282) on 2008-09-04 16:29:31 (Show Source):
You can put this solution on YOUR website!find the vertex, intercepts (x and y), axis of symmetry and sketch of
y=-3x^2-6x-2
-------------------
The vertex occurs at x = -b/2a = 6/(-6) = -1
-----------------
f(-1) = -3(-1)^2 - 6(-1) -2 = -3 + 6 -2 = 1
-----------------------------------------------
Vertex: (-1,1)
Axis of symmetry: x = -1
----------------------------------------------
Graph:
============================================
Cheers,
Stan H.
|
Equations/155082: This question is from textbook algebra
Tina,Dawn, and Harry have $175.00 together. Tina has 3 times as much money as Dawn. Dawn has twice as much money as harry. How much money does each have?
1 solutions
Answer 114188 by stanbon(57282) on 2008-09-04 16:25:16 (Show Source):
You can put this solution on YOUR website!Tina,Dawn, and Harry have $175.00 together. Tina has 3 times as much money as Dawn. Dawn has twice as much money as harry. How much money does each have?
---------------------------------------------------
Let Harry have "x" dollars.
Then Dawn has "2x" dollars.
And Tina has 3(2x) = "6x" dollars
----------------------------------
EQUATION:
x + 2x + 6x = 175 dollars
9x = 175
x = $19.44 (Harry's amount)
2x = $38.89 (Dawn's amount)
6x = $116.67 (Tina's amount)
===============================
Cheers,
San H.
|
Linear-systems/155090: Why is x = 4 a vertical line
1 solutions
Answer 114177 by stanbon(57282) on 2008-09-04 16:07:49 (Show Source):
You can put this solution on YOUR website!Plot two points with x=4
For example: (4,-2) and (4,3)
Draw a line thru them and you will see you get a vertical line.
--------------------------------
Also if you calculate the slope of the line thru those two points
you get m = (3--2)/(4-4) = 5/0
Such a slope is a vertical line.
=================================
Cheers,
Stan H.
|
Graphs/155094: How do you find the slope of the line containing the points (-1, -1/5) and (2/3, 3/4)? I am confused about this because I do not understand how to find the slope when the points contain fractions and/or decimals.
1 solutions
Answer 114173 by stanbon(57282) on 2008-09-04 16:02:56 (Show Source):
You can put this solution on YOUR website!How do you find the slope of the line containing the points (-1, -1/5) and (2/3, 3/4)?
-----------------
slope = (y2-y1)/(x2-x1)
----------------------
slope = ((3/4)-(-1/5))/((2/3)-(-1))
slope = [(15+4)/20] / [5/3]
slope = [19/20] * [3/5]
slope = 57/100
==================
Cheers,
Stan H.
|
logarithm/155093: Solve: log base x of 81=4/3
1 solutions
Answer 114171 by stanbon(57282) on 2008-09-04 15:56:54 (Show Source):
You can put this solution on YOUR website!Solve: log base x of 81=4/3
---------------------------
Your problem says:
the exponent is 4/3
the base is x
the result is 81
------------------------
Rewrite as:
x^(4/3) = 81
Raise both sides to the 3/4 power to get:
x = 81^(3/4)
x = 3^3
x = 27
=============
Cheers,
Stan H.
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Coordinate-system/155091: Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coordinate is the number of cars sold (hours, cars). After plotting each point, explain if there is a linear relationship between the number of hours worked and the number of cars sold.
Sales Hours Worked Cars
Sold
Tim 40 3
Bob 26 5
Brandi 10 1
Kurt 60 1
Kelly 30 7
Graph:
Explanation of linear relationship:
What is the first step I take to answer this question?
1 solutions
Answer 114169 by stanbon(57282) on 2008-09-04 15:54:08 (Show Source):
You can put this solution on YOUR website!
Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coordinate is the number of cars sold (hours, cars). After plotting each point, explain if there is a linear relationship between the number of hours worked and the number of cars sold.
Sales Hours Worked Cars
Sold
Tim 40 3
Bob 26 5
Brandi 10 1
Kurt 60 1
Kelly 30 7
Graph:
Explanation of linear relationship:
------------------------------------------
I entered the hours worked and cars sold data into
a TI-83 and ran a Linear Regression program on the
data. The "r" correlation coefficient turned out to
be -0.178542 which is not significant.
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/155027: Allyson plays for the cook county regoinal football league whuch has ten teams. DURING A SEASON, EACH TEAM PLAYS THE OTHER TEAM TWICE, ONCE AT HOME AND ONE AWAY.HOW MANY TOTAL GAMES ARE PLAYED IN ONE SEASON?
1 solutions
Answer 114132 by stanbon(57282) on 2008-09-04 07:21:45 (Show Source):
You can put this solution on YOUR website!It takes two teams to play a game.
Number of pairs of ten is 10C2 = 10*9/1/2 = 45 games
They do that twice, so 90 games would be required for
each team to play the other teams twice..
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/155026: Find the horizontal asymptote, if any, of the graph of the rational function.
f(x)=8x/2x^2+1
a. y=1/4
b. y=0
c. y=4
d. no horizontal asymptote
1 solutions
Answer 114131 by stanbon(57282) on 2008-09-04 07:17:26 (Show Source):
You can put this solution on YOUR website!No horizontal awymptote because 2x^2+1=0 has no Real Number solution.
-----------------
Another way to look at it: That 2x^2 term can never be negative.
When you add 1 to it you always get a positive number---never zero.
-----------------
cheers,
Stan H.
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Linear-equations/154991: Hello,
I am trying to graph the following but I been out of school for 15 years can someone please help me.
I trying to graph a polynomial of three terms
6x² - 4xy + 2xy
I really need your help. I am sorry for having to ask someone to help me but I am stuck and I do not remember how to graph.
If you could show me I really would appreciate it.
Thank you so much,
Jackie
1 solutions
Answer 114109 by stanbon(57282) on 2008-09-03 22:44:11 (Show Source):
You can put this solution on YOUR website!6x² - 4xy + 2xy
-----------------------
Difficulties:
1st: Normally, you would be asked to graph an equation.
You have not posted an equation.
------------
2nd: Normally, a three term expression would look like ax^2 + bx + c,
which graphs as a parabola. Your posting has "xy" terms and there
is no way to resolve how y is a function of x.
--------------
I would try to graph your three term expression but I cannot
because of the difficulties listed.
============================
Cheers,
Stan H.
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Travel_Word_Problems/154987: Two missiles speed directly toward each other, one at 9,000 mph and the other at 21,000 mph. If they start 1,317 miles apart, how far apart are they on minute before they collide?
1 solutions
Answer 114108 by stanbon(57282) on 2008-09-03 22:36:01 (Show Source):
You can put this solution on YOUR website!Two missiles speed directly toward each other, one at 9,000 mph and the other at 21,000 mph. If they start 1,317 miles apart, how far apart are they on minute before they collide?
--------------------------------------
Find the closing rate: 9000+21000 = 30,000 mph
Change to miles per minute: 30,000/60 = 500 miles per minute
--------------------------------------
How far apart are they one minute before they collide?
Ans: 500 miles
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/154985: Karl Schmidt just scored a 96 on his last biology unit test. The mean score of the 36 students in his class was 78, and the standard deviation was 12. What is Karl’s z-score?
1 solutions
Answer 114107 by stanbon(57282) on 2008-09-03 22:14:39 (Show Source):
You can put this solution on YOUR website!Karl Schmidt just scored a 96 on his last biology unit test. The mean score of the 36 students in his class was 78, and the standard deviation was 12. What is Karl’s z-score?
---------------------
Formula:
z(x) = (x-u)/sigma
z(96) = (96-78)/12 = 18/12 = 1.5
===================================
Cheers,
Stan H.
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Functions/154986: Write a function for the rule represented by the graph. Identify the domain and tge range of the function.When the functions are (1,0),(2,2)(3,4)(4,6)? I get the graph part but I'm suppose to solve like y=x? I don't understand how to solve this.
1 solutions
Answer 114105 by stanbon(57282) on 2008-09-03 22:08:59 (Show Source):
You can put this solution on YOUR website!Write a function for the rule represented by the graph.
Identify the domain and the range of the function. When the functions are
(1,0),(2,2)(3,4)(4,6)?
I get the graph part but I'm suppose to solve like y=x?
I don't understand how to solve this.
------------------------------------
y = 2x-2
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Cheers,
Stan H.
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Age_Word_Problems/154973: WENDY'S AND DANIEL'S AGES COMBINED ARE TWICE JAMIE'S AGE. WENDY IS 8 YEARS OLDER THAN DANIEL. JAMIE'S AGE PLUS DANIEL'S AGE IS 20 YEARS. HOW OLD ARE EACH OF THEM?
1 solutions
Answer 114100 by stanbon(57282) on 2008-09-03 21:38:45 (Show Source):
You can put this solution on YOUR website!WENDY'S AND DANIEL'S AGES COMBINED ARE TWICE JAMIE'S AGE. WENDY IS 8 YEARS OLDER THAN DANIEL. JAMIE'S AGE PLUS DANIEL'S AGE IS 20 YEARS. HOW OLD ARE EACH OF THEM?
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Let Daniel's age be "x".
Wendy's age is "x+8".
Jamie's age is "x+8 + x" = "2x+8"
----------------------------------
EQUATION:
Jamie's age Plus Daniel's age is 20 years.
2x+8 + x = 20
3x = 12
-----------------
x = 4 (Daniel's age Now)
x+8 = 12 (Wendy's age NOW)
2x+8 = 2*4+8 = 16 (Jamie's age NOW)
========================================
Cheers,
Stan H.
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Age_Word_Problems/154972: My son is back in school, and my algebra from 20+ years ago is not coming back to me...
Please help me with this:
Julie is 4 times older than Aaron. In 10 years Julie will be twice as old as Aaron. How old are Julie and Aaron?
1 solutions
Answer 114099 by stanbon(57282) on 2008-09-03 21:32:53 (Show Source):
You can put this solution on YOUR website!Julie is 4 times older than Aaron. In 10 years Julie will be twice as old as Aaron. How old are Julie and Aaron?
------------------------------------------
Now DATA:
Let Aaron be x yrs old.
Then Julie is 4x yrs old
-------------------------
10 years from now DATA:
Aaron will be x+10 yrs old.
Julie will be 4x+10 yrs old.
------------------------------
EQUATION:
Julie = twice Aaron's age.
4x+10 = 2(x+10)
4x + 10 = 2x + 20
2x = 10
x = 5 (Aaron's age NOW)
4x = 20 (Julie's age NOW)
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Cheers,
Stan H.
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Functions/154968: how do i find the domain of f(x)= x^3 + 5x / x^2 - 4x
1 solutions
Answer 114098 by stanbon(57282) on 2008-09-03 21:27:48 (Show Source):
You can put this solution on YOUR website!find the domain of f(x)= x^3 + 5x / x^2 - 4x
------------------------------------------------
Factor f(x)
f(x) = [x(x^2+5)] / [x(x-4)]
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The domain is all real numbers except x = 0 and x = 4
=======================================================
Cheers,
Stan H.
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