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Recent problems solved by 'stanbon'
stanbon answered: 57304 problems
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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, >>Next
Evaluation_Word_Problems/94460: Sally bought 3 choclate bars and a pack of gum and paid $1.75. Jake bought 2 chocolate bars and 4 packs of gum and paid $2.00. Write a system of algebraic equations using c=chocolate bar, and g=gum to represent the given information. Solve using the adding method or substitution to fing the cost of a chocolate bar and the cost of a pack of gum. 1 solutions
Answer 68866 by stanbon(57377) on 2007-08-26 21:23:20 (Show Source):
You can put this solution on YOUR website!Sally bought 3 choclate bars and a pack of gum and paid $1.75. Jake bought 2 chocolate bars and 4 packs of gum and paid $2.00. Write a system of algebraic equations using c=chocolate bar, and g=gum to represent the given information. Solve using the adding method or substitution to find the cost of a chocolate bar and the cost of a pack of gum.
------------
EQUATIONS:
3c+g = 175 cents
2c+4g = 200 cents
-----------------
Multiply the 1st equation by 4 to get:
12c + 4g = 700
2c+4g = 200
---------------
Subtract the 2nd equation from the 1st to get:
10c = 500
c = 50 cents (cost of a chocolate bar)
----------
Substitute into 3c+g = 175 to solve for g:
3*50 + g= 175
g = 25 cents (cost of a pack of gum)
==============
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/94543: which conic is this
7x^2-12y^2-14x+24y-28=0? 1 solutions
Answer 68863 by stanbon(57377) on 2007-08-26 21:17:43 (Show Source):
You can put this solution on YOUR website!which conic is this
7x^2-12y^2-14x+24y-28=0?
Rearrange to get:
7(x^2 - 2x + 1) -12(y^2-2y+1) = 28+7-12
7(x+1)^2 - 12(y-1)^2 = 23
Divide thru by 23 to get:
(x+1)^2/(23/7) -(y-1)^2/(23/12) = 1
------------------------
Depending on what you know about conic equations, not all this
work was necessary to see that the equation is that of a hyperbola.
The fact that the x^2 term and the y^2 term have different signs
is enough to show that it is an equation of a hyperbola.
--------------
Cheers,
Stan H.
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Linear-equations/94540: This question is from textbook COLLEGE ALGEBRA
x2 + y2 = 4 The question is find the center and the radius of the circle. I need to know how to solve this. 1 solutions
Answer 68861 by stanbon(57377) on 2007-08-26 21:09:58 (Show Source):
You can put this solution on YOUR website!x2 + y2 = 4 The question is find the center and the radius of the circle. I need to know how to solve this.
-------------
The form you want is (x-h)^2 + (y-k)^2 = r^2
which has center at (h,k) and has a radius of r
--------------
Rearranging your equation you get:
(x-0)^2 + (y-0)^2 = 2^2
This has center at (0,0) and radius = 2
===============
Cheers,
Stan H.
|
Inequalities/94536: I'm not sure how to type the symbol for less than/or equal to, so I'm going to just use this <=
hope that isn't too confusing!
Solve the inequality: 3<=2-x<5 1 solutions
Answer 68844 by stanbon(57377) on 2007-08-26 20:15:42 (Show Source):
You can put this solution on YOUR website!3<=2-x<5
Subtract 2 along the line to get:
1 <= -x < 3
Divide thru by -1; remember that dividing or multiply by a negative reverses
the inequality.
-3 < x <= -1
=================
Cheers,
Stan H.
|
Angles/94531: Hi, my name is Norma and I've been working on this problem for about half an hour but I cant seem to get a reasonable answer. The problem is:
The supplement of an angle is 36 degrees less than twice the supplement of the complement of the angle. Find the measure of the supplement.
So far I have: 180-x=2(90-x)-36
180-x=180-2x-36
180-x=144-2x
180=144-x
x= -36 degrees
I'm not sure if this is right because of the fact that my answer is a negative.So if you can help on this problem I would really appreciate it.
1 solutions
Answer 68839 by stanbon(57377) on 2007-08-26 20:04:23 (Show Source):
You can put this solution on YOUR website!The supplement of an angle is 36 degrees less than twice the supplement of the complement of the angle. Find the measure of the supplement.
================
Let the angle be "x"; the supplement = "180-x"; the complement = "90-x"
-------------------
EQUATION:
180-x + 36 = 2(180-(90-x))
216 - x = 2(90+x)
216 - x = 180 + 2x
3x= 36
x = 12 degrees
The measure of the supplement = 180-12 = 168 degrees.
=================
Cheers,
Stan H.
|
Mixture_Word_Problems/94528: A 27 gallon solution contain 9 gallon acid and 18 gallon water. How much water must be added to get 25% Acid? 1 solutions
Answer 68835 by stanbon(57377) on 2007-08-26 19:56:27 (Show Source):
You can put this solution on YOUR website!A 27 gallon solution contain 9 gallon acid and 18 gallon water. How much water must be added to get 25% Acid?
--------------
Starter Solution:
amt of solution = 27 gallons ; Amt of acid = 9 gallon
-----------------
Additional solution:
amt = x gallons ; Amt of acid = 0
---------------------
Mixture solution:
Amt = (27+x) gallons ; amt of acid = 0.25(27+x) = 6.75 + 0.25x gallons
-------------------
EQUATION:
acid + acid = acid
9 + 0 = 6.75 + 0.25x
0.25x = 2.25 gallons
x = 9 gallons (# of gallons of water that must be added)
==========================
Cheers,
Stan H.
|
Average/94512: I am loosing it over this one
Solve the following system of linear inequalities by graphing.
x – y < 3
x + 2y < 6
1 solutions
Answer 68830 by stanbon(57377) on 2007-08-26 19:40:23 (Show Source):
You can put this solution on YOUR website!Solve the following system of linear inequalities by graphing.
x – y < 3
x + 2y < 6
--------------
Graph the boundary lines as dashed lines.
y = x-3
y = -(1/2)x+3
----------------

------------------
Pick a test point that is not on either line, like (0,0)
Check it isn the two INEQUALITIES to see if the region containing
(0,0) is in or out of the solution region:
0 - 0 <3 ; true
0 +2*0 <6; true
----------------
Darken the area containing the test point above y>x-3 and below y<-(1/2)x+3
That is the solution of the system
=================
Cheers,
Stan Hl
|
Graphs/94516: ok i cannot figure this one out-
DIRECTIONS SAY:
SOLVE EACH EQUATION OR FORMULA FOR THE SPECIFIED VARIABLE-
#32
a-4b <--(squared)
------ = d for a
2c 1 solutions
Answer 68826 by stanbon(57377) on 2007-08-26 19:25:06 (Show Source):
You can put this solution on YOUR website!SOLVE EACH EQUATION OR FORMULA FOR THE SPECIFIED VARIABLE-
#32
a-4b <--(squared)
------ = d for a
2c
----------------
(a-4b)/(2c) <= d^2
Multiply both sides by 2c to get:
a-4ab <= 2cd^2
a <= 4ab+2cd^2
===============
Cheers,
Stan H.
|
Trigonometry-basics/94471: Without solving each equation, determine the nature of the roots.
a. 3y^2-10y+1=0
b. 2w^2+6w+10=0 1 solutions
Answer 68799 by stanbon(57377) on 2007-08-26 15:35:39 (Show Source):
You can put this solution on YOUR website!Without solving each equation, determine the nature of the roots.
a. 3y^2-10y+1=0
b^2-4ac = 100-4*3*1>0 so there are two unequal Real Number roots.
---------------------
b. 2w^2+6w+10=0
b^2-4ac = 36-4*2*10<0 so there are two unequal complex number roots.
=================
Cheers,
Stan H.
|
Graphs/94363: Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result. 1 solutions
Answer 68792 by stanbon(57377) on 2007-08-26 13:39:42 (Show Source):
You can put this solution on YOUR website!Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result
---------
Convert to slope-intercept form:
y = (2/3)x-2
y = -2x-10
--------------

------------
The intersection of the two lines is at (-3,-4)
The solution for the system of two equations is (-3,-4)
=====================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/94330: This question is from textbook
the cost of medical care increased 142.2 points in a 6-year period. if the cost of medical care reached the 326.9 mark, what was it 6 years ago? 1 solutions
Answer 68791 by stanbon(57377) on 2007-08-26 13:33:21 (Show Source):
You can put this solution on YOUR website!the cost of medical care increased 142.2 points in a 6-year period. if the cost of medical care reached the 326.9 mark, what was it 6 years ago?
-------------------
325.9-142.2 = 183.7
=============
Cheers,
Stan H.
|
Exponents/94450: in 2000, the government collected approximatly $1.9 trillion in taxes. What is the per capita tax burden or the amount that each U.S. citizen paid in taxes? When 10 to the 12 power is one trillion and the popuation in the U.S. is 2.8 time 10 to the 8th power. Round to the nearest hundred dollars. 1 solutions
Answer 68790 by stanbon(57377) on 2007-08-26 13:04:23 (Show Source):
You can put this solution on YOUR website!the government collected approximatly $1.9 trillion in taxes. What is the per capita tax burden or the amount that each U.S. citizen paid in taxes? When 10 to the 12 power is one trillion and the popuation in the U.S. is 2.8 time 10 to the 8th power. Round to the nearest hundred dollars.
----------------
[1.9x10^12] / [2.8x10^8] = 6.785714x10^3 = $6785.71 per person
Rounded: $6800.00
Cheers,
Stan H.
|
Equations/94417: I have some problems and I was wanting to make sure I am doing them right.
Can you take a look and help me?
equation what i did
problem#1
3-6[2x-1(8x+3)-6]+9
3-6[-6x+2-6]+9
-3[-6x-4]+9
18x+12+9
18x+31
problem #2
6(-3)/(-32)
-18/-32
.5625
problem #3
6x^5(4x^2)
1 solutions
Answer 68778 by stanbon(57377) on 2007-08-26 12:24:01 (Show Source):
You can put this solution on YOUR website!3-6[2x-1(8x+3)-6]+9
3-6[2x-8x-3-6]+9
3-6[-6x-9]+9
3+36x+54+9
36x+66
----------------
problem #2
6(-3)/(-32)
-18/-32
.5625
problem #3
6x^5(4x^2)
= 24x^7
===========
Cheers,
Stan H.
|
Linear-equations/94428: the equation y -2=3(x + 2) is in stanard form.
graph the equation on a coordinate plane 1 solutions
Answer 68771 by stanbon(57377) on 2007-08-26 12:12:47 (Show Source):
You can put this solution on YOUR website!the equation y -2=3(x + 2) is in standard form
-------
FYI: It is not in standard form which is ax+by=c
-----------
To graph it, solve for y:
y = 3(x+2)+2
y = 3x+8
Plot two points and draw a line thru them.
If x=0, y=8
If x=1, y=11
---------

Cheers,
Stan H.
|
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