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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

Quadratic_Equations/94542: x^3-x^2-12x=0


I think the answer is x=0, x=4, x=-3, but I'm not really sure how I got that...
1 solutions

Answer 68872 by stanbon(57377) About Me  on 2007-08-26 21:34:51 (Show Source):
You can put this solution on YOUR website!
x^3-x^2-12x=0
x(x^2-x-12)=0
Factor to get:
x(x-4)(x+3)=0
x=0 or x=4 or x=-3
==========
Cheers,
Stan H.


Trigonometry-basics/94546: Please solve.
(t-1)^2=7
1 solutions

Answer 68871 by stanbon(57377) About Me  on 2007-08-26 21:32:46 (Show Source):
You can put this solution on YOUR website!
(t-1)^2=7
Take the square root of both sides to get:
t-1 = sqrt(7) or t-1 = -sqrt(7)
t = 1+sqrt(7) or t = 1-sqrt(7)
=============
Cheers,
Stan H.


Trigonometry-basics/94547: Use the quadratic formula to solve 5s^2-13s+6=0
1 solutions

Answer 68869 by stanbon(57377) About Me  on 2007-08-26 21:30:04 (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula to solve 5s^2-13s+6=0
s = [13+-sqrt(13^2-4*5*6)]/10
s = [13+-sqrt(49)]/10
x = [13+7]/10= 2 or x = [13-7]/10 = (3/5)
==============
Cheers,
Stan H.


Polygons/94548: what do you call polygons in which all sides have the same length?
1 solutions

Answer 68867 by stanbon(57377) About Me  on 2007-08-26 21:26:27 (Show Source):
You can put this solution on YOUR website!
They are said to be regular polygons.
Cheers,
Stan H.


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) About Me  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) About Me  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.


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) About Me  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) About Me  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.


decimal-numbers/94397: find the product of the following;
1 0.1*10
2 16.17*90
1 solutions

Answer 68842 by stanbon(57377) About Me  on 2007-08-26 20:11:41 (Show Source):
You can put this solution on YOUR website!
find the product of the following;
1 0.1*10 = 1
--------------
2 16.17*90 = 1455.3
======================
Chers,
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) About Me  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.


real-numbers/94532: The square root of 5 times the square root of 125.
1 solutions

Answer 68837 by stanbon(57377) About Me  on 2007-08-26 19:58:34 (Show Source):
You can put this solution on YOUR website!
The square root of 5 times the square root of 125.
= sqrt(5*125)
= sqrt(625)
= 25
===========
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) About Me  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.


Graphs/94527: Please help me solve 90%3E5%282r%2B6%29
1 solutions

Answer 68831 by stanbon(57377) About Me  on 2007-08-26 19:42:12 (Show Source):
You can put this solution on YOUR website!
90>5(2r+6)
90 > 10r+30
10r < 60
r < 6
=============
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) About Me  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
----------------
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx-3%2C-%281%2F2%29x%2B3%29
------------------
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) About Me  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.


Polynomials-and-rational-expressions/94518: Find the degree of the polynomial: 3x^2+3x+3x^3-3

Thanks!
1 solutions

Answer 68824 by stanbon(57377) About Me  on 2007-08-26 19:20:49 (Show Source):
You can put this solution on YOUR website!
It's always the degree of the highest power term.
Your Problem
Degree is 3
Cheers,
Stan H.


Exponents/94520: Rewrite the expression using positive exponents: 5AB^-2
Thanks!
1 solutions

Answer 68823 by stanbon(57377) About Me  on 2007-08-26 19:18:52 (Show Source):
You can put this solution on YOUR website!
5AB^-2
= [5A]/B^2
===========
Chers,
Stan H.


Numeric_Fractions/94451: Convert 0.48 to a fraction and write answer in lowest terms.
1 solutions

Answer 68800 by stanbon(57377) About Me  on 2007-08-26 15:37:46 (Show Source):
You can put this solution on YOUR website!
0.48 = 48/100 = 24/50 = 12/25
12/25 can no longer be reduced.
==============
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) About Me  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.
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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.


Trigonometry-basics/94465: Please simplify.
4 x the square root of -3 + 2 x the square root of -27
1 solutions

Answer 68797 by stanbon(57377) About Me  on 2007-08-26 14:06:52 (Show Source):
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Please simplify.
4 x the square root of -3 + 2 x the square root of -27
4sqrt(-3) + 2sqrt(-27)
= 4sqrt(3)i + 6sqrt(3)i
= 10sqrt(3)i
=================
Cheers,
Stan H.


Expressions-with-variables/94469: -x^3(9-x^2)^(-1/2)+2x(9-x^2)^(1/2)
1 solutions

Answer 68796 by stanbon(57377) About Me  on 2007-08-26 14:00:53 (Show Source):
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-x^3(9-x^2)^(-1/2)+2x(9-x^2)^(1/2)
= -x[(9-x^2)^(1/2)][x^2-2]
==============
Cheers,
Stan H.


Expressions-with-variables/94467: 4x^4-19x^3-5x^2
1 solutions

Answer 68795 by stanbon(57377) About Me  on 2007-08-26 13:56:41 (Show Source):
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4x^4-19x^3-5x^2
=x^2[4x^2-19x-5]
= x^2[4x^2-20x+x-5]
= x^2[4x^2(x-5)+(x-5)]
= x^2(4x^2+1)(x-5)
=====================
Cheers,
Stan H.


Trigonometry-basics/94464: Please simplify.
2+3i/4-5i
1 solutions

Answer 68794 by stanbon(57377) About Me  on 2007-08-26 13:53:03 (Show Source):
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Please simplify.
(2+3i)/(4-5i)
Multiply numerator and denominator by 4+5i to get:
=[(2+3i)(4+5i)]/[(4-5i)(4+5i)]
=[(8-15)+(12+10)i] / [16+25]
= [ -7 + 22i ] / [41]
= (-7/41) + (22/41)i
============================
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) About Me  on 2007-08-26 13:39:42 (Show Source):
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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
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%282%2F3%29x-2%2C-2x-10%29
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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) About Me  on 2007-08-26 13:33:21 (Show Source):
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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) About Me  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.


Linear-equations/94453: Simplify: -(-(-36)).
1 solutions

Answer 68788 by stanbon(57377) About Me  on 2007-08-26 12:58:26 (Show Source):
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Simplify: -(-(-36)) = -36
Any odd number of negative signs will give you a negative result.
Any even number of negative signs will give you a positive result.
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) About Me  on 2007-08-26 12:24:01 (Show Source):
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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.


Equations/94442: Solve for x. Find any restrictions. bx-cx=-c
1 solutions

Answer 68775 by stanbon(57377) About Me  on 2007-08-26 12:18:25 (Show Source):
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Solve for x. Find any restrictions. bx-cx=-c
x = c/(b-c)
Restriction: b cannot equal c as that would make the denominator zero.
=============
cheers,
Stan H.


Equations/94441: Solve for the indicated variable r. I=prt
1 solutions

Answer 68773 by stanbon(57377) About Me  on 2007-08-26 12:14:10 (Show Source):
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r = I/(pt)
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) About Me  on 2007-08-26 12:12:47 (Show Source):
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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
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graph%28400%2C300%2C-10%2C10%2C-10%2C20%2C3x%2B8%29
Cheers,
Stan H.