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solver91311 answered: 5073 problems
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Numeric_Fractions/241211: what is the connection between rational numbers and division?
1 solutions

Answer 176635 by solver91311(5072) on 2009-11-20 18:37:23 (Show Source):

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A rational number is an integer divided by an integer. The root of the word "rational" is "ratio"

John

Triangles/241181: Hello.
I am doing a geometry problem and I have to find the measure of the sides and classify each triangle by its side.
But.. one of the coordinates/points are a radical . for example.
A(0,5) B(5 radical 3,2)
How can I solve this problem with the radical in it ?
Thank You
1 solutions

Answer 176634 by solver91311(5072) on 2009-11-20 18:35:48 (Show Source):

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Use the distance formula to calculate the measure of a side.

where

and

are the coordinates of the given points, so:

A radical is just another number. Just because it looks funny doesn't mean you should treat it any differently than any other number. Would you want people to laugh at you if you had a big wart on your nose?

John

Pythagorean-theorem/241197: Can someone please tell me how to find the dimensions of a box that has a volume of 504 cubic inches and its sides measure x, x+1 and x+2. Much appreciated!
1 solutions

Answer 176632 by solver91311(5072) on 2009-11-20 17:49:06 (Show Source):

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,

So:

Using the Rational Root Theorem

http://en.wikipedia.org/wiki/Rational_root_theorem

To determine the possible rational roots. You can also use your graphing calculator to find a root of the equation. You could also realize that x + 1 will probably be very close to the cube root of 504. Use your calculator to find a numeric approximation of cube root of 504, then take the nearest integer as x + 1.

John

Polynomials-and-rational-expressions/241180: a decorator plans to place a rug in a room 9m by 12m in such a way that a uniform strip of flooring around the rug will remain uncovered. if the rug is to cover half the floor space, what should the dimensions of the rug be?
1 solutions

Answer 176628 by solver91311(5072) on 2009-11-20 17:32:53 (Show Source):

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Solve for

. Exclude the negative root. Subtract 2x from 9 for one dimension, subtract 2x from 12 for the other dimension.

John

logarithm/241186: please help me solve this
log (6x+5) - log (3) = log (2) - log (x)
1 solutions

Answer 176624 by solver91311(5072) on 2009-11-20 17:16:33 (Show Source):

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Presuming equal bases:
1. The sum of the logs is the log of the product.

2. The difference of the logs is the log of the quotient.

3. If the logs are equal, the arguments are equal.

Solve the quadratic. The quadratic does not factor over the rationals, so you will need to use the quadratic formula. (or complete the square, if you prefer -- though I would recommend against it in this case). You must then exclude any root that would cause either of the log arguments containing the variable to be negative.

John

Percentage-and-ratio-word-problems/241190: Bonnie And Tim do some yardwork for their neighbor. The ratio comparing the amount of time each one works is 7:4. The neighbor pays them 88 dollars. If Bonnie worked more, how much should each of them receive?
1 solutions

Answer 176621 by solver91311(5072) on 2009-11-20 17:05:42 (Show Source):

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If the ratio is 7:4, then one of them did

of the work and the other did

. One should get

of the money and the other should get

of the money.

John

logarithm/241188: ln (3x-4)= 7
1 solutions

Answer 176619 by solver91311(5072) on 2009-11-20 17:02:43 (Show Source):

You can put this solution on YOUR website!

I'm just going to guess that you want to solve for

. Just so you know, your laziness in not taking the trouble to tell us what you want is rather annoying.

Use:

To write:

Since

is a constant, this equation can be solved for

in terms of a sum of the two constant terms you will have remaining after you simplify. Leave your answer in terms of

to express the exact answer. Use your calculator to obtain a numerical approximation.

John

Human-and-algebraic-language/241182: If the sum of 3 consecutive odd integersis 237,then what are the integers?
1 solutions

Answer 176618 by solver91311(5072) on 2009-11-20 16:53:03 (Show Source):

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Let

represent the first odd integer. Then the next consecutive odd integer must be

, and the one after that must be

.

Since the sum of the three is 237, we can say:

Just solve for

to find the smallest one. Add 2 to get the next one. Add 2 again to get the one after that.

John

Linear_Algebra/241173: the annual social security benefit of a retiree depends on the age at the time of retirement. the accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later. What is the annual benefit for a person who retires at age 64? at what retirement age does a person recieve an annual benefit of $11,600? find the slope of each line segment on the graph and interpret your results.Why do people who postpone retirement until 70 years of age get get the highest benefit?
1 solutions

Answer 176617 by solver91311(5072) on 2009-11-20 16:39:27 (Show Source):

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You didn't provide the graph, so I can only answer your questions in either very general or procedural terms.

Look at the

value of the point on the graph where

Look at the

value where

on the graph.

Write down the ordered pairs that represent the end points of each segment of the graph, (

) = (age, amount)

For each pair of endpoints that define a segment, use the slope formula to calculate the slope of that segment:

where

and

are the coordinates of the endpoints. The highest slopes give the greatest benefit for waiting that particular year.

People wait until 70 to draw their social security because they are betting that they will live long enough to accumulate more benefits than would accrue if you took the lower benefit earlier.

For example, if the annual benefit is 18000 at age 65 and the annual benefit is 24000 at age 70 and

You live to be 80 years old: You will accumulate 15 times $18,000 = $270,000 if you take the benefit at 65, but only 10 times 24,000 = $240,000 if you take the benefit at 70. So if you are only going to live to be 80, it is better to start taking the money earlier

At age 85, with the given amounts, you break even. That is, it doesn't matter which you do, so you might as well enjoy the additional years of retirement -- leave early.

But if you are planning to live beyond age 85, you start to make money by delaying retirement to age 70.

John

Quadratic-relations-and-conic-sections/241169: How do I put x^2-6x-y+11=0 in standard form for a parabola? Please help!
1 solutions

Answer 176614 by solver91311(5072) on 2009-11-20 16:12:53 (Show Source):

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Standard form is:

Just add

to both sides of your equation and then swap the LHS with the RHS.

John

logarithm/241166: so im not sure if i need to go another step when they say "write the following expression as a single logarithm"
Equation: 1/4log(x)-slog(y)+7/10log(z)
My anzwer: log(x^4 square root (z^7))/square root (y)
Do i need to go another step?
1 solutions

Answer 176611 by solver91311(5072) on 2009-11-20 16:04:51 (Show Source):

You can put this solution on YOUR website!

In the first place, how did you get from

when using

?

It should have been

What does "slog" mean? Were you trying to represent

?

Also:

John

Rectangles/240948: A rectangular sign must have an area of 22 square yards. Its length must be 4 yards more than its width. Find the dimensions of the sign.
1 solutions

Answer 176497 by solver91311(5072) on 2009-11-19 19:52:41 (Show Source):

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Let

represent the width. Then

is the length.

Since the area is the length times the width:

Solve for

. Then add 4 to get the length. Exclude the negative root. This quadratic does not factor over the rationals, so you will need to use the quadratic formula. If you are actually building a sign, then use your calculator to find a numeric approximation that will suit your tolerances. Otherwise, simplify the radical and leave it in radical form for the exact answer.

John

Triangles/240911: what is the heigth of an equalateral triangle that is 30 ft wide by 30 ft on each side and formula to solve this problem?
1 solutions

Answer 176477 by solver91311(5072) on 2009-11-19 19:17:31 (Show Source):

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The altitude of an equilateral triangle is also a perpendicular bisector of the base. Therefore, the height is the measure of one leg of a right triangle where the hypotenuse is the measure of one side of the equilateral triangle and the other leg measures one-half of the side of the equilateral triangle.

So, applying Pythagoras, given the measure of the side,

, the height,

is:

Hence, for a 30 foot equilateral triangle, the height is:

John

Polynomials-and-rational-expressions/240909: How do you solve
(px+q)(2x+5)=6xx+11x+r
1 solutions

Answer 176462 by solver91311(5072) on 2009-11-19 18:47:56 (Show Source):

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If you FOIL

You get

Clearly then,

and

You should be able to derive the values of

, and

from that information.

John

Rational-functions/240901: g(x)=x^2+3x
h(x)=(x+3)/2
find (h*g)(-1)
when finding the answer it is evaluating as composition. the * symbol is really a small o in the problem. thanks for your help
1 solutions

Answer 176459 by solver91311(5072) on 2009-11-19 18:38:51 (Show Source):

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Wherever you see an

in the definition of

, substitute the entire definition of

. Once you have done that, replace every

with (-1), then do the arithmetic.

John

Word_Problems_With_Coins/240903: The cost of a chocolate shake is 40 cents less than the cost of a hamburger. If h represents the cost, in cents, of a hamburger, represent in terms of h the cost of a hamburger and a chocolate shake in dollars.
1 solutions

Answer 176458 by solver91311(5072) on 2009-11-19 18:36:07 (Show Source):

You can put this solution on YOUR website!

John

real-numbers/240882: what are the properties of real numbers
1 solutions

Answer 176457 by solver91311(5072) on 2009-11-19 18:34:06 (Show Source):

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Associative Property of Addition:

Associative Property of Multiplication:

Commutative Property of Addition

Commutative Property of Multiplication

Distributive Property of Multiplication over Addition

Density Property

Identity Property of Addition

Identity Property of Multiplication

John

Mixture_Word_Problems/240881: please help me....
How many grams of a 25% silver alloy is to be melted with 30 grams of a 55% silver alloy to obtain a 32% silver alloy?
1 solutions

Answer 176452 by solver91311(5072) on 2009-11-19 18:15:23 (Show Source):

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Let

represent the amount of 25% alloy.

Solve for

John

Linear-equations/240854: Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point.
y=7;(2,4)
1 solutions

Answer 176445 by solver91311(5072) on 2009-11-19 18:00:31 (Show Source):

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A line described by

set equal to a constant is a horizontal line with slope of 0. Any line parallel must have the same slope, and therefore also be a horizontal line. If the line is horizontal and passes through (2, 4), then all of the ordered pairs that are in the solution set of the equation must have a

coordinate equal to 4.

John

Rate-of-work-word-problems/240843: It takes 6 hours to fill a pool. It takes 8 hours to drain it. How long does it take to fill the pool if the drain is left opened when the pool is started to be filled?
1 solutions

Answer 176427 by solver91311(5072) on 2009-11-19 17:02:17 (Show Source):

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If A can do a job in x time periods, then A can do

of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do

of the job in 1 time period.

So, working together, they can do

of the job in 1 time period.

Therefore, they can do the whole job in:

time periods.

All of that works nicely when people or things work together, but in the case of your problem, they are working against one another, so:

So, working against one another, they can do

of the job in 1 time period.

Therefore, they can do the whole job in:

time periods.

John

Linear-equations/240840: Find the equation of the line that passes through the point (-2, 13) and is perpendicular to y = -2/5x + 3.
1 solutions

Answer 176422 by solver91311(5072) on 2009-11-19 16:50:41 (Show Source):

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The given equation is already in slope-intercept form, so you can determine the slope of the given line by inspection of the coefficient on

.

Use the fact that perpendicular lines have slopes that are negative reciprocals of each other, that is:

to determine the slope of the desired line.

Now use the point-slope form of the equation of a line to write an equation of the desired line, that is:

where

is the given point and

is the slope you determined in the previous step.

You should ask your instructor or check for any instructions in your text as to the required final form of your answer such as slope-intercept or standard form.

Unfortunately, I cannot answer your question exactly as you stated it. One cannot find the equation of a line. That is because for any given set of ordered pairs that describe a straight line in a plane, there are an infinite number of equations that describe the relationship. The best anyone can ever do is provide an equation of a line.

John

Miscellaneous_Word_Problems/240830: a cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers. The pigeons reach the grain at the same time.
How far is the grain from the foot of the cathedral tower?
1 solutions

Answer 176420 by solver91311(5072) on 2009-11-19 16:41:00 (Show Source):

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Let

represent the distance from the base of the cathedral tower where the two birds meet.

Then the distance from the meeting point to the base of the church tower is

Now you have one right triangle with legs of 200 and

and another right triangle with legs of 150 and

. Since the birds left at the same moment and flew the same speed, the hypotenuses of the two right triangles must be equal.

Therefore:

Just solve for

John

Trigonometry-basics/240829: 2cosA-secA=cosA-(tanA divided by cscA)
1 solutions

Answer 176417 by solver91311(5072) on 2009-11-19 16:32:34 (Show Source):

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I can't tell whether you mean this is Problem Number 2 and you want to prove the identity:

Or if you want to solve the equation:

for

I know it is a terrible burden to place on you poor over-worked students, but a little helpful information telling us what it is you want would be highly appreciated. I hope that isn't too much to ask given that the tutors on this site are all uncompensated volunteers giving of their time to help you.

John

Probability-and-statistics/240765: accordin to goverment data, the probability that an adult was never married is 15%, in a random survey of 10 adults, what is the probability that at least 8 were married?
1 solutions

Answer 176415 by solver91311(5072) on 2009-11-19 16:19:36 (Show Source):

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The probability of

successes in

trials given the probability of success

in one trial such that the probability of failure in one trial is

is given by

Where

is the number of ways to select

things from

things where order doesn't matter, or:

You want to calculate

where

.

That gives you the probability that exactly 8 were married.

You also need to calculate

and

where

which gives you the probability that exactly 9 and exactly 10 of them, respectively, were married.

Then:

Which is the probability that either 8, 9, or 10 (i.e. at least 8) of them were married.

The arithmetic is yours to do.

John

Coordinate-system/240773: find an equation of the line containing the point (-3,9) and (2,2)
1 solutions

Answer 176378 by solver91311(5072) on 2009-11-19 14:37:57 (Show Source):

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Use the two-point form of the equation of a line:

where

and

are the coordinates of the given points.

For your question as stated, simply substituting the values of the coordinates is sufficient. However, you should find out if your instructor or the instructions in your text require your answer to be in some particular form such as slope-intercept or standard form. In such case, you will need to manipulate the results of the substitution in order to arrange your equation correctly.

John

Numbers_Word_Problems/240770: the numbers on karl's three raffle tickets are consecutive integers.The sum of the numbers is 138.What are the numbers? For me consecutive integers are hard to understand,but i did try to figure it out.This is how i did it:x+(x+1)=138, 2x+1=138,2x=137.of course if you divide 2 and 137 you will get a number that has a decimal in it,so then i wasn't sure what to do.
1 solutions

Answer 176376 by solver91311(5072) on 2009-11-19 14:33:51 (Show Source):

You can put this solution on YOUR website!

You only missed it by THAT much (holds thumb and forefinger a tiny distance apart)

Your method would have worked just fine if he had only two tickets (of course, in that case, the sum would necessarily have been odd). But he had three tickets, so you need three consecutive integers.

If you let

represent the first integer, then

is most certainly the next consecutive integer -- just as you stated. But you needed the next one as well, which is

Now, the sum of all three is 138, so:

Solve that and you will find that

is a nice, tidy integer.

Write back and let me know how you did.

John

Probability-and-statistics/240763: Powerball jackpot can be won by picking 5 numbers out of 59 numbers then also picking 1 powerball number from a seperate 39 numbers. The order of the first 5 numbers doesn't matter.
A. how many ways are there to pick the first five numbers?
B. How many ways are there to pick the powerball number?
C. How many ways are ther to pick all six numbers? ( the powerball number comes from a different set of numbers than the first five)
1 solutions

Answer 176371 by solver91311(5072) on 2009-11-19 14:18:05 (Show Source):

You can put this solution on YOUR website!

Use:

to determine the number of

things taken

at a time.

For your first question, you need 59 things taken 5 at a time:

For your second question, you need 39 things taken 1 at a time:

Hint: for any

The answer to the third question is the sum of the first two answers.

You get to do your own arithmetic.

John

Exponents-negative-and-fractional/240753: rewrite as a radical:
(2x+7)^5/2
1 solutions

Answer 176370 by solver91311(5072) on 2009-11-19 14:09:12 (Show Source):

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Use the following rule:

Then you might want to determine if you are expected to do the binomial expansion of the 5th power radicand, and, if so, use the following formula:.

John

percentage/240756: $8 dollarsis what percent of $20 dollars?
1 solutions

Answer 176369 by solver91311(5072) on 2009-11-19 14:01:04 (Show Source):

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Let

represent the decimal fraction representation of the percentage value you want to determine.

Then

Solve for

, then convert the result to a percentage.

John

Functions/240748: 4,-5;

a.x=4
is 4 a zero of the polynomial?
b.x=-5
is -5 a zero of the polynomial?
1 solutions

Answer 176368 by solver91311(5072) on 2009-11-19 13:56:39 (Show Source):

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There are two ways to tell if a given number is a zero of a given polynomial function.

First, and probably easiest conceptually, is:

is a zero of the polynomial function

if and only if

For one of your examples:

is a zero of the polynomial function

if and only if

.

You can do your own arithmetic to check whether 4 is or is not a zero.

The second method is by using Polynomial Long Division. The Polynomial Long Division method relies on the following theorem:

is a zero of the polynomial function

if and only if

is a factor of

. That is to say that there exists a polynomial function

such that

This leads to the process of polynomial long division. For your other example, divide

using polynomial long division. If the result is a quotient with a remainder of zero, then

is a factor meaning -5 is a zero. If there is a non-zero remainder (meaning p(x) in the theorem above is a rational function rather than a polynomial function), then

is NOT a factor meaning -5 is NOT a zero.

Use the procedure for polynomial long division found at either of the following websites:

http://www.purplemath.com/modules/polydiv2.htm

or

http://en.wikipedia.org/wiki/Polynomial_long_division

John

Linear-systems/240749: How do you Graph 5x+2y=4
1 solutions

Answer 176365 by solver91311(5072) on 2009-11-19 13:35:22 (Show Source):

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Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.

Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results.

Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y).

Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis.

Step 5. Repeat steps 1 through 4 with a different value for x.

Step 6. Draw a line across your graph that passes through the two points that you plotted.

John