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Numbers_Word_Problems/275864: how do i find the solution for the following problem? The sum of two consecutive integers is 146. Find the numbers.
1 solutions

Answer 201144 by solver91311(16877) on 2010-03-01 19:34:43 (Show Source):

You can put this solution on YOUR website!

Your problem has no solution as stated. If you have two consecutive integers, one of them must be odd and the other must be even in some order. The sum of an even number and an odd number must be odd -- but 146 is even.

Now if you meant two consecutive even integers, it would work out. But that isn't what you said, and I don't want to guess.

John

Divisibility_and_Prime_Numbers/275854: I need some help with a proof.
Let p & q be 2 consecutive primes. Then p+q=2n for some n. Is n always composite. I have some examples but not sure how to write proof.
Examples: 11, 13 11+13=24 13,17 13+17=30
Thank you
1 solutions

Answer 201143 by solver91311(16877) on 2010-03-01 19:30:33 (Show Source):

You can put this solution on YOUR website!

All you need to do to prove that it is NOT true is to find a counter-example.

2 plus 3 = 5. 5 is prime.

On the other hand, if you exclude 2 by saying p and q are 2 consecutive odd primes, then the theorem is true. Except for 2, all primes are odd and of the form

. So we can say that

and

for some

and

.

Then

which is clearly an even, and therefore composite, number.

John

Money_Word_Problems/275838: Write an equation of the line containing the given point and parallel to the given line. Express you answer in the form of y=mx+b.
(7,8);x +8y=9. The equation of the line is y=???
1 solutions

Answer 201138 by solver91311(16877) on 2010-03-01 19:18:53 (Show Source):

You can put this solution on YOUR website!

Step 1: Determine the slope of the line represented by the given equation. Put the given equation into slope-intercept form: Add

to both sides, then multiply both sides by

. Once the given equation is in slope-intercept form, the slope of the line will be equal to the coefficient on

.

Step 2: Use the point-slope form of the equation of a line, namely:

where

are the coordinates of the given point and

is the slope calculated in Step 1. You can use the same slope number because parallel lines have equal slopes, in other words:

Step 3: Once you have plugged in the values for the coordinates of the given point and for the calculated slope, solve the resulting equation for

(similar to the process used to rearrange the equation in step 1) to put the desired equation into slope-intercept form.

John

Travel_Word_Problems/275840: if a train is traveling at 72 mph how far will it go in 40 minutes
1 solutions

Answer 201136 by solver91311(16877) on 2010-03-01 19:10:43 (Show Source):

You can put this solution on YOUR website!

Hint: 40 minutes is

of 1 hour.

John

Numbers_Word_Problems/275833: Points A, B, C, and D lie in consecutive order on a line. If AC=4/3AB and BD=6BC, then what is AB/CD?
1 solutions

Answer 201135 by solver91311(16877) on 2010-03-01 19:09:45 (Show Source):

You can put this solution on YOUR website!

and since

we can say:

Therefore

Furthermore,

Substituting:

Now we have both AB and CD in terms of BC, so:

John

Money_Word_Problems/275829: Find the slope intercept equation of the line that has the given characteristics. Slpe 3 and y-intercept (0,2). The slope-intercept equation is y=??
1 solutions

Answer 201130 by solver91311(16877) on 2010-03-01 18:55:17 (Show Source):

You can put this solution on YOUR website!

The slope-intercept form of the equation of a line is:

where

is the slope of the line and

is the

-coordinate of the point where the graph of the line intersects the

-axis.

You are given the two numbers directly -- just substitute them.

John

Rate-of-work-word-problems/275821: I had a question about a work word problem. It says: Jane, Paul, and Peter can finish a painting in 2 hours. Jane can paint the same painting in 5 hours. Paul can paint it alone in 6 hours. How long would it take Peter to paint it on his own?
the equation was 1/5+1/6+1/x=1/2
and I dont understand where they got the 1/2 from.......If you could help me with this it would be great. Thanks!!!
1 solutions

Answer 201127 by solver91311(16877) on 2010-03-01 18:52:45 (Show Source):

You can put this solution on YOUR website!

If person A can complete an entire job in

time periods, then that person can complete

of the job in one time period. Jane can do the whole job in 5 hours, so she can do

of the job in one hour. Likewise, Paul is 6 hours and

of the job, while Peter is

hours and

of the job. In the same way, the three of them working together can do the job in 2 hours, which is to say that the three of them working together can do

of the job in one hour.

The equation works out to "The fraction of the job that Jane can do in one hour" plus "The fraction of the job that Paul can do in one hour" plus "The fraction of the job that Peter can do in one hour" adds up to "The fraction of the job that the three of them working together can do in one hour"

John

Volume/275816: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s)= s^3 13s^2 + 54s 72.
a) Find V(10).
b) If the new width is s 6 centimeters, then what are the new length and height?
c) Find the volume when s=10 by multiplying the length, width, and height.

Can someone help me please!
1 solutions

Answer 201122 by solver91311(16877) on 2010-03-01 18:35:35 (Show Source):

You can put this solution on YOUR website!

Show the signs in your polynomial

John

Trigonometry-basics/275801: how do i solve this i need like a step by step breakdown
5 cos^2(theta)-4 sin(theta)-4 = 0
1 solutions

Answer 201121 by solver91311(16877) on 2010-03-01 18:34:48 (Show Source):

You can put this solution on YOUR website!

Remember

Therefore

So substitute

Simplify:

Let

represent

Factor the quadratic:

Hence,

But since

And finally, considering the interval

and

John

Inequalities/275798: how do you work out the problem, d - 1 _> 6
1 solutions

Answer 201108 by solver91311(16877) on 2010-03-01 18:12:03 (Show Source):

You can put this solution on YOUR website!

Just add 1 to both sides. Then

is 7 or anything larger than 7.

John

Volume/275797: Decreasing cube. Each of the three dimensions of a
cube with sides of length s centimeters is decreased by a
whole number of centimeters. The new volume in cubic
centimeters is given by
V(s)= s^3 13s^2 + 54s 72.
a) Find V(10).
b) If the new width is s 6 centimeters, then what are the
new length and height?
c) Find the volume when s=10 by multiplying the
length, width, and height.
1 solutions

Answer 201106 by solver91311(16877) on 2010-03-01 18:10:24 (Show Source):

You can put this solution on YOUR website!

You left out the signs in your polynomial expression.

John

Triangles/275796: a right triangle has sides of 4 ft, 5 ft, and 1 yd. what is its perimeter in feet?
1 solutions

Answer 201105 by solver91311(16877) on 2010-03-01 18:09:32 (Show Source):

You can put this solution on YOUR website!

1 yard is 3 feet. Add the measures of the three sides in feet to get the perimeter in feet.

John

Quadratic_Equations/275778: x^2+6x+27 help me can you solve it for me
1 solutions

Answer 201103 by solver91311(16877) on 2010-03-01 18:08:37 (Show Source):

You can put this solution on YOUR website!

In a word, no. You can't "solve" something that doesn't have an equals sign in it somewhere. Now if your problem is really:

That is another story altogether. But you didn't say that, and I'm not going to guess.

John

Polygons/275785: why do you think each letter in a polygon's name can be used only once
1 solutions

Answer 201098 by solver91311(16877) on 2010-03-01 17:58:39 (Show Source):

You can put this solution on YOUR website!

What makes you think your premise is true in the first place? Counterexample: nonagon, also known as an enneagon.

John

Probability-and-statistics/275782: Two shaded circles are inside a rectangle that has one side that is 2" and the bottom side is 4". What is the probibilty of an object landing randomly on the figure in the shaded circle. " Express the probability as a percent."
1 solutions

Answer 201091 by solver91311(16877) on 2010-03-01 17:48:10 (Show Source):

You can put this solution on YOUR website!

That would depend a great deal on the size of the circles in relation to the size of the rectangle and whether the random falling of objects is constrained to inside the rectangle or not. Presuming the rectangle as a universal constraint, find the area of each of the circles. Add the two areas of the circles. The sum of the areas of the two circles is the numerator of your probability fraction. The area of the rectangle is your denominator.

John

Quadratic_Equations/275775: i need help on this problem x^2+5x-25
1 solutions

Answer 201090 by solver91311(16877) on 2010-03-01 17:44:21 (Show Source):

You can put this solution on YOUR website!

You have a handsome little quadratic trinomial there. What would you like to do with it?

John

Surface-area/275765: Why can you find an excact Surface Area measurement for a prism but not a cylinder
1 solutions

Answer 201089 by solver91311(16877) on 2010-03-01 17:40:03 (Show Source):

You can put this solution on YOUR website!

The underlying premise of your question is not true in general.

In the first place, you can never find the exact measurement of anything. ALL measurements are approximate, no matter how precisely taken. Therefore you can never exactly represent the surface area of a prism because the measurements of the edges begin as approximations.

On the other hand, who says you cannot represent the surface area of a cylinder exactly? Typically the surface area calculation for a cylinder involves

, the ratio of the circumference of a circle to its diameter.

is a transcendental irrational number, and irrational numbers can never be represented by an exact decimal fraction. However, that is not to say that you cannot represent a quantity involving

exactly, because you can. All you need to do is leave the result in terms of

and you have your exact representation. So presuming an ideal theoretical cylinder whose height was exactly

and base radius exactly

, you would have a lateral surface area of exactly

or a total surface area of exactly

. Example: If you had a cylinder that was purported to be exactly 5 units in height and exactly 2 units in radius (even though no one would ever be able to measure it and determine whether it was indeed 5 high and 2 in radius), then the lateral surface area would be exactly

, and the total surface area would be exactly

John

Volume/275761: Decreasing cube. Each of the three dimensions of a
cube with sides of length s centimeters is decreased by a
whole number of centimeters. The new volume in cubic
centimeters is given by
V(s)= s^3 13s^2 + 54s 72.
a) Find V(10).
b) If the new width is s 6 centimeters, then what are the
new length and height?
c) Find the volume when s=10 by multiplying the
length, width, and height.
1 solutions

Answer 201086 by solver91311(16877) on 2010-03-01 17:21:32 (Show Source):

You can put this solution on YOUR website!

Why do you insist on leaving the signs out of your expressions?

John

logarithm/275646: please help me graph this equation. F(x)=log base 3 of (x-1)
1 solutions

Answer 201085 by solver91311(16877) on 2010-03-01 17:16:14 (Show Source):

You can put this solution on YOUR website!

Graphs/275611: Graph on a number line, where x is a real number. -4 < x greater than or equal to 4.
1 solutions

Answer 201018 by solver91311(16877) on 2010-03-01 13:37:21 (Show Source):

You can put this solution on YOUR website!

On your number line, make a little circle at -4. Make a solid dot at 4. Make a heavy line connecting the circle and the dot -- without coloring in the little circle.

John

Graphs/275649: Given f(x) = –3x + 7
graph and show work.
1 solutions

Answer 201014 by solver91311(16877) on 2010-03-01 13:24:30 (Show Source):

You can put this solution on YOUR website!

Step 1: Pick a value for

. It can be anything you like, but small integers generally make the arithmetic a little easier.

Step 2: Substitute the value you selected in step 1 into your equation in place of

. Do the required arithmetic to determine the value of

Step 3: Create an ordered pair

where

is the value you selected in step 1, and

, the value you calculated in step 2.

Step 4: Plot the point you just created in step 3.

Step 5: Repeat steps 1 through 4 using a different value for

Step 6: Once you have two points plotted, draw a line all the way across your coordinate axes through the two points you plotted.

John

Inequalities/275648: a sheet of standard size copy paper measures 8.5 by 11 in. If a ream (500 sheets) of this paper has a volume of 187 un 3, how thick is the ream?
1 solutions

Answer 201013 by solver91311(16877) on 2010-03-01 13:14:17 (Show Source):

You can put this solution on YOUR website!

The volume of a rectangular solid is given by:

Here, you are given the volume, length, and width, so:

You can do your own arithmetic.

John

Exponential-and-logarithmic-functions/275645: is the following statement true, log4 power2 = 1/2
1 solutions

Answer 201012 by solver91311(16877) on 2010-03-01 13:09:50 (Show Source):

You can put this solution on YOUR website!

I'm not sure what you mean by "power" in your problem statement, but I'll simply assume you meant:

Use the definition of logarithms:

So:

Well, since

We can say:

And your original statement is indeed true.

John

Rectangles/275642: How do I solve this problem:
There is a rectangular shape and the width is 24 feet. The diagonal (through the middle) is 30 feet. How do I solve for the height of the rectangle?
Thank You! :)
1 solutions

Answer 201011 by solver91311(16877) on 2010-03-01 13:04:14 (Show Source):

You can put this solution on YOUR website!

Since it is a rectangle, any vertex is a right angle. That means that the length, width, and diagonal form a right triangle. Use Pythagoras:

You can do your own arithmetic.

John

Linear-equations/275630: Write the equation of the line that has a slope of zero that goes through the point (5, -2)
Can you give my grandson a hand on this?? thank you
1 solutions

Answer 201010 by solver91311(16877) on 2010-03-01 13:00:46 (Show Source):

You can put this solution on YOUR website!

A line with a slope of zero has the characteristic that ALL of the points included in the line have identical

-coordinates. So if you have a line with slope zero passing through

, then the equation of the line would be:

Which is another way of saying: "Give me the set of ordered pairs such that the

-coordinate is the same value in every one of the ordered pairs, and I don't care what the

-coordinate is.

John

Polynomials-and-rational-expressions/275641: Write the simplest polynomial with zeros: 1, 4, and -3.
1 solutions

Answer 201009 by solver91311(16877) on 2010-03-01 12:55:16 (Show Source):

You can put this solution on YOUR website!

I just did one like this. Different numbers, but the same idea. See:

http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.275639.html

John

Polynomials-and-rational-expressions/275639: I'm not sure how to go about figuring this out:
Write the simplest polynomial with zeros:
½, 5, and -2.
1 solutions

Answer 201008 by solver91311(16877) on 2010-03-01 12:53:04 (Show Source):

You can put this solution on YOUR website!

If

is a zero of a polynomial function, then

is a factor of the polynomial.

Therefore,

, and

are the factors of your desired simplest polynomial. All you need to do is multiply the three binomials together to get a single 3rd degree polynomial.

John

Proportions/275637: What are the two x values?
x+3/12=6/x-3
1 solutions

Answer 201007 by solver91311(16877) on 2010-03-01 12:49:44 (Show Source):

You can put this solution on YOUR website!

Presuming that you meant to write (x+3)/12=6/(x-3), which would mean

, as opposed to what you wrote which means

, proceed as follows:

Cross-multiply:

Simplify:

Finally, use the difference of two squares factorization to factor and solve the quadratic.

John

Linear-equations/275632: My grandson needs help and I am lost:
find the slope of any line that is perpendicular to the line 5x-2y=12. what are the steps??
1 solutions

Answer 201004 by solver91311(16877) on 2010-03-01 12:42:23 (Show Source):

You can put this solution on YOUR website!

Start by determining the slope of the line represented by your given equation. To do that, put the given equation into slope-intercept form. To do that, solve the equation for

in terms of everything else. For your problem, add

to both sides of the equation and then multiply both sides of the equation by

. The slope of the line represented by the given equation will then be the resulting coefficient on

.

The slopes of perpendicular lines are negative reciprocals. That is to say:

So, once you have determined the slope of the line represented by the given equation, determine the negative reciprocal of that slope. If the slope is a fraction, turn the fraction over and change the sign.

John

Rational-functions/275631: i am having trouble with this. i would appreciate some help thanks. factor this polynomial 8x^3-2x
1 solutions

Answer 201003 by solver91311(16877) on 2010-03-01 12:35:26 (Show Source):

You can put this solution on YOUR website!