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MathLover1 answered: 6630 problems
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Polynomials-and-rational-expressions/651356: 8/r^3s^2 divided by 6/rs^4
1 solutions

Answer 407611 by MathLover1(6632) on 2012-09-14 09:07:44 (Show Source):

You can put this solution on YOUR website!
%288%2F%28r%5E3s%5E2%29%29%2F%286%2F%28rs%5E4%29%29

Sequences-and-series/651209: What is the nth number in the sequence?
1,5,12,22...n
1 solutions

Answer 407579 by MathLover1(6632) on 2012-09-13 22:06:09 (Show Source):

You can put this solution on YOUR website!
your sequence represents pentagonal

numbers are given by n%283n-1%29%2F2

with n=0, +/-1, +/-2, ...
in your case we will start with n=1

n%283n-1%29%2F2=1%283%2A1-1%29%2F2=2%2F2=1

Length-and-distance/651177: Find the midpoint of the segment with endpoints (√48, √6) and (√3,√24)
1 solutions

Answer 407571 by MathLover1(6632) on 2012-09-13 21:30:23 (Show Source):

You can put this solution on YOUR website!
( sqrt%2848%29

) and (

)

the midpoint of the segment:( %28sqrt%2848%29%2Bsqrt%283%29%29%2F2

)
(

)

(

)
(

)

Expressions-with-variables/651149: a^2 - 64 = 0 solve and express in simplest radical form
1 solutions

Answer 407570 by MathLover1(6632) on 2012-09-13 21:06:38 (Show Source):

You can put this solution on YOUR website!

a%5E2+-+64+=+0

and

Numeric_Fractions/651127: 5/4 times 7/10 equal what?
1 solutions

Answer 407559 by MathLover1(6632) on 2012-09-13 20:28:30 (Show Source):

You can put this solution on YOUR website!

Polynomials-and-rational-expressions/651113: What type of polynomial can 25k2+10k +1 be classified as ? why?

Thank you, for all your help have nice day! :)

1 solutions

Answer 407555 by MathLover1(6632) on 2012-09-13 20:01:55 (Show Source):

You can put this solution on YOUR website!

Polynomials are classified according to two attributes: number

and

.
your polynomial has three

terms,

, and a polynomial with three

is a

The

of a polynomial is the largest

of the degrees of its monomial terms.
So, your polynomial has the degree

test/651107: Q/8 = 4/5
1 solutions

Answer 407552 by MathLover1(6632) on 2012-09-13 19:49:15 (Show Source):

You can put this solution on YOUR website!

Q%2F8+=+4%2F5

test/651092: One number is eight less than twice the other their sum is 100 what are the numbers
1 solutions

Answer 407550 by MathLover1(6632) on 2012-09-13 19:39:28 (Show Source):

You can put this solution on YOUR website!

let's

and

be the numbers
if the number

is eight less than twice the

, we have

........1
if their sum is 100

,we have

...........2
now, we have to solve this system:
x%2B8=2y

........1
-
x%2By=100

...........2
______________________ we can subtract 2 from 1
x-x%2B8-y=2y-100

...now find

...........2
x=100-y

Angles/651077: m< ABD =(12x-12)degrees, m< BDE = (3x+48) degrees
1 solutions

Answer 407549 by MathLover1(6632) on 2012-09-13 19:25:12 (Show Source):

You can put this solution on YOUR website!
< ABD

and <

are

; so, they add up to 180

degrees
if

degrees,

degrees, then

%2812x-12%29%2B%283x%2B48%29=180

... now you can first find

now you can find {{x}}}

and

degrees,
m< ABD+=%2812%2A9.6-12%29

degrees
m< ABD+=%28115.2-12%29

degrees
m< highlight%28ABD+=103.2%29

degrees

m< BDE+=+%283x%2B48%29

degrees

Matrices-and-determiminant/651018: how do i determine whether (1,-5,10) is a solution of the following system.
x+y+z=6
3x-y-z=-2
2x-y+4z=37
1 solutions

Answer 407537 by MathLover1(6632) on 2012-09-13 18:19:44 (Show Source):

You can put this solution on YOUR website!

to determine whether , plug in values for x=1

and

. I you get that left side of equation is equal to right side, than (1,-5,10) is a solution of the following system
x%2By%2Bz=6

..->..

->..

->..

..->..

->..

->..

->..

..->..

.->..

->..

...not true
so, the ordered triple (

) is NOT a solution of this system

here is a solution:

Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables

system%281%2Ax%2B1%2Ay%2B1%2Az=6%2C3%2Ax%2B-1%2Ay%2B-1%2Az=-2%2C2%2Ax%2B-1%2Ay%2B4%2Az=37%29

First let

A=%28matrix%283%2C3%2C1%2C1%2C1%2C3%2C-1%2C-1%2C2%2C-1%2C4%29%29

. This is the matrix formed by the coefficients of the given system of equations.

Take note that the right hand values of the system are

, and

and they are highlighted here:

These values are important as they will be used to replace the columns of the matrix A.

Now let's calculate the the determinant of the matrix A to get abs%28A%29=-20

. To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver.

Notation note: abs%28A%29

denotes the determinant of the matrix A.

---------------------------------------------------------

Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix A%5Bx%5D

(since we're replacing the 'x' column so to speak).

Now compute the determinant of A%5Bx%5D

to get

. Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant.

To find the first solution, simply divide the determinant of A%5Bx%5D

by the determinant of

to get:

x=%28abs%28A%5Bx%5D%29%29%2F%28abs%28A%29%29=%28-20%29%2F%28-20%29=1

So the first solution is x=1

---------------------------------------------------------

We'll follow the same basic idea to find the other two solutions. Let's reset by letting A=%28matrix%283%2C3%2C1%2C1%2C1%2C3%2C-1%2C-1%2C2%2C-1%2C4%29%29

again (this is the coefficient matrix).

Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix A%5By%5D

(since we're replacing the 'y' column in a way).

Now compute the determinant of A%5By%5D

to get

.

To find the second solution, divide the determinant of A%5By%5D

by the determinant of

to get:

y=%28abs%28A%5By%5D%29%29%2F%28abs%28A%29%29=%2860%29%2F%28-20%29=-3

So the second solution is y=-3

---------------------------------------------------------

Let's reset again by letting A=%28matrix%283%2C3%2C1%2C1%2C1%2C3%2C-1%2C-1%2C2%2C-1%2C4%29%29

which is the coefficient matrix.

Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix A%5Bz%5D

Now compute the determinant of A%5Bz%5D

to get

.

To find the third solution, divide the determinant of A%5Bz%5D

by the determinant of

to get:

z=%28abs%28A%5Bz%5D%29%29%2F%28abs%28A%29%29=%28-160%29%2F%28-20%29=8

So the third solution is z=8

====================================================================================

Final Answer:

So the three solutions are x=1

, and

giving the ordered triple (1, -3, 8)

Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant.

as you can see, the three solutions are x=1

, and

giving the ordered triple (

)

test/650982: how do you find the answers to a georgia 8th grade math book online
1 solutions

Answer 407532 by MathLover1(6632) on 2012-09-13 17:54:03 (Show Source):

You can put this solution on YOUR website!

follow this link and you can download full version of that book...I think the answer keys are in...
http://www.downloadprovider.me/search/8th_grade_math_georgia_coach_book.rar.html?aff.id=1750&aff.subid=101

Linear-equations/650947: Is 2x+3y=12 a linear equation?
1 solutions

Answer 407510 by MathLover1(6632) on 2012-09-13 16:11:55 (Show Source):

You can put this solution on YOUR website!

2x%2B3y=12

compare your equation to the standard

form of linear equation which is typically ax%2Bby=c

, or to

form which is y=ax%2Bb

as you can see, your equation 2x%2B3y=12

is in the

form of linear equation; so, it

equation

Linear-equations/650938: Can you please explain how to solve equations such as (9k+30)-(4k+10)=100 ? thanks
1 solutions

Answer 407495 by MathLover1(6632) on 2012-09-13 15:43:26 (Show Source):

You can put this solution on YOUR website!
%289k%2B30%29-%284k%2B10%29=100

first remove the parentheses,
recall:
When parentheses are preceded by a plus sign + simply remove them. Nothing changes.
When parentheses are preceded by a minus sign−change the sign of every term within the parentheses.
9k%2B30-4k-10=100

....round

Number-Line/650917: Which set of numbers does not contain 1000?
- Integers
- Whole numbers
- Irrational numbers
- Real numbers
1 solutions

Answer 407489 by MathLover1(6632) on 2012-09-13 15:21:09 (Show Source):

You can put this solution on YOUR website!

your answer is:

recall:
An irrational number is a number that cannot

be written as a fraction; in other words, an irrational number is a "non-terminating, non-repeating" decimal.

Trigonometry-basics/650919: Determine whether the three points are collinear.
(5,-1), (-3,6), (4,-2)
1 solutions

Answer 407481 by MathLover1(6632) on 2012-09-13 15:01:37 (Show Source):

You can put this solution on YOUR website!

Three or more points

are said to be collinear

they

on a

.
let's check it:

Solved by pluggable solver: To determine if 3 points lie in a line

The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.

In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.

Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.

Slope of line taking points (X1,Y1) and (X2,Y2) is

slope+=+%28Y2-Y1%29%2F%28X2-X1%29

slope+=+%28%286--1%29%2F%28-3-5%29%29+=+-0.875

........................(1)

Slope of line taking points (X3,Y3) and (X1,Y1) is

slope+=+%28Y3-Y1%29%2F%28X3-X1%29

slope+=+%28%28-2--1%29%2F%284-5%29%29+=+1

........................(2)

From conditions (1) and (2)

The 3 points do not a same line.

For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.

Here the slopes are unequal hence the points do not lie on same line.

To read more on equations of a line refer to articles on wikipedia

since your points do NOT lie

on a

, they are NOT collinear

Distributive-associative-commutative-properties/650880: can you help me simplfy these problems for homework due tommorow ? please .
8y-(3-6y)
-7+(9x-8)
-(-2r+7s)+2(r+s)
2x+3y-(x+5y)
2a+3b+2(a-2b)
5m+4n+3(2m-5n
4m+3n-2(m+3n)
7x-4y-5(2y-x)
1 solutions

Answer 407466 by MathLover1(6632) on 2012-09-13 14:08:08 (Show Source):

You can put this solution on YOUR website!

8y-%283-6y%29

...be careful with sign minus in front of parenthesis; means, everything inside parenthesis you multiply by

Problems-with-consecutive-odd-even-integers/650861: The sum of three consective odd integers is -3, what is the largest odd integer?
The sum of three consective integers is 0. What is the smallest integer?
1 solutions

Answer 407456 by MathLover1(6632) on 2012-09-13 13:45:32 (Show Source):

You can put this solution on YOUR website!
1.
If we start with an odd number and each number in the sequence is

more than the previous number then we will get consecutive odd integers.
if first one is

, second one will be x%2B2

, and third one will be x%2B4

the sum is: x%2B%28x%2B2%29%2B%28x%2B4%29=-3

...solve for

....first number
second one will be x%2B2

...->...

...->...

third one will be x%2B4

...->...

...->...

so, the numbers are: highlight%28-3%29

, and

; as you can see, the greatest one is highlight%281%29

2.
The sum of three consecutive

integers is

. What is the smallest integer?
If we start with an integer, each next consecutive

integer in the sequence is

more than the previous one
if first one is

, second one will be x%2B1

, and third one will be x%2B2

the sum is: x%2B%28x%2B1%29%2B%28x%2B2%29=0

...solve for

second one will be x%2B1

...->...

...->...

third one will be x%2B2

...->...

...->...

so, the numbers are: highlight%28-1%29

, and

; as you can see, the smallest integer is highlight%28-1%29

Linear-systems/650850: Here is the problem:
2/x + 3 = 3/2x + 25/8
1 solutions

Answer 407446 by MathLover1(6632) on 2012-09-13 13:12:49 (Show Source):

You can put this solution on YOUR website!

2%2Fx+%2B+3+=+3%2F2x+%2B+25%2F8

....find common denominators

2%2A2%2F2x-3%2F2x+=+25%2F8-3%2A8%2F8

......cross multiply

1%2A8+=+1%2A2x

test/650805: Write the equation for the following relation.Q = {( x , y ): (2, 8), (3, 27), (4, 64), (5, 125), . . .}
Help please!
1 solutions

Answer 407413 by MathLover1(6632) on 2012-09-13 11:06:19 (Show Source):

You can put this solution on YOUR website!

= {(

): (

), (

), . . .}
take a look at ordered pairs:
(

) = (

) = (

)
(

) = (

) = (

)
(

) = (

) = (

)
(

) = (

) = (

)
(

) = (

) = (

)
Therefore y+=+x%5E3

Polynomials-and-rational-expressions/650796: Solve the inequality.
d-2/25 > d/10 - 1/2
1 solutions

Answer 407403 by MathLover1(6632) on 2012-09-13 10:29:38 (Show Source):

You can put this solution on YOUR website!

d-2%2F25+%3E+d%2F10+-+1%2F2

%2810d-d%29%2F10+%3E+2%2A2%2F%2825%2A2%29+-+1%2A25%2F%282%2A25%29

Solved by pluggable solver: Plot Any Inequality

Graphing function x%3E-7%2F15

graph%28+600%2C+600%2C+-10%2C+20%2C+-10%2C+20%2C+x%3E-7%2F15+%29

Expressions-with-variables/650798: 2 less than the product of 5 and n
1 solutions

Answer 407399 by MathLover1(6632) on 2012-09-13 10:11:00 (Show Source):

You can put this solution on YOUR website!

+5n-2+

Rectangles/650774: the perimeter of a rectangle is 46 ft the width is 3ft less than twice the length finf the length and width of the rectangle
1 solutions

Answer 407394 by MathLover1(6632) on 2012-09-13 09:37:10 (Show Source):

You can put this solution on YOUR website!

the perimeter of a rectangle is P=46ft

the width is

less than

the length

....->...

....substitute

%28%28W%2B3ft%29%2F2%2B2W%2F2%29=46ft%2F2

now find

Linear_Algebra/650765: What are all intercepts to x^2+y=18^2?
1 solutions

Answer 407393 by MathLover1(6632) on 2012-09-13 08:54:38 (Show Source):

You can put this solution on YOUR website!
intercepts to x%5E2%2By=18%5E2

to find

, set

and solve for

and

to find

, set

and solve for

...there is only one y-intercepts

+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+350%2C+-x%5E2%2B324%29+

Functions/650759: ((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1/2)))/(1+x^2)
What is the domain of the question above? and also would you be kind enough to show me the steps?
1 solutions

Answer 407392 by MathLover1(6632) on 2012-09-13 08:46:18 (Show Source):

You can put this solution on YOUR website!

To find the domain, I'll ignore the "

" in the numerator (since the numerator does

cause division by zero

) and instead I'll look at the

.
I'll set the denominator equal to zero

, and solve.
1%2Bx%5E2=0

The

in the solution will be the x-values

which would cause
division by zero

. The domain will then be all other x-values

and

...as you can see here, whatever

is, the denominator will NOT be equal
to zero

so, the domain will be all real numbers from -infinity

(

)

Triangles/650553: A right, isosceles triangle has hypotenuse length 50 cm. How long are the two legs?
1 solutions

Answer 407342 by MathLover1(6632) on 2012-09-12 20:53:54 (Show Source):

You can put this solution on YOUR website!
An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees.
; consequently, it has the two legs of same length
use Pythagorean theorem
c%5E2=a%5E2%2Bb%5E2