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Geometry_proofs/65768: Hello, I really can't figure this proof out, I've been trying for hours now and I just can't get it. Maybe you can help?
Prove: triangleTSW = triangleQPW
Given:
TQ bisects SP
SP bisects TQ
1 solutions
Answer 46492 by checkley71(8403)   on 2006-12-29 18:23:21 (Show Source):
You can put this solution on YOUR website!TQ BISECTS SP THEN SW=WP
SP BISECTS TQ THEN TW=TQ
BECAUSE THESE LINES BISECT THE OPPOSITE ANGLES ARE EQUAL THUS
NOW WE HAVE TWO EQUAL SIDES AND THE INTERNAL ANGLE EQUAL THEN THE TRIANGLES ARE EQUAL.
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Rate-of-work-word-problems/65774: A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
1 solutions
Answer 46491 by checkley71(8403) on 2006-12-29 18:16:11 (Show Source):
You can put this solution on YOUR website!(30-2x)(20-2x)=400
600-40x-60x+4x^2=400
4x^2-100x=-600+400
4x^2-100x=-200
4x^2-100x+200=0
x^2-25x+50=0
using the quadratic equation for x we get
x=(-b+-sqrt[b^2-4ac])/2a
x=(25+-sqrt625-4*1*50])/2*1
x=(25+-sqrt[625-200])/2
x=(25+-sqrt425)/2
x=(25+-20.6155)/2
x=(25+20.6155)/2
x=45.6155/2
x=22.8 not a solution because it is longer than the garden.
x=(25-20.6155)/2
x=4.3845/2
x=2.19 feet for the path
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Numbers_Word_Problems/65771: Find two consecutive positive intergers such that the sum of their square is 85.
Thank you for the help
1 solutions
Answer 46490 by checkley71(8403) on 2006-12-29 18:01:11 (Show Source):
You can put this solution on YOUR website!X^2+(X+1)^2=85
X^2+X^2+2X+1=85
2X^2+2X+1-85=0
2X^2+2X-84=0
X^2+X-42=0
(X+7)(X-6)=0
X=7=0
X=-7
X-6=0
X=6 SOLUTION FOR THE FIRST INTERGER
6=1=7 FOR THE SECOND INTERGER
PROOF
6^6+7*7=84
36+49=85
85=85
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happy new year
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Rectangles/65775: The length of a rectangle is 1cm longer than its width. If the diaganol of rectangle is 4cm, what are the dimensions (length and width) of the rectangle?
Thank you
1 solutions
Answer 46489 by checkley71(8403) on 2006-12-29 17:41:33 (Show Source):
You can put this solution on YOUR website!using the pathagorian theorum a^2+b^2=c^2 a=x, b=(x+1), c=4
x^2+(x+1)^2=4^2
x^2+x^2+2x+1=16
2x^2+2x-15=0 using the quadratic equation x=(-b+-sqrt[b^2-4ac])/2a
x=(-2+-sqrt[2^2-4*2*-15])/2*2
x=(-2+-sqrt[4+120])/4
x=(-2+-sqrt124)/4
x=(-2+-11.1355)/4
x=(-2+11.1355)/4
x=9.1355/4
x=2.2839 cm for the width.
length is 2.2839+1=3.2839
proof
2.2839^2+3.2839^2=4^2
5.216+10.784=16
16=16
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HAPPY NEW YEAR.
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Graphs/65765: This question is from textbook Beginning Algebra
Graph the following equation, using the intercept method.
2x + 3y = 6
I am a bit confusded on how to graph these since there are two variables. If I worked the problem right I came up with 1.
2x + 3y = 5
6-5 = 1
This is as far as I got.
1 solutions
Answer 46488 by checkley71(8403) on 2006-12-29 17:18:57 (Show Source):
You can put this solution on YOUR website!TRO PUT THESE EQUATIONS IN THE LINE FORM WE HAVE:
2X+3Y=6
3Y=-2X+6
Y=-2X/3+6/3
Y=-2X/3+2 THUS THIS LINE HAS A SLOPE OF -2/3 & A Y INTERCEPT OF 2
-----------------------------------------------------------------------
2X+3Y=5
3Y=-2X=5
Y=-2X/3+5/3 THUS THIS LINE ALSO HAS A SLOPE OF -2/3 & A Y INTERCEPT OF 5/3
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -2/3X+2 and
-2/3X+5/3).
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions x^2 and x^2/10-x).
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Equations/65704: Solve for X:
2(x-5)^2=3
I know the first step I believe is to multiply the 2 towards the x and the 5:
2*x = 2x
2*5 = 10
(2x - 10)^2 = 3
The next step is to figure out what X is correct?
2(x) - 10^2 = 3
Gosh I am lost on this step, could someone please give me a hand, thank you
1 solutions
Answer 46424 by checkley71(8403) on 2006-12-27 22:43:14 (Show Source):
You can put this solution on YOUR website!FIRST YOU MUST RESOLVE THE ITEMS WITHIN THE ( )
(X-5)^2=X^2-10X+25 NOW MULTIPLY THIS BY 2
2(X^2-10X+25)=2X^2-20X+50 NOW SET THIS =3
2X^2-20X+50=3 NOW SUBTRACT 3 FROM BOTH SIDES
2X^2-20X+50-3=0
2X^2-20X+47=0 THIS EQUATION DOESN'T FACTOR NORMALLY THUS WE NEED THE QUADRATIC EQUATION TO FIND THE X VALUES THUS
X=(-B+-SQRT[B^2-4AC])/2A
X=(20+-SQRT[400-4*2*47])/2*2
X=(20+-SQRT[400-376])/4
X=(20+-SQRT[24])/4
X=(20+-4.899)/4
X=(20+4.899)/4
X=6.22 SOLUTION
X=(20-4.899)/4
X=15.101/4
X=3.77 SOLUTION
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Inequalities/65717: This question is from textbook Pre-Algebra
Evalute the expression.
5/8 + 5/12 divided by 10/21
Thanks! Please work fast! Don't forget to post it! Happy Holidays!~!~!~!~!
1 solutions
Answer 46422 by checkley71(8403) on 2006-12-27 22:28:02 (Show Source):
You can put this solution on YOUR website!(5/8+5/12)/(10/21)
[(5*12+5*8)/96]/(10/21)
[(60+40)/96]/(10/21)
(100/96)/(10/21) INVERT THE DENOMINATOR & MULTIPLY
(100/96)(21/10)
(10*21)/96
210/96
35/16
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Equations/65705: Solve for X
x^2 + 4x + 4 = 7
(factor the left hand side)
4x + 4 = 8x
x^2 + 8x = 7
I have 2 X's and this confuses me since I can not factor them to come up with it to = 7, can someone please explain, thank you
1 solutions
Answer 46420 by checkley71(8403) on 2006-12-27 22:14:26 (Show Source):
You can put this solution on YOUR website!X^2+4X+4=7
X^2+4X+4-7=0
X^2+4X-3=0 THIS QUADRATIC DOES NOT FACTOR NORMALLY THUS WE NEED TO USE THE QUADRATIC FORMULA TO FIND THE VALUES OF X THUS
X=(-B+-SQRT[B^2-4AC])/2A
X=(-4+-SQRT[4*4-4*1*-3])/2*1
X=(-4+-SQRT[16+12])/2
X=(-4SQRT[28])/2
X=(-4+-5.29)/2
X=(-4+5.29)/2
X=1.29/2
X=.645 SOLUTION
X=(-4-5.29)/2
X=-9.29/2
X=-4.645 SOLUTION
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Square-cubic-other-roots/65723: This question is from textbook An Incremental Development
simplify
(5 times the square root of 16 - 3)(2 times the square root of 10 + 2)
1 solutions
Answer 46416 by checkley71(8403) on 2006-12-27 21:54:02 (Show Source):
You can put this solution on YOUR website!(5*SQRT16-3)(2*SQRT10+2) I ASSUME BECAUSE THERE ARE NO () AROUND THE 16 & 10
THAT THIS IS THE PROBLEM?
(5*4-3)(2*3.16+2)
(20-3)(6.32+2)
17*8.32
141.44
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HOWEVER IF THERE SHOULD BE () AROUND THE (16-3) & THE (10+2) THEN
(5SQRT13)(2SQRT12)
(5*3.61)(2*3.46)
18.05+6.92
24.97
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Radicals/65683: Use the properties for radicals to simplify the espression. Assume all variables represent positive real numbers.
sqrt 5/3
This is not a real number correct? Or do I need to divide them like a regular fraction to get:
1 sqrt2/3?
1 solutions
Answer 46380 by checkley71(8403) on 2006-12-27 16:11:03 (Show Source):
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Radicals/65686: Multiply then simplify the radical expression:
sqrt13 * sqrt5 =
13 * 5 = sqrt65?
I believe this is how I would perform this operation. Thanks for the help.
1 solutions
Answer 46377 by checkley71(8403) on 2006-12-27 16:02:38 (Show Source):
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Radicals/65685: Simplify by co,bining like terms:
sqrt 63 - 2sqrt28 + 5sqrt7
I sure thope this makes sense to someone else more than it does to me. I can not see any like terms involved in this process. Thank you for the help.
1 solutions
Answer 46374 by checkley71(8403) on 2006-12-27 15:55:34 (Show Source):
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Radicals/65678: This question is from textbook Beginning algebra
Problem 24:
3 sqrt -8/27
I believe this is not a real number, is this correct? If it is I would say it is -2/3 From here I am lost, hope you can help me:-)
1 solutions
Answer 46370 by checkley71(8403) on 2006-12-27 15:47:13 (Show Source):
You can put this solution on YOUR website!3SQRT-8/27 IF THIS IS 3 TIMES THE SQRT -8/27
3SQRT-(2*2*2)/(3*3*3)
3*2/3SQRT-2/3
6/3SQRT-2/3
2SQRT-2/3
________________________________
IF THIS IS THE CUBERT-8/27 THEN
CUBERT(-2*-2*-2)/(3*3*3)
-2/3
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Inequalities/65670: This question is from textbook Pre-Algebra
Find the quotient.
- 18/35 divided by( - 2 4/5 )
Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!~!~!
1 solutions
Answer 46362 by checkley71(8403) on 2006-12-27 14:35:29 (Show Source):
You can put this solution on YOUR website!(-18/35)/(-2 4/5)
(-18/35)/(-14/5) NOW INVERT THE DENOMINATOR AND MULTIPLY THE TWO FRACTIONS THUS
(-18/35)(-5/14)
(18*5)/(35*14)
90/490
9/49
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HAPPY NEW YEAR
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Graphs/65643: DOes this mean that i have to show 3different graphs separate or all in one graph.
which the equations that i would graph from this would be:
3x-6
x = 1
y=3
Solve each of the following systems of linear inequalities graphically.
3x – y LESS THAN OR EQUAL TO 6
x GREATER THAN OR EQUAL TO 1
y LESS THAN OR EQUAL TO 3
1 solutions
Answer 46348 by checkley71(8403) on 2006-12-27 10:20:23 (Show Source):
You can put this solution on YOUR website! (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, function 3X-6).
 (graph 300x200 pixels, x from -6 to 5, y from -5 to 5, function X-1).
 (graph 300x200 pixels, x from -6 to 5, y from -5 to 5, function Y-3).
_________________________________________________________
HAPPY NEW YEAR
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Graphs/65646: Graph each of the following inequalities.
4x + y > 4
Graph each of the following inequalities.
3x – 4y < 12
1 solutions
Answer 46347 by checkley71(8403) on 2006-12-27 10:11:15 (Show Source):
You can put this solution on YOUR website! (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, function 4x-y-4).
 (graph 300x200 pixels, x from -6 to 5, y from -12 to 10, function y+4x-4).
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THIS IS AN UP DATE.
________________________________________________________________
HAPPY NEW YEAR
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Miscellaneous_Word_Problems/65659: why are variables useful in algebra?
What makes the use of variables difficult to understand?
Create one statement in english representing an algebraic relationship.
1 solutions
Answer 46345 by checkley71(8403) on 2006-12-27 09:54:38 (Show Source):
You can put this solution on YOUR website!SIMPLE PROBLEM: A DOZEN EQQS COST $1.20. WHAT IS THE PRICE OF EACH (1) EGG.
ALGEBRAIC REPRESENTATION OF THIS PROBLEM, QUESTION IS
12E=$1.20 OR 12 EGGS = $1.20 NOW YOU NEED TO DIVIDE 12 EGGS BY 12 TO GET 1 EGG WHICH SAYS YOU NEED TO ALSO DIVIDE THE $1.20 BY 12 TO MAINTAIN A BALANCED EQUATION.
12E/12=$1.20/12
1E=$.10 OR ONE EGG EQUALS $ .10
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HAPPY NEW YEAR.
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Exponential-and-logarithmic-functions/64634: A volcano that is currently about one-half mile below the surface of the pacific ocean near the big island of Hawaii will eventually become a new Hawaiian island, Loihi. The volcan will break the surface of the ocean in about 50000 years. On average, how many inches does the volcano rise in a year. State your answer in per year.
1 solutions
Answer 46322 by checkley71(8403) on 2006-12-26 12:45:10 (Show Source):
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Inequalities/65620: This question is from textbook Pre-Algebra
Find the quotient.
-24 4/9 divided by 8/15
Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!
1 solutions
Answer 46259 by checkley71(8403) on 2006-12-25 22:05:20 (Show Source):
You can put this solution on YOUR website!(-24 4/9)/(8/15)
[((-24*9)+4)/9]/(8/15)
[((-216+4))/9]/(8/15)
(-220/9)/(8/15 now invert the denominator and multiply the two fractions thus
(-220/9)(15/8) NOW MULTIPLY NUMERATORS & DENOMINATORS THUS
(-220*15)/(9*8)
3300/72
45 5/8
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MERRY CHRISTMAS
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Polynomials-and-rational-expressions/65587: This question is from textbook Algebra for college students
Hello,
How do I find the vertex and intercept, and sketch its graph:
g(x) = x^2 + 2x - 24
Thank you so much!
1 solutions
Answer 46243 by checkley71(8403) on 2006-12-25 16:35:56 (Show Source):
You can put this solution on YOUR website!x^2+2x-24
(x-4)(x+6)
x-4=0
x=4 one intercept on the x axis
x+6=0
x=-6 another x intercept
coordinates of vertex
x=(4-6)/2
x=-2/2
x=-1
y=-1*-1+2*-1-24
y=1-2-24
y=1-26
y=-25 then the vertex is (-1,-25)
 (graph 300x200 pixels, x from -10 to 10, y from -30 to 10, of functions x^2+x-24).
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MERRY CHRISTMAS
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expressions/64934: I need to simplify these but can't figure it out. I'm awful at math. Thanks for any help.
a. y^3 (10x^2 + 3y-1) (5x^3 - 3xy - y)
b. (a^2 + 2b)(5a^3 - 3b^-3/2 - 1)/b^-2
1 solutions
Answer 46239 by checkley71(8403) on 2006-12-25 11:48:28 (Show Source):
You can put this solution on YOUR website!Y^3(10X^2+3Y-1)(5X^3-3XY-Y) FIRST WE MULTIPLY BOTH TERMS ( )( ) BY Y^3 THUS
(10X^2Y^3+3Y^4-Y^3)(5X^3Y^3-3XY^4-Y^4) NOW MULTIPLY THESE TWO TERMS THUS
(5X^3Y^3-3XY^4-Y^4)
---------------------------------------
50X^5Y^6+15X^3Y^7-5X^3Y^6
*********-30X^3Y^7-9XY^8+3XY^7
******************-10X^2Y^7-3Y^8+Y^7
-------------------------------------------------------
50X^5Y^6-15X^3Y^7-5X^3Y^6-9XY^8+3XY^7-10X^2Y^7-3Y^8+Y^7
###############################################################
MERRY CHRISTMAS
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Graphs/64969: Solve the system of inequalities by graphing.
y>x
2x+y
2. graph:5x+3y greater than or equal to 15
x is less than or equal to y
x is less than or equal to 4
3. find the max. and min. values and where they occur for z=4x+7y subject to the constraints:
x+y is greater than or equal to 2
3x-4y is less than or equal to 6
6y is less than or equal to x+12
1 solutions
Answer 46238 by checkley71(8403) on 2006-12-25 11:15:24 (Show Source):
You can put this solution on YOUR website!Y>X & 2X+Y<-3
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y>x and 2x+y<-3).
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5x+3y>=15 & x<=y & x<=4
 (graph 300x200 pixels, x from -6 to 5, y from -30 to 30, of THREE functions 5x+3y>=15, x<=y, x<=4).
_______________________________________________________________________
4x+7y, x+y>=2, 3x-4y<=6, 6y<=x+12
 (graph 300x200 pixels, x from -20 to 20, y from -10 to 10, of FOUR functions 4x+7y, x+y>=2, 3x-4y<=6, 6y<=x+12).
____________________________________________________________________________
MERRY CHRISTMAS
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