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6^2=X^2+(X+2)^2
36=X^2+X^2+4X+4
2X^2+4X+4-36=0
2X^2+4X-32=0
X^2+2X-16=0USING THE QUADRATIC EQUATION WE GET
X=(-B+-SQRT[B^2-4AC])/2A
X=(-2+-SQRT[4-4*1*-16)/2*1
X=(-2+-SQRT[4+64])/2
X=(-2+-SQRT68)/2
X=(-2+-8.246)/2
X=(-2+8.246)/2
X=6.246/2
X=3.123 SOLUTION
X=(-2-8.246)/2
X=-10.246/2
X=-5.123 SOLUTION

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249.99S+329.99L=8379.70
S+L=30 THEN
S=30-L SO
249.99(30-L)+329.99L=8379.70
7499.7-249.99L+329.99L=8379.70
80L=8379.70-7499.70
80L=880
L=880/80
L=11 LARGE HAWN MOWERS SOLD THEN
30-11=19 SMALL MOWERS SOLD
PROOF
249.99*19+329.99*11=8379.70
4749.81+3629.89=8279.70
8379.70=8379.70

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TO GUARANTEE SHE GETS ONE OF EACH COLOR SHE HAS TO TAKE 4 FOR GREEN + 4 FOR BLUE & 1 MORE TO GUARANTEE SHE GETS A RED ONETHUS SHE HAS TO PICK 9.

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THE BASE OF THIS 11 BY 14 IN PIECE OF CARDBOARD AFTER SQUARES ARE REMOVED FROM ALL FOUR CORNERS IS
(11-2X)(14-2X)=80
154-28X-22X+4X^2=80
4X^2-50X+154-80=0
4X^2-50X+74=0
2X^2-25X+37=0 USING THE QUADRATIC EQUATION TOSOLVE THIS EQUATION WE GET
X=(-B+-SQRT[B^2-4AC])/2A
X=(25+-SQRT[625-4*2*37])/2*2
X=(25+-SQRT[625-296])/4
X=(25+-SQRT329)/4
X=(25+-18.138)/4
X=(25+18.138)/4
X=43.138/4
X=10.78 SOLUTION
X=(25-18.138)/4
X=6.862/4
X=1.716 SOLUTION

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3X-(7X-5)=15
3X-7X+5=15
-4X=15-5
-4X=10
X=10/-4
X=-2.5
PROOF
3*-2.5-(7*-2.5-5)=15
-7.5-(-17.5-5)=15
-7.5-(-22.5)=15
-7.5+22.5=15
15=15

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4X^2+X=3
4X^2+X-3=0
(4X-3)(X+1)=0
4X-3=0
4X=3
X=3/4 SOLUTION
X+1=0
X=-1 SOLUTION

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Y=X/4+1 THIS EQUATION IS FOR A LINE WITH A SLOPE OF 1/4 & A Y INTERCEPT OF 1
IF X=2 THEN
Y=2/4+1
Y=1.5
IF Y=-7/2 THEN
-7/2=X/4+1
X/4=-7/2-1
X/4=-9/2
2X=-36
X=-36/2
X=-18
SO TWO POINTS ARE (2,1.5)(-18,-7/2)

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X-Y=7 OR X=7+Y
4X-5Y=25 SO
4(7+Y)-5Y=25
28+4Y-5Y=25
-Y=-3
Y=3 THEN
X-3=7
X=7+3
X=10
PROOF
4*10-5*-3=25
40-15=25
25=25

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2X^2=48
X^2=48/2
X^2=24
X=+-SQRT24
X=+-2SQRT6 OR
X=+-2*2.4494897 OR
X=+-4.8989794

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-4X+3Y=2 MULTIPLY THIS EQUATION BY 5 WE GET -20X+15Y=10
5X-2Y=-3 MULTIPLY THIS EQUATION BY 4 WE GET 20X-8Y=-12
NOW ADD THESE TWO EQUATIONS THUS
-20X+15Y=10
20X-8Y=-12
-------------------------------------
7Y=-2
Y=-2/7 THEN
-4X+3*-2/7=2
-4X-6/7=2
-4X=2+6/7
-4X=20/7
X=(20/7)/-4
X=(20/7)(-1/4)
X=-5/7
PROOF
5(-5/7)-2(-2/7)=-3
-25/7+4/7=-3
(-25+4)/7=-3
-21/7=-3
-3=-3

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(4*X)/(4+X)=3 THIS FORMULA IS THE PRODUCT DIVIDEDBY THE SUM OF THE TWO MACHINES EQUALS THE COMBINED TIME FOR BOTH MACHINES.
4X=3(4+X)
4X=12+3X
4X-3X=12
X=12HOURS FOR THE SECOND MACHING TO PROCESS THE CHECKS.

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33X-6(4X-0.305)=8X+.105
33X-24X+1.83=8X+.105
9X-8X=.105-1.83
X=-1.725
PROOF
33*-1.725-6(4*-1.725-.305)=8*-1.725+.105
-56.925-6(-6.9-.305)=-13.8+.105
-56.925-6(-7.205)=-13.695
-56.925+43.23=-13.695
-13.625=-13.695

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4W-3W+2W=24
3W=24
W=24/3
W=8 PROOF 4*8-3*8+2*8=24
32-24+16=24
48-24=24
24=24
----------------------------------------------------
4(X+3)=20
4X+12=20
4X=20-12
4X=8
X=8/4
X=2
-----------------------------------------------------
-8+T/3=7
T/3=7+8
T/3=15
T=15*3
T=45
-------------------------------------------------------
(4Y+3)/7=9
4Y+3=9*7
4Y+3=63
4Y=63-3
4Y=60
Y=60/4
Y=15

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X+Y=21 SO X=21-Y AND
3X=2Y-2
3(21-Y)=2Y-2
63-3Y=2Y-2
-3Y-2Y=-2-63
-5Y=-65
Y=-65/-5
Y=13
THEN X+13=21
X=21-13
X=8
PROOF
3*8=2*13-2
24=26-2
24=24

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-4-(-3)(-2)
-4-(6)
-4-6=-10

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THE DIAGONAL OF A SQUARE 20 FOOT RING IS SOLVED BY THE FORMULA A^2+B^2=C^2 WHERE THE A & B SIDES ARE 20 FEET. THUS THE DIAGONAL (C) IS
20^2+20^2=C^2
400+400=C^2
800=C^2
C=SQRT800
C=28.28 FEET IS THE DIAGONAL ACROSS THE RING

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(-2-0)/(0-2)
-2/2=-1
Y=-X+b SUBSTITUTING ONE SET OFPOINTS WE FIND THE Y INTERCEPT
0=-1*-2+b
0=2+b
b=-2THUS THE EQUATION IS
Y=-X-2

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L*W=352
2L+W=60
W=60-2L
L(60-2L)=352
60L-2L^2-352=0
-2L^2+60L-352=0
L^2-30L+176=0
(L-22)(L-8)=0
L-22=0
L=22 SOLUTION
L-8=0
L=8 SOLUTION
22*W=352
W=352/22
W=16 SOLUTION
PROOF
2*22+16=60
44+16=60
60=60

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6x-21=33+9x
6x-9x=33+21
-3x=54
x=54/-3
x=-18
proof
6*-18-21=33+9*-18
-108-21=33-162
-129=129

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5,876,000,000=5.876*10^8
0.00203=2.03*10(^-3)
7.5*105^5=910,529,667.5
7.8*10(^-4)=7.8*.0001=.00078

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LET N= THE NUMBER OF NUICLES & D = THE NUMBER OF DIMES THEN
YOU NEED TWO FORMULAS AS YOU HAVE TWO UNKNOWNS.
N+D=20 OR N=20-D
SEEING AS A NICKEL IS WORTH 5 CENTS AND THE DIMES ARE WORTH 10 CENTS THEN
5N+10D=160
SUBSTITUTING (20-D)FOR N IN EQUATION #2 WE GET
5(20-D)+10D=160
100-5D+10D=160
5D=60
D=60/5
D=12 NUMBER OF DIMES THEN
N+12=20
N=20-12
N=8 NUMBER OF NICKELS
PROOF
5*8+12*10=160
40+120=160
160=160

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24% OF 300=72
.24*300=72
72=72
OR
72/300=.24
.24=.24 OR 24%

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-4(2X+1)+2(4X-3)=X-10
-8X-4+8X-6=X-10
-8X+8X-X=-10+4+6
-X=0
X=0
PROOF
-4(2*0+1)+2(4*0-3)=0-10
-4(1)+2(-3)=-10
-4-6=-10
-10=-10

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L=2W+2
2L+2W=52
2(2W+2)+2W=52
4W+4+2W=52
6W=52-4
6W=48
W=48/6
W=8 THE WIDTH IS 8 CM. THEN
L=2*8+2
L=16+2
L=18 THE LENGTH IS 18 CM.
PROOF
2*18+2*8=52
36+16=52
52=52

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(X/8)/(5/(X+6)
(X/8)(X+6)/5
(X^2+6X)/40

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(X+2)/(X-3)=(X-5)/X+3)
(X-3)(X-5)=(X+2)(X+3)
X^2-8X+15=X^2+5X+6
X^2-X^2-8X-5X=6-15
-13X=-9
X=9/13
PROOF
(9/13+2)/(9/13-3)=(9/13-5)/(9/13+3)
(35/13)/(-30/13)=(-56/13)/(48/13)
(-30/13)(-56/13)=(35/13)(48/13)
1680/13=1680/13

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I'LL HELP YOU WITH THE FIRST 3 THEN YOU'RE ON YOUR OWN.
X+Y=3
Y=-X+3 THIS LINE HAS A SLOPE (m) OF -1 & THE Y INTERCEPT IS 3.
SETTING Y=0 WE GET THE X INTERCEPT IN THE EQUATION Y=mX+b
0=-X+3
-X=-3
X=3 NOW WE HAVE 2 POINTS (0,3) & (-3,0) AND THE SLOPE OF -1.
PLOT THESE 2 POINTS (0,3)(-3,0)AND YOPU HAVE A LINE WITH A SLOPE OF -1.
-------------------------------------------------------------------------
5X-2Y=10
-2Y=-5X+10
Y=-5X/-2+10/-2
Y=2.5X-5 NOW WE HAVE SLOPE OF 2.5 AND THE Y INTERCEPT OF -5 (0,-5)
SETTING Y=0 WE SOLVE FOR THE X VALUE
0=2.5X-5
2.5X=5
X=5/2.5
X=2 OR THE POINT (2,0) ALONG WITH THE POINT(0,-5) & A SLOPE OF 2.5 WE PLOT THESE 2 POINTS & DRAW A LINE THROUGH THEM WITH A SLOPE OF 2.5.
-------------------------------------------------------------------------
Y=1/2X-3 THIS LINE HAS A SLOPE OF 1/5 OR 0.5 & A Y INTERCEPT OF -3 (0,-3)
NOW WE SET Y=O & SOLVE FOR X
0=1/2X-3
1/2X=3
X=3/(1/2)
X=3*2
X=6 NOW WE HAVE 2 POINTS (0,-3)(6,0) & A SLOPE OF 0.5.
PLOT THESE 2 POINTS (0,-3)(6,0) & DRAW LINE THROUGH THEM WITH A SLOPE OF 0.5.
-----------------------------------------------------------------------------
HAPPY CALCULATING :)

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Y=mX+b m=5 THE SLOPE
Y=5X+b NOW SUBSTITUTE THE GIVEN POINTS FOR Y & X WE GET
1=5*2+b
b=1-10
b=-9
THEN THE EQUATION FOR THIS LINE IS
Y=5X-9

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(3X^3Y)^2
9X^6Y^2

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ON YOUR GRAPH PAPER DRAW A VERTICLE LINE THROUGH THE POINT (-2,0)THAT IS
X=-2, Y=0
YOU ARE LOOKING FOR ALL VALUES LESS THAN <-2 SO YOU FILL-IN THE AREA TO THE LEFT OF THE X=-2 LINE WHICH COVERS ALL POINTS LESS THAN -2.

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what you have given is not an equation.
for an equation you need an = sign.
should you have added =0 after the 30g?
if yes then
6(5g+2)+30g=0
30g+12+30g=0
60g+12=0
60g=-12
g=-12/60
g=-1/5 or -0.2
proof
6(5*-0.2+2)+30*-0.2=0
6(-1+2)-6=0
6*1-6=0
6-6=0
0=0