All Answers 356585 Answers

3td quadrant

Here's the last one

Since    OA / OB  = OD / OC

We must have that triangle  OAB   is similar to triangle ODC

And  angle  CDB  = angle CDO  = angle BAO = angle BAC = angle CAB

 (2,1) and (3,4)

Slope

[ Subtract the y coordinates in some order]            [ 4 - 1]          3

_____________________________________ =  ______  =   __   =    3

[Subtract the x coordinates in the same order ]      [ 3 - 2 ]        1

 y= -3/2x - 3

Slope  =  -3/2

y intercept  =   -3

This site:

https://math.stackexchange.com/questions/402451/evaluating-a-summation-of-inverse-squares-over-odd-indices

has both the answer and an explanation.

-3x + 4y= -8       we want to get y by itself  

add 3x to  both sides

4y  =  3x - 8      divide both sides by  4

y  =  (3/4)x - 2      this is the slope-intercept form

The slope is  (3/4)    and the y intercept is  -2 

Slope  =  (-1/2)

Y intercept  =  3   = ( 0, 3) =  1st point

From  (0,3)   we use the slope.......go down 1 in y  and over 2 on x

So.......the 2nd point is  ( 2 , 2)       

Connect the two points with a line.......there's your  graph  !!!!

If we consider 942 as the last term, then the number of terms of multiples of 2 would be:

942 / 2=471 terms - which counts 2 as the first term and 942 as the last term:

[F + L] / 2 x N =, where F=First term, L=Last term, N=Number of terms

[2 + 942] / 2 x 471=222,312

If we consider 940 as the last term, then the number of terms of multiples of 5 would be:

940 / 5 =188 terms.

[5 + 940] / 2 x 188 =88,830

5)  Since BAD  is trisected,  angle SAD = 30°

And triangle SAD  is a 30 - 60 - 90  triangle

So.......AD  =  √3SD  = √3 * 1  = √3

And angle TAD  = 60°    so   triangle  ATD  is also a 30 - 60 - 90  triangle

And TD  =  √3 AD  =  √3 √3  =  3

So CD  = CT + TD  = 2√3 - 3  + 3  =  2√3

So......the area of  ABCD  =  CD * AD =  2√3 * √3    =  6  units^2

4)  Since QX bisects  PQR, then  angles  PQX = RQX = QPX  = 30°

Then angle QXP  =  120°...so angle QXR  = 60°

And triangles  QRP and QRX   are   30 - 60 - 90  triangles

So.........since QR is opposite a 30° angle, it is  (1/2)PQ =  (1/2) 4√3  = 2√3

So.......QX =  [ 2 / √3 ] * [ 2√3 ]  =  4

3)  AO  = BO   and CO = DO

Then the angles opposite these sides  =  45°

And since triangles ABO and DCO   are 45 - 45 - 90  triangles

Then    DO  =  DC/√2     and  BO  = AB / √2

So   DO  + BO  =    DC/√2 +  AB/√2   =   [ DC + AB ] / √2

And  DO + BO  = BD  =    [ DC + AB ] / √2   =  [ 5 √2 ]  /  √2  =     5

2)  Draw DB

Then DB   is a hypotenuse of triangles DBA, DBC

And its length  is  √  [  (√13)^2  + (√5)^2 ]  =  √18  = 3√2

Then because BC  = CD  then angle CDB  =   angle CBD  = 45°

So because  triangle  DBC  is a 45 - 45 - 90 triangle, BC  =   [ 3√2  ] / √2  =  3

1)  Draw altitude  BD.....this will bisect angle ABC

Then angle BCA  = 30°

And since  triangle BDC is a 30 - 60- 90 triangle...then  CD  =  [√3 / 2] [ 6 √3]  = 9

And CD  =  (1/2) AC

So   AC  = 2CD =  18

Same here!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!thank you                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                sripes                                                                                                                                                                                                                                                                                                                                           

[(3*8+1 )/8 ]  -  [(8*1+7)/8] 

[25/8]        -         [15/8]           

[25 - 15] / 8 

10 / 8           

1 2/8 =1 1/4

1 meter =1,000 millimeters. So, the scale is:

7 mm:1,000 mm                      Divide both sides by 7

1 mm:142 6/7 mm - This is the scale that Tess used.

Well, if I was truly not allowed to use a calculator during any step throughout this problem, I would do the following:
 

\(264^2=(200+60+4)(200+60+4)=200(200+60+4)+60(200+60+4)+4(200+60+4)\)

There are a lot of friendly numbers here, do you agree? Now, let's continue the expansion.

\(200(200+60+4)+60(200+60+4)+4(200+60+4)=40000+12000+800+12000+3600+240+800+240+16\)

WOAH! That's a lot of terms! I would first rearrange the numbers such that the largest are added to the smallest.

\(40000+12000+12000+3600+800+800+240+240+16\)

You can do addition in any order you'd like. The colors indicate an addition where the result will be friendly and will end in another 0.

Now, just do the addition. 

\(40000+12000+12000+3600+800+800+240+240+16=69696\)

I wouldn't do 495 the same way, however. I would break that into \((500-5)(500-5)\). Now, do the same thing like before.

\(500(500-5)-5(500-5)\)

\(250000-2500-2500+25\)

\(245025\)

The square root is where I would hit a barrier, though...

\(27^{-\frac{1}{2}} \\~\\ =\,\frac1{27^{\frac12}} \\~\\ =\,\frac1{\sqrt{27}} \\~\\ =\,\frac{1}{\sqrt{3*3*3}} \\~\\ =\,\frac1{3\sqrt3} \\~\\ =\,\frac{\sqrt3}{9}\)

The knot (/nɒt/) is a unit of speed equal to one nautical mile (1.852 km) per hour, approximately 1.15078 mph. The ISO Standard symbol for the knot is kn. ... The knot is a non-SI (International Standard) unit that is "accepted for use with the SI".[This is from Google] !!.

4x(x + 2) - 2x (3 - x)

4x^2 + 8x - 6x + 2x^2

(4x^2 + 2x^2) + (8x - 6x)

6x^2  +  2x

Simplify the following:
4 x (x + 2) - 2 x (3 - x)

Factor 2 out of 4 x (x + 2) - 2 (3 - x) x giving 2 (2 x (x + 2) - (3 - x) x):
2 (2 x (x + 2) - (3 - x) x)

2 x (x + 2) = 2 x^2 + 4 x:
2 (2 x^2 + 4 x - (3 - x) x)

-x (3 - x) = x^2 - 3 x:
2 (x^2 - 3 x + 2 x^2 + 4 x)

Grouping like terms, 4 x + 2 x^2 - 3 x + x^2 = (2 x^2 + x^2) + (4 x - 3 x):
2 ((2 x^2 + x^2) + (4 x - 3 x))

2 x^2 + x^2 = 3 x^2:
2 (3 x^2 + (4 x - 3 x))

4 x - 3 x = x:
2 (3 x^2 + x) = 6x^2  +  2x

\(3\frac18-1\frac78 \\~\\ =\,(3+\frac18)-(1+\frac78) \\~\\ =\,3+\frac18-1-\frac78 \\~\\ =\,3-1+\frac18-\frac78 \\~\\ =\,2-\frac68 \\~\\ =\,1+\frac88-\frac68 \\~\\ =\,1+\frac28 \\~\\ =\,1\frac14\)

Guys dont do this proble but do the other one one question beneath this one!!!

From the Creator of this Problem

a - 4(a + b)            Distribute the  -4  to each term in the parenthesees.

=   a  -  4a  -  4b         Combine  a  and  -4a  to get  -3a  .

=  -3a - 4b

2x( 3 - x )

=   2x * 3   +   2x * -x

=   2 * 3 * x   +   2 * x * x * -1

=   6x   +   - 2x²

=   6x - 2x²