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Just graph it:

0 points, they head in opposite directions.

Given a point P(8,1) on Segment AB with A(-2,3), find the coordinates of B if AP/AB= 2/3

Hello Guest!

\(m={\color{black}\frac{y_P-y_A}{x_P-x_A}=-\frac{2}{10}=-}0.2\)

\(f(x)=m(x-x_P)+y_P\)

\(f(x)=-0.2(x-8)+1\)

\(f(x)=-0.2x+2.6\)

\(\color{blue}(x_P-x_A):(x_B-x_A)=2:3\\ 2x_B-2x_A=3x_P-3x_A\\ 2x_B=3x_P-3x_A+2x_A\\ 2x_B=3\cdot 8-3\cdot (-2)+2\cdot (-2)\\ x_B=12+3-2\)

\(x_B=13\)

\(y_B=-0.2\cdot 13+2.6\)

\(y_B=0\)

The coordinates of B: \( B\ (13,0)\)

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8x = 180 - 2x     solve for x

In order for the work-energy theorem to have meaning, work (F·d) and kinetic energy (0.5 .M.v^2 should have the same units. Show that they do.

Hello Guest!

\(W=F\cdot d\\ W=1N\cdot 1m=1Nm\\ W=1Nm\cdot \frac{kg\cdot m}{N\cdot s^2}\\ \color{blue}W=1\ \frac{kg\cdot m^2}{s^2}\ = 1\ Joule\)    

\(E=\frac{1}{2}\cdot m\cdot v^2\\ E=\frac{1}{2}\cdot 1kg\cdot (1.414\ \frac{m}{s})^2\\ \color{blue}E=1\ \frac{kg\cdot m^2}{s^2}=1\ Joule\)

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10 people must shake hands with 9 other people    10 x 9 = 90

  BUT each handshake invilves TWO peole...so divide by 2     90/ 2 = 45 handshakes

Angle at F is equal to the angle labelled 'x'

Sum of angles in a triangle = 180

4x + 65  + x = 180      solve for x

Step - by - step:

Sum of angles in a triangle = 180

23 + 54 + x = 180

then  x + 'angle next to it' = 180

then 'angle next to it' + 36 + 'angle next to y'  = 180

then ' angle next to y'   +  y = 180                  <------ solve for y

How many liters of a 40% acid solution should be mixed with 8 liters of a 25% acid solution to obtain a solution that is 30% acid?

Hello Guest!

\(x\cdot 40\%+ 8\cdot 25\%=(x+8)\cdot 30\%\)

\(0.4x+0,25\cdot 8=0.3x+0.3\cdot 8\\ 0.1x=2.4-2\\0.1x=0.4\)

\(x=4\)

4 liters of a 40% acid solution should be mixed with 8 liters of a 25% acid solution to obtain a solution that is 30% acid?

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AD = BC = ED = FD = 37

EF = 2 * 37 = 74 

P A R A B O L A =8! / 3! =6,720 Arrangements.

Let the number of Liters of 10% acid that is needed =T

Then, the numbers of Liters of 5% acid that is needed =5 - T

0.10T  +  0.05*[5 - T] =0.07 * 5, solve for T

T = 2 Liters of 10% acid

5 - 2 = 3 Liters of 5% acid.

1 - 10 , 12 , 18 , 20 , 21 , 24 , 27 , 30 , 36 , 40 , 42 , 45 , 48 , 50 , 54 , 60 , 63 , 70 , 72 , 80 , 81 , 84 , 90 , Total =  23 such numbers.

2 - a=1;b=0;c=0;d=0;p=0; cycle:n=a*1000+b*100+c*10+d;if(n +(b*100+c*10+d)+ (c*10+d)+d==2012, goto loop, goto next); loop:printn," ",;p=p+1; next:d++;if(d<10, goto cycle, 0);d=0;c++;if(c<10, goto cycle, 0);d=0;c=0;b++;if(b<10, goto cycle,0);b=0;c=0;d=0;a++;if(a<10, goto cycle,0);print"Total = ",p

OUTPUT = 1,468

1 - P=10000;   R=0.04;  N=10;    FV=P*((1 + R)^N - 1)/ R

FV = $ 120,061.07

2 - PV=0; P=10000; R=0.04; N=5;    P*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)

PV = $44,518.22

10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?  

What would this be, combinations or permutations. 

Combinations would be how many ways could you group 2 different people. 

Permutations would be the same, except it would count A & B and B & A as two different handshakes, which is wrong. 

So, it's combinations. 

                                                                                                            n!        

The formula for combinations of n things, taken r at a time is:    ——————   

                                                                                                    ( r! (n – r)! )      

                                                                                                        10!               3,626,800

Just plug in the numbers and get                                                ————   =   —————— 

                                                                                                    (2!) (8!)          (2) (40,320)    

Break out the old calculator to do the arithmetic and obtain            45         

_.

0.6 * 0.4 = 0.24

I need to find angle j.

"A person moves 500 meters to the north, later changes direction and now moves 800 meters to the east. Determine the resultant displacement, as well as the angle and inclination of the resultant, with respect to the east."

Pythagoras gives:  d = sqrt(500^2 + 800^2) meters,    where d = displacement

Angle with respect to the east is given by tan^-1(500/800) radians

You can do the number crunching.

Pitágoras da: d = sqrt (500 ^ 2 + 800 ^ 2) metros, donde d = desplazamiento

El ángulo con respecto al este está dado por tan^-1 (500/800) radianes

Puedes hacer el cálculo de números.

H + 4 = J

J + 2 = 2(H + 2)  so J = 2H  + 2   Put this in the first equation:

H + 4 = 2H  + 2  so   H = 2,  Hence J = 6.

The smallest 2-digit integer = 25

25  x  9 = 225 which is the smallest AAB

n^3 = (n-1)^3+(n-2)^3+(n-3)^3

\(n^3 = (n-1)^3+(n-2)^3+(n-3)^3\\ n^3 = (n^3-3n^2+3n-1)+(n^3-3*2n^2+3*4n-8)+(n^3-3*3n^2+3*9n-27)\\ n^3 = n^3-3n^2+3n-1+n^3-6n^2+12n-8+n^3-9n^2+27n-27\\ 0= 2n^3 -18n^2 +42n -36 \\ 0= n^3 -9n^2 +21n -18 \\\)

You can take if from there.

A dairy needs 244 gallons of milk containing 7% butterfat. How many gallons each of milk containing 9% butterfat (x) and milk containing 1% butterfat must be used to obtain the desired 244 gallons?

Hallo Guest!

\(244\ gal\cdot 7\%=x\cdot9\%+(244\ gal-x)\cdot1\%\)

\(244\ gal\cdot 0.07= 0.09x+244\ gal\cdot 0.01-0.01x\\ 14.64\ gal=0.08x \)

\(x=183\ gal\)

The dairy uses 183gal milk with 9% butterfat
and 61gal milk with 1% butterfat,
to get the 244gal you want.

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THANK YOU!!!

The line with equation y = mx + b is perpendicular to the line with equation y = 16 - x/3.  The value of m is?

a) -3

b) -1/4

c) 3

d) -1/3

e) 1/3

Hello SmartMathMan!

\(y=16-x/3\)

\( is\ identical\ to \\ y=-\frac{1}{3}x+16\)

\(m=-\frac{1}{(-\frac{1}{3})}\)

\(m=3\)

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