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Quadrant II

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Q III

Pythagorean theorem

( sqrt19)^2  + 9^2   = hypotenuse ^2       solve for hypotenuse.......= ........

For all the AOPS students here, the solution is 1936. I turned it in and it said it was correct so have fun cheating!

Does that mean from t=7 to t=8 it changed to a positive direction?

sqrt (6^2 + (-3)^2)  = sqrt 45  = 3 sqrt 5

Rotate around the line   x = y

y,x

2400 miles / (13 x 24+8) hr     = ............. m/hr

Figure 1:  1 block and 4 triangular regions

Figure 2:  2 blocks and 4 triangular regions

Figure 3:  3 blocks and 4 triangular regions.

The triangular regions remain the same (they are always 4) but the number of blocks go up by one each time.

So, I would expect that the next figure would have 4 blocks and 4 triangular regions.

Area = pi r^2     cm²        r is given as 4.1 cm

each section will be 1/3 of the total you find above.....

6x + 3y  =  9     --->     3y  =  -6x + 9     --->     y  =  -2x + 3

4x + 2y  =  8     --->     2y  =  -4x + 8     --->     y  =  -2x + 4

Each line has a slope of -2.

5 (x^2 - 6x+5)

5 (x-1)(x-5) = 0

or   (5x-5)(x-5)= 0     

or  (x-1) (5x-25) = 0

Area of parallelogram = b x h =  10 x 4  m²

Let me give you a hint as to how to read the graph:

At t = 0 it is stopped (velocity is 0).

From t = 0 to t = 2 it accelerates (Its velocity is increasing)

From t = 2 to t = 3 it is travelling at a constant velocity (neither increasing nor decreasing -- on cruise control)

From t = 3 to t = 4 it is decellerating (slowing down)

At t = 4 the velocity is zero (it is stopped, but just for that moment)

From t = 4 to t = 5 it is accelerating in a negative direction (in other words, it has turned around and began driving backwards - returning)

From t = 5 to t = 6 it is decreasing its acceleration in a negative direction (its slowing down)

From t = 6 to t = 7 it is stopped (velocity is 0)

From t = 7 to t = 8 it is again accelerating.

You mean like   # tiles = x + 4       assuming the squares and triangles are both tiles.......

Make sure your calculator is in 'radian' mode:

2= 15 cos(pi/30(x-30))

2/15 = cos (pi/30(x-30))

arcos 2/15 = 1.437   =  pi/30(x-30)        Now can you solve for 'x' ?

You didn't give a range over which to find x      arcos 2/15  also =  -1.437

    so   -1.437 = pi/30 (x-30)       Solve for  'x'

Using Pythagorean Theorem to

find the distance from  0,0      to     10,14

find the distance          0,0       to     13,9        which is lesser?  

If it takes four painters 1.25 work-days to finish a job, one painter could finish the job in five days, which means that one painter does one-fifth of the job each day.

At the same rate, 3 painters can finish three-fifths of the job in one day.

To finish the whole job:  1 / (3/5)  =  5/3  =  1 2/3 days.

Total surface area  =  2·length·width + 2·length·height + 2·width·height

                               =  2·20·20  +  2·20·40  +  2·20·40  =  4000 cm²

Adding an extra 20%:  20% of 4000  =  800     --->     4800 cm²

There are  10 000 cm²  in 1 m², so there are 3.5 x 10 000  =  35 000 cm²  of wrapping paper.

35 000 cm²  /  4800 cm²  =  7.3 boxes  =  7 boxes.

The formula for circumference:  C  =  pi · diameter.

                                                   C  =  pi · 28 feet

                                                   C  =  87.965 feet

Since PS is a diameter, arc(ST)  =  180^o - 125^o  =  55^o

So, arc(ST), in feet, will be  (55/360) · 87.965 feet  =  13.4 feet

Arc(RPT)  =  360^o - arc(RS) - arc(ST)  =  360^o - 97^o - 55^o  =  208^o

Arc(RPT, in feet, will be (208/360) · 87.965 feet  =  ......... 

We can generalize from a specific example.

Let's assume that the season is 100 games long.

We have played 75% of the season, which is 75 games

We have won 40% of the games that we have played, so we have won 40% of 75 games, which is 30 games.

So, we must have lost 45 games.

To finish the season with as many wins as losses, of the 25 games we have left to play, we will have to win 20 games and lose 5.

To win 20 out of the last 25 games will be 20/25  =  0.80  =  80%

x + 3y  =  kx     --->     divide by x     --->     1 + 3(y/x)  =  k

3x + y  =  ky     --->     divide by y     --->     3(x/y) + 1  =  k

Setting these two equations equal to each other:     1 + 3(y/x)  =  3(x/y) + 1

                                                                                        3(y/x)  =  3(x/y)

                                                                                            y/x  =  x/y

                                                                                              y²  =  x²

So:  either  x = y   or   x = -y

If  x = y,  x can be any number and y will be the same number.     (k = 4)

If  x = -y, x can be any number and y will be its additive inverse.   (k = -2) 

Probability of getting two black balls:  4/8 x 3/7  =  12/56

Probability of getting the first ball to be black and the second ball to be white:  4/8 x 4/7  =  16/56

Now, put back the white ball and draw; the probability of getting a black ball on this draw is 3/7.

Final probability for this case:  16/56 x 3/7  =  48/392.  

Probability of getting the first ball to be white and the second ball to be black:  4/8 x 4/7  =  16/56

Now, put back the white ball and draw; the probability of getting a black ball on this draw is 3/7.

Final probability for this case:  16/56 x 3/7  =  48/392.

Probability of getting two white balls:  4/8 x 3/7  =  12/56

Now, put back the two white balls and draw; the probability of getting two white balls:  4/8 x 3/7  =  12/56.

Final probability for this case:  12/56 x 12/56  =  144/3136.

To find the total probability, we need to add these answers:  12/56 + 48/392 + 48/392 + 144/3136  =  99/196.

First, let's find the equation of the line through  (5, 5)  and  (-3, 1).

  slope  =  (1 - 5) / (-3 - 5)  =  -4 / -8  =  ½

  equation:  y - 5  =  ½(x - 5)     --->     y  =  ½x + 2½

For the point  (6, c)   --->   c  =  ½(6) + 2½     --->     c  =  3 + 2½     --->     c  =  5½

If you can do long division, divide  x³ + 30x - c  by  x + 5.

You get a quotient of  x² - 5x + 55.

Then you will have to subtract  275  from  -c  to get a remainder of 5.

The only value that  -c  can have is  280  which means that   c  must equal to  -280.