CPhill

Divide both sides by 6

3x -1  = -7  

Add 1 to both sides

3x = -6    

Divide by 3 on both sides

x = -2

Notice that the point (-1, 7) is three units up and 1 unit to the right of point (-2, 4)

So, D will be three units up and one unit to the right of (5, -3)

So D is at (5 + 1, -3 + 3)  = (6, 0)

The probability that X = 2 is given by

C(12,2)* C(8,6) / C(20,8) = about 1.47%

The probability that X ≤ 2 = probability that none, one or two of the two slot models are chosen =

C(12,0)* C(8,8) / C(20,8) + C(12,1)* C(8,7) / C(20,8) + C(12,2)* C(8,6) / C(20,8) = about 1.54%

The probabliity that X ≥ 2 = 1 minus the probability that none or one of the two slot models are chosen =

1 - [C(12,0)* C(8,8) / C(20,8) + C(12,1)* C(8,7) / C(20,8)]  = about 99%

I didn't get it at first either, Anonymous.....

Here you go......

Nice answer, TJM.........!!!

Let x be the price of the children's ticket and y be the price of the adult...so we have

12x + 3y = 70

12x + 12y = 216    subtract the first equation from the second...this gives

9y = 156  divide both sides by 9

y = $16.22    this is the approx cost of the adult ticket

And using the first equation to find the cost of the child's ticket, we have

12x + 3(16.22) = 70

12x + 48.66 = 70     subtract 48.66 from each side

12x = 21.34     divide both sides by 12

x = $1.78  and this is the cost of the child's ticket

A new amusement park is going to be built near 2 major highways. On a cordinate grid of the area, with the scale 1 unit representing 1 km, the park is located at P(3,4). Highway 2 is represented by the equation y=2x+5, and highway 0 is represented by the equation y=-0.5x+2. Determine the coordiantes of the exits that must be built on each highway to result in shortest road to the park.

We first need to find equations of the lines that are perpendicular to these two lines and pass through (3,4)

The equation for the  perpendicular line to Highway 2 is  y - 4 = -.5(x - 3) →  y = .5x + 5.5   (1)

The equation of the perpendicular line to Highway 0 is y - 4 = 2(x -3) →  y = 2x - 2       (2)

We could set the equation for Highway 2 equal to (1) and the equation for Highway 0 equal to (2)  and find the intersection points, but here's a graphical solution...

Sorry, Tetration, but that won't give us an angle...that will just give us an area

To find an angle, we need to know three sides, two sides and an angle, or two other angles...

Suppose we have

3x - 10 = 26    add 10 to each side

3x = 36           divide by 3 on both sides

x = 12

And that's a linear equation solved in two steps.....

Using a proportion, we have

9/6 = x/2  where x is the fence post height

Cross multiply

9*2 = 6*x  divide both sides by 6

9*2/6 = x

18/6 = x  = 3m