CPhill

Each vertical angle corresponding to 40°,50° and 60° will be acute....so that's 6

In addition...the angle between the 50° angle and the horizontal line will have measure of 180 - 50 - 60 - 40 = 30°

And its corresponding vertical angle will also have the same measure...so...

All 8 angles formed by the 4 intersecting lines will be acute will be acute

Nice, Alan  !!!

Distance  / Rate  = Speed...so

Jack's speed   =  Jill's speed

x^2 -11x - 22   =  (x^2 - 3x - 54) / (x + 6)

x^2 - 11x - 22  = (x - 9)(x + 6) / (x + 6)

x^2 - 11x - 22 =  x -  9     rearrange as

x^2 - 12x - 13   = 0     factor

(x - 13) ( x + 1)   = 0

Set each factor to 0 and solve for x and we get that  x = 13  or x  = -1

Reject the second answer since itleads to a negative speed

If x  = 13, the speed is 4  mph

Look at line   20

$67,400 is between $56800  and $114,649.99....so the tax  is :

.25 (67400) - 6380   =   $10470 ⇒  "A"

Allie has   5 (5 + 3)   = 5 * 8  = 40  items

So...in 4 baskets, Alex must have  40/4  = 10  items

So....she must have 2 toys in each basket

6 = 35/x  - 49/x^2       mutliply through by x^2

6x^2 = 35x   - 49      rearrange as

6x^2 - 35x  + 49   =  0        factor as

(3x - 7) (2x - 7)   = 0

Set both factors  = 0   and solve for x and we get that    x  = 7/3   or x  = 7/2

Rate * Time  = Distance

Since the distances are equal, we have that

x^2 * 3  = (16 - 4x) * 4

3x^2 = 64  - 16x      rearrange as

3x^2  + 16x   - 64   = 0    factor

(3x - 8) (x + 8)   = 0

Set both factors  = 0   and solve for x  and we have

x  = 8/3    or  x  = -8

Since x > 0, then   x  = 8/3  is correct

Thanks, Rom....tricky....to say the least.....!!!

No prob, ML....!!!

We have 5 locations and we wish to visit 3 of them in any order....so   5C3   = 10 ways