Santa and his elves had a workshop that allowed them to produce 22,912,546,99222{,}912{,}546{,}9922 2,912,546,99222, comma, 912, comma, 546, comma, 992 toys each year. the world population increased, so they built a new workshop. the new workshop allows them to produce 4,134,232,638,9374{,}134{,}232{,}63 8{,}9374,134,232,638,9374, comma, 134, comma, 232, comma, 638, comma, 937 toys each year. approximately how many times as many toys can the new workshop produce each year compared to the old workshop?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation:

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: