Solve each quadratic equation by factoring and using the zero product property. n^2 - 49 = 0

n = 7     n=-7

Step-by-step explanation:

n^2 - 49 = 0

This is the difference of squares

(a^ - b^2) = (a-b) (a+b)

n^2 -49  = (n-7) (n+7) =0

Using the zero product property

n-7 = 0   n+7 =0

n-7+7 =0+7      n+7-7 = 0-7

n = 7     n=-7

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

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)