When looking at a rational function f of x equals the quantity x plus three times the quantity x minus two times the quantity x plus five all divided by the quantity x minus three times the quantity x plus two times the quantity x minus 5, charles and bobby have two different thoughts. charles says that the function is defined at x = −2, x = 3, and x = 5. bobby says that the function is undefined at those x values. who is correct? justify your reasoning.

Bobby is correct

Step-by-step explanation:

∵ f(x) is undefined for all values of x make the denominator = 0

∵ The denominator = (x - 3)(x + 2)(x - 5)

∵ x - 3 = 0 ⇒ x = 3

∵ x + 2 = 0 ⇒ x = -2

∵ x - 5 = 0 ⇒ x = 5

∴ f(x) is undefined if x = -2 , x = 3 , x = 5

∴ The domain of f(x) is all the real number except -2 , 3 , 5

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

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