[pre-calc]
verify the following equations:
show your work and start using the left side of the equation.

sin(α+β)=sinαcosβ+cosαsinβ,

and the double angle formula of cosine:

cos(2α)=cos2α−sin2α=2cos2α−1=1−2sin2α

then:

sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx=

=(2sinxcosx)⋅cosx+(1−2sin2x)sinx=

=2sinxcos2x+sinx−2sin3x=

=2sinx(1−sin2x)+sinx−2sin3x=

=2sinx−2sin3x+sinx−2sin3x=

=3sinx−4sin3x.

cos3x
=cos(x+2x)
=cosxcos2x−sinxsin2x using cos(A+B)=cosAcosB-sinAsinB
=cosx(2cos^2x−1)−sinx(2sinxcosx) using cos2A=2cos^2A-1 and sin2A=2sinAcosA
=2cos^3x−cosx−2sin^2xcosx 
=2cos^3x−cosx−2(1−cos^2x)cosx  using sin^2x+cos^2x=1
=2cos^3x−cosx−2(cosx−cos3^x) [open the brackets]
=2cos^3x−cosx−2cosx+2cos^3x
=4cos^3x−3cosx [collect terms]

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation:

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.