Algebra One: word problems, factoring, radicals, etc. 10 points.?

Question

Hi,

Need some quick help on the last of my algebra review packet (almost done) =[]. So here goes...

The Rooney family drives to Pittsbugh at 60 mph and returns by a road 10 miles shorter at 65 mph. The return trip takes 30 minutes less. How long is each road?

Factor Completely:

z^5 - 4z^4 - 21z^3

Solve by factoring:

30^3 = 21x^2 + 135x

Solve for h. A = 1/2hb(subscript 1) + 1/2hb (subscript 2)

Simplify the expression, rationalize any denominators:

sqrt 243x^13 (all in the square root.)

Thanks in advance. Answer any you can, need ASAP.

Answer 1

Word problem

let the length of the road to Pittsburgh be x miles

time use to Pittsburgh = x/60 hours

now length of the road from Pittsburgh to home = x-10 miles

time use to return home = (x-10)/65 hours

given that time use to return home takes 30min (0.5hour) less:

x/60 - (x-10)/65 = 0.5

solve the equation:

I simply multiply both sides by 65*60 = 3900:'

65 x - 60(x-10) = 0.5*3900 = 1950

65x - 60x + 600  = 1950

5x = 1350

x = 270 miles

Factor Completely

z^3 (z^2-4z-21)

Solve by factoring

30^3 = 21x^2 + 135x

900 = 21x^2 + 135x

21x^2 +135x - 900 = 0

divided both sides by 3:

7x^2 + 45x - 300 = 0

use x = [-b +/- square-root(b^2-4ac)] / 2a

now a = 7, b = 45, c =-300

x = [-45 +/- square-root(45^2-4*7*-300)]/(2*7)

= (-45 +/- 102.1) / 14

= 4.08 or -10.51

Solve for h (I think the question is like this):

A = (1/2)h(b1) + (1/2)h(b2)

A = [(1/2)h](b1+b2)

h = 2A/(b1+b2)

Simplify (I hope this is what you are asked to do):

sqrt [243(x^13)] = [243(x^13)]^(0.5) = (243^0.5)[(x^13)^0.5]

= 15.588(x^7.5)