SOLUTION: Algebra 2: Please help me understand to solve these problems. Thank you! 1. Factor completely: 3x2 - 75 2. A car travels for 2½ hours and covers a distance of 125 miles.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Algebra 2: Please help me understand to solve these problems. Thank you! 1. Factor completely: 3x2 - 75 2. A car travels for 2½ hours and covers a distance of 125 miles.       Log On


   

Question 1133112: Algebra 2: Please help me understand to solve these problems. Thank you!
1. Factor completely: 3x2 - 75
2. A car travels for 2½ hours and covers a
distance of 125 miles. What was the
car’s average speed?
3. If f(x) = 2x - 3, g(x) = x2, and
h(x) = !3x, find (g f h )(2).
4. Factor: 15x2 + 7x - 36
5. Find the zeros of the polynomial
function f(x) = 15x2 + 7x - 36.
6. If g(x) = 5x + 6, find g -1(x) solved for y.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. Factor completely:
3x%5E2+-+75+
3x%5E2+-+3%2A25+
3%28x%5E2+-+25+%29
3%28x%5E2+-+5%5E2+%29
3%28x+-+5+%29%28x%2B5%29

2. A car travels for 21%2F2=2.5 hours and covers a distance of 125 miles. What was the car’s average speed?

distance=+speed%2Atime
given:
distance=125mil
time+=2.5h
125mil=+speed%2A2.5h
speed=125mil%2F2.5h
speed=50%28mil%2Fh%29


3. If f%28x%29+=+2x+-+3,+g%28x%29+=+x%5E2, and h%28x%29+=+3x, find %28g+f+h+%29%282%29.=> I guess you have product here
+%28g+f+h+%29%28x%29=g%28x%29%2Af%28x%29+%2Ah%28x%29
+%28g+f+h+%29%28x%29=x%5E2%2A%282x+-+3%29+%2A3x
%28g+f+h+%29%28x%29=3x%5E3%2A%282x+-+3%29+
%28g+f+h+%29%28x%29=6x%5E4+-+9x%5E3
if x=2, we have
%28g+f+h+%29%282%29=6%2A2%5E4+-+9%2A2%5E3
%28g+f+h+%29%282%29=6%2A16+-+9%2A8
%28g+f+h+%29%282%29=96+-+72
%28g+f+h+%29%282%29=24

4. Factor:
15x%5E2+%2B+7x+-+36 ..........write 7x as 27x-20x
15x%5E2+%2B27x-20x-36.....group
%2815x%5E2+-20x%29%2B%2827x-36%29
5x%283x+-4%29%2B9%283x-4%29%7D%7D%0D%0A%0D%0A%7B%7B%7B%283+x+-+4%29+%285+x+%2B+9%29

5. Find the zeros of the polynomial function f%28x%29+=+15x%5E2+%2B+7x+-+36.
=>f%28x%29+=0
0+=+15x%5E2+%2B+7x+-+36....use already factored form above
+0=%283+x+-+4%29+%285+x+%2B+9%29
solutions:
if 0=%283+x+-+4%29+=>3x=4 =>+x=4%2F3
if 0=+%285+x+%2B+9%29 =>5x=-9 =>+x=-9%2F5


6. If g%28x%29+=+5x+%2B+6, find g%5E+-1%28x%29+solved for+y.

g%28x%29+=+5x+%2B+6..........since g%28x%29+=y
y+=+5x+%2B+6..........swap x and y variables
x=+5y+%2B+6.........solve for y
x-6=+5y+
y=%28x-6%29%2F5
y=%281%2F5%29%28x-6%29
=>g%5E+-1%28x%29=%281%2F5%29%28x-6%29