Suppose a frog gets launched vertically into the air as this frog did during the launch of NASA's LADEE (Lunar Atmosphere and Dust Environment Explorer) spacecraft:
http://www.universetoday.com/104679/absolutely-incredible-photo-frog-launches-with-ladee/
A NASA scientist gives you the task of calculating the frog's initial launch velocity provided by the spacecraft blast. ...
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During the first week or so of your physics class, your teacher will most likely talk about the various length scales present in the universe. These length scales range from very small elementary particles such as electrons, protons, and neutrons with widths of ~5x10-15 meters, to the width of our very own galaxy the Milky Way of ~1.2x1021 meters.
Physicists study all of these length...
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The point slope form is written like this:
y-y1=m(x-x1) where m is the slope, and (x1,y1) can be either one of the two points you are given. First, we need to find the slope m from the given points.
The slope m=rise/run=(y2-y1)/(x2-x1). Let (2,3)=(x1,y1) and (5,1)=(x2,y2). Then...

It is important to use parentheses when multiplying/dividing by fractions. Do you want to solve:
(1/3)x+2/3=(5/3)x
or
1/(3x)+2/3=5/(3x)
The answer will be different depending on where the parentheses are placed. In the first equation, the fractions are being multiplied...

The first thing we want to do is to find the slope between these two points. The equation for the slope, m, is:
m=rise/run=(y2-y1)/(x2-x1).
Let the first point (-1,0)=(x1,y1) and the second point (1,2)=(x2,y2), then
m=(2-0)/(1-(-1))=2/2=1, so the slope between these two points...

The first thing you probably noticed is those pesky x's in the denominator. To get rid of those, we will want to multiply the entire equation by x:
x(1/(4x)+x)=x(-3+1/(2x)) And distribute the x's through
1/4+x2=-3x+1/2 Now move all of the...

The problem I believe you are trying to solve is:
(2x-1)/3=(x+2)/4
The first step we want to take is to cross multiply. When we do that, the result is:
4(2x-1)=3(x+2)
Now we distribute the 4 and 3 through the parentheses:
8x-4=3x+6
Next we solve the equation...

Here is a Hint:
Multiply the whole equation by t. The result will then be:
ct=3t2+8 (subtract ct from both sides)
0=3t2-ct+8
Now apply the quadratic formula to solve for t.
Hope this answer is useful!

We have 3 Equations:
Eq.1) 35=A+B+C
Eq. 2) A=2B
Eq. 3) C=A+5
Notice that all three equations have the variable A. What we want to do is to replace B and C in Eq. 1 in terms of A. If we solve Eq. 2 for B, we get that B=(1/2)A. Note that in Eq. 3, C is...