What is an equation of the line that passes through the points ( −4 , − 6 ) and (4,4)?
2 answers:
Answer:
Step-by-step explanation:
Find the slope of this line by using the slope formula: . Substitute both given points into this formula.
The slope of the line is 5/4. Now this can be plugged into point-slope form since we have the point and the slope of the line.
Use any pair of given points, I'll be using (4,4).
Point-slope form:
Substitute 4 for , 4 for
, and 5/4 for m.
Simplify this equation.
The equation in slope-intercept form of the line is .
You might be interested in
If you do this with a complex set of fractions and let
K = G Me m_space be the same in both parts, there should be some cancellation.
W_earth = 180 lbs
W_earth = K /3900 miles^2
W_space =K /(3900 + 850)^2
180 / W_space = k/3900^2
x = k / (4750)^2
![\frac{180}{Wspace} = \frac{ \frac{k}{3900^{2} } }{ \frac{k}{4750^{2}} /[tex]\\Now you need to invert and multiply the bottom fraction on the left.\\[tex] \frac{180}{x} {=} \frac{k}{3900^{2}} {*} \frac{4750^{2}}{k}](https://tex.z-dn.net/?f=%20%5Cfrac%7B180%7D%7BWspace%7D%20%3D%20%20%5Cfrac%7B%20%5Cfrac%7Bk%7D%7B3900%5E%7B2%7D%20%7D%20%7D%7B%20%5Cfrac%7Bk%7D%7B4750%5E%7B2%7D%7D%20%2F%5Btex%5D%5C%5CNow%20you%20need%20to%20invert%20and%20multiply%20the%20bottom%20fraction%20on%20the%20left.%5C%5C%5Btex%5D%20%5Cfrac%7B180%7D%7Bx%7D%20%7B%3D%7D%20%5Cfrac%7Bk%7D%7B3900%5E%7B2%7D%7D%20%7B%2A%7D%20%5Cfrac%7B4750%5E%7B2%7D%7D%7Bk%7D%20)
The ks cancel out.
You are left with 180/x = 4750^2 / 3900^2 Now cross multiply
180 * 3900^2 = 4750^2 = x
180 * 3900^2 / 4750^2 = x
180 * 0.67413 = x
x = 121 pounds. Weight is a force, but because all the units on one side are equivalent to the units on the other, the conversions become part of k. Normally you would have to do the conversions, but not in this particular case.
K = G Me m_space be the same in both parts, there should be some cancellation.
W_earth = 180 lbs
W_earth = K /3900 miles^2
W_space =K /(3900 + 850)^2
180 / W_space = k/3900^2
x = k / (4750)^2
The ks cancel out.
You are left with 180/x = 4750^2 / 3900^2 Now cross multiply
180 * 3900^2 = 4750^2 = x
180 * 3900^2 / 4750^2 = x
180 * 0.67413 = x
x = 121 pounds. Weight is a force, but because all the units on one side are equivalent to the units on the other, the conversions become part of k. Normally you would have to do the conversions, but not in this particular case.
Answer:
Step-by-step explanation:
Pattern 1 consists of
small squares (here n = 1 and
).
Pattern 2 consists of
small squares (here n = 2 and
).
Pattern 3 consists of
small squares (here n = 3 and
).
Thus, pattern n consists of
small squares.
Answer:
<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>
Step-by-step explanation:
<u>Relative Speed</u>
When a body is moving at a constant speed v, the distance traveled in a time t is:
When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.
When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.
Let's call
x = Roberto's rowing speed in still water
y = Speed of the river current
The speed when rowing downstream is x+y, thus the distance traveled is
Where t1=2.5 hours. Substituting values:
Rearranging, we find the downstream equation:
The speed when rowing upstream is x-y, and the distance traveled is
Where t2=5 hours. Substituting values:
Rearranging, we find the upstream equation:
Multiplying [1] by 2:
Adding this equation to [2]:
Solving:
Dividing [2] by 5:
Solving for y
Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour