1. Find the midpoint of the given endpoints. (This is the average of the coordinates of the two endpoints.)
2. Find the slope of the given line segment. (This is the difference in y coordinates divided by the difference in corresponding x coordinates.)
3. Use the point-slope form of the equation for a line to write the equation of the line through the midpoint with a slope that is the negative reciprocal of the slope of the given segment.
y = m(x-h) +k . . . . . . . . line with slope m through point (h, k)
When sorting fractions without expressing them as decimal values you have to keep in mind that the greater the denominator is, the smaller the value of the fraction.
For
![\frac{5}{4}>\frac{9}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%3E%5Cfrac%7B9%7D%7B10%7D)
The denominator in the first fraction is smaller than the denominator in the second one, so we know that the value of the first fraction is greater than the value of the second one.
To prove it you may express them as decimal values:
![\begin{gathered} \frac{5}{4}=1.25 \\ \frac{9}{10}=0.9 \\ 1.25>0.9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B5%7D%7B4%7D%3D1.25%20%5C%5C%20%5Cfrac%7B9%7D%7B10%7D%3D0.9%20%5C%5C%201.25%3E0.9%20%5Cend%7Bgathered%7D)
This inequation is true.
For
![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%3C%5Cfrac%7B3%7D%7B2%7D)
The denominator of the first fraction is greater than the denominator of the second one → 4>2, this means that the first fraction represents a value smaller than the second one.
This inequation is true
For
![\frac{7}{8}>\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D%3E%5Cfrac%7B4%7D%7B3%7D)
The denominator of the first equation is greater than the denominator of the second one 8>3, this means that the value the first fraction represents is less than the value of the second fraction.
This inequality is false.
For
![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%3C%5Cfrac%7B5%7D%7B7%7D)
The denominator of the first fraction is less than the denominator of the second one 2<7, this means that the first fraction is greater than the second one, so this inequation is false.
With these given values:
<span> f(0)=4 and f′(x)≤4
</span>
The solution is as follows:
<span>f(0) = 4
f ' (x) ≤ 4 for all x
The Mean Value Theorem says there is a c between 0 and 4 such that f ' (c) = [f(4) - f(0)] / (4 - 0)
But since f ' (x) ≤ 4 for all x, then [f(4) - f(0)] / (4 - 0) ≤ 4
Since f(0) = 4, then [f(4) - 4] / (4 - 0) ≤ 4
Multiplying both sides by 4 you get f(4) - 4 ≤ 16
Adding 4 to both sides you get f(4) ≤ 20
So f(4) ≤ 20
</span>
By examining the solution, it could guide you on answering the problem on your own. Hope that helps
There are two ways you could go about solving this.
You could divide the length of the base (6mm) by 2 and use that to find the area or you could find the area of the whole triangle using 6mm and divide that by 2.
I will use the first method I described:
base = 6/2
base = 3 mm
height = 5.2 mm
area = bh/2
area = (3 * 5.2)/2
area = 7.8 square mm
(don't forget your units)
Using the other method would look like this:
area = bh/2
b = 6
h = 5.2
area = (6 * 5.2)/2
area = 15.6 square mm
area/2 = 7.8 square mm
As you can see either method yields the same result.
Hope this helped.
Cheers and good luck,
Brian
When you do the multiplication yo get 9 for the top and get 81 for the bottom and that means to divide so when you divide 9 by 81 you get 9 it’s as simple as that.