Point slope formula is y= mx+b. To find the slope, or m, you need to find the "rise over run". rise = y coordinates, run = x coordinates. And the slope equation is y1-y2/x1-x2. So let's say the first point is (x1,y1) and the second is (x2,y2). that would be 35-(-31)/5-(-6)= 66/11 or 6/1 aka up six, across one. That is your slope. So far you have y=6x+b, next plug (5,35) into that equation and solve for b (aka the y intercept). So: 35=6(5)+b. 35-30=b, b=5. So your final equation is y=6x+5.
Answer:
Step-by-step explanation:
Just so you know, for your information, composite numbers have more than <em>two</em> factors, and prime numbers have EXACTLY two factors [1 and itself (that number)].
* A common mistake is that people make is that they say that all even numbers are composite, and that is false because there are odd numbers that are PERFECT SQUARES and can be divided evenly without leaving a remainder. So, using the Prime Factorization Method, you can do this in two structures:
- Ladder Diagram
- Factor Tree
Factor Tree
85
/ \
17 5
Ladder Diagram
17|<u>85</u>
5|<u>5</u>
1
In the Ladder Diagram, when you are down to 1, you know that factorization is over and there is nothing else to do.
So, with that being said, the prime factorization of 85 is 17 × 5.
I am joyous to assist you anytime.
Answer:
- 12 ft parallel to the river
- 6 ft perpendicular to the river
Step-by-step explanation:
The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.
72 = W(2W)
36 = W²
6 = W . . . . . . the width perpendicular to the river
12 = 2W . . . . the length parallel to the river
_____
<em>Development of this relation</em>
Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...
A = xy = x(T -x)/2
Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...
x = (0 +T)/2 = T/2
The corresponding area width (y) is ...
y = (T -T/2)/2 = T/4
Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.
