6 points are placed on the line a , 4 points are placed on the line b . How many triangles is it possible to form such that thei
2 answers:
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Answer:
n=4
Step-by-step explanation:
To solve combine your like terms.
You can start by adding 0.8 to both sides and subtracting 0.7n from both sides.
Next, divide both sides by 0.7 to isolate for n.
Answer:
-8
Step-by-step explanation:
Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:
(1,1) and (-3,-1).
We'll find a line equation using the point slope form format to start:
(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.
(x,y) = (1,1)
(x1,y1) = (-3,-1)
Rearrange the equation:
(y - y1) = m * (x - x1)
m = (y - y1)/ (x - x1)
m = (1-(-1))/(1-(-3))
m = 2/4, or 1/2: The slope is 1/2. [<u>This is "m."]</u>
We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:
y = (1/2)x + b
Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.
y = (1/2)x + b
1 = (1/2)(1) + b for (1,1)
b = 1/2
This makes the reference line: y = (1/2)x+(1/2)
===
The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.
We can then write y = -2x + b
To find be, enter the one given point for this line: (-3,-2)
y = -2x + b
-2 = -2(-3) + b
-2 = 6 + b
b = -8
The perpendicular line is thus:
y = -2x - 8
It has a y-intercept of -8
