Find the perimeter of the triangle whose vertices are (−7,−1), (5,−1), and (5,4). Write the exact answer. Do not round.
1 answer:
The perimeter of the triangle is 30 units
<h3>How to determine the perimeter?</h3>The vertices are (−7,−1), (5,−1), and (5,4).
Start by calculating the distance between the vertices using:
So, we have:
d1 = 12
d2 =5
d3 = 13
The perimeter is then calculated as:
P = d1 + d2 + d3
This gives
P = 12 + 5 + 13
Evaluate
P = 30
Hence, the perimeter of the triangle is 30 units
Read more about perimeter at:
#SPJ1
You might be interested in
You want to multiply two consecutive numbers, and see when you get a multiple of three.
Since two consecutive numbers share no divisors (except 1), either n or n+1 must be a multiple of 3.
So, your experiments succeeds if n is itself a muliple of three, or if lies immediately before one. So, 2 numbers out of 3 are ok.
Let me try to visualize the situation: I'll list some integers. Below, I'll write if they are multiple of three (M) or not (N). Above, I will write if they will cause the experiment to succeed (S), i.e. n(n+1) will be dibisible by 3, or to fail (F), i.e. n(n+1) will not be a multiple of three. We have
So, since there are exactly 99 numbers between 1 and 99, and 2/3 of the numbers work, the probability that you will choose a number n such that n(n+1) is divisible by 3 is 2/3.
Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is