Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.
A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'
B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)
C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)
D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n
_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.
The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
Hello and Good Morning/Afternoon:
<u>Let's take this problem step-by-step</u>:
<u>Let's define some terms</u>:
- Domain: the set of inputs in the function (<em>in this case, it is x)</em>
- Range: the set of all of the possible outputs (in this case, it is y)
<u>Let's find the domain:</u>
For log(x),
⇒ the only inputs that are accepted are nonnegative and nonzero
⇒ therefore: Domain is (0, ∞)
<u>Now let's find out the range</u>:
The biggest constraint of the output is log(x)
⇒ however log(x) has a range of (-∞,∞)
⇒ therefore the entire equation's range is
(-∞,∞)
<u>Answer:</u>
- <u>Domain: (0,∞)</u>
- <u>Range: (-∞,∞)</u>
Hope that helps!
#LearnwithBrainly
Answer: The cost per pound for bananas is $1.5 per pound.
Step-by-step explanation:
To get this answer you will divide the cost by the amount of bananas you have.
Answer:
<u>The correct answer is C. 21x³y</u>
Step-by-step explanation:
Let's simplify the product, this way:
(49x²y)^1/2 * (27x⁶y^3/2)^1/3
Let's recall that x^1/2 = √x and x^1/3 = ∛x
√(49x²y) * ∛(27x⁶y^3/2)
7x √y * 3x² √y
Let's recall that √y * √y = √y² = y
21x³y
<u>The correct answer is C. 21x³y</u>
Vowels include AEIOU, so in the first box there is 2 vowel out of the 5 letters so 2/5 probability for the first box. Box 2 includes 2,4,6,8 as the even numbers out of the 9 numbers so 4/9
If you were solving the probability for each box individually that would be your answer
However if you are doing statistics and need to do it in a certain order you multiply the fractions
2/5 x 4/9 = 8/45
(.17777)
This leaves you with a 17% (8/45) chance of picking a vowel then an even number.
