the equation is a quadratic one, and it has a positive coefficient on the leading term, meaning, is opening upwards, so it has a "burrow" for the vertex.
the minimum or lowest point for a quadratic opening upwards is, well, the vertex point :), the "x" value is the year, the "y" or f(x) value is the population, we're asked for the year, or the x-coordinate of the vertex
well
Answer: -1
Step-by-step explanation:
Find the Slope
(0, 2) , (1, 1)
Slope is equal to the change in y over the change in x, or rise over run.
change in y
m = _________
change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called r ise).
y2 − y1
m =
_____
x2 − x1
Substitute in the values of x and y into the equation to find the s lope.
1 − (2)
m =
_____
1 − (0)
Simplify.
Simplify the numerator.
−1
m =
____
1 − (0)
Simplify the denominator.
−1
m =
___
1
Divide −1 by 1.
m = −1
Answer:
25x - 45 = 5(5x - 9)
Step-by-step explanation:
Find the greatest common factor (GCF) of 25 and 45.
You can do this several ways, but one way is to list all the factors of both numbers and find the greatest common one:
Factors of 25: 1, 5, 25
Factors of 45: 1, 3, 5, 9, 15, 45
Therefore, 25 and 45 have 2 common factors: 1 and 5
So the greatest common factors is 5
25x - 45 = 5(ax - b)
To find the value of a, simply divide 25 by 5: 25 ÷ 5 = 5
To find the value of b, divide 45 by 5: 45 ÷ 5 = 9
25x - 45 = 5(5x - 9)
Answer:
B=58
Step-by-step explanation:
Complementary angles are angles where the sum equals 90°. So all you have to do is 90-32 and you get 58.
Answer:
a) |n -11| = 5
b) n ∈ {6, 16}
Step-by-step explanation:
The wording of the question is ridiculous. We assume it is intended to read, "The distance between two numbers is 5. One of the numbers is 11. What are the possibilities for the other?"
a) The distance between a number (n) and 11 can be written as ...
|n -11|
Since we want that distance to be 5, we can write the equation ...
|n -11| = 5
__
b) The equation resolves to two:
Adding 11 to both sides of both equations gives ...
The two solutions are n=6 and n=16.
_____
<em>Comment on the question statement</em>
Increasingly, we see curriculum materials written in Pidgin English or where the words have a meaning different from that understood by a native English speaker. It appears you are the lucky recipient of such materials, so must do occasional "interpretation". Here, it seems that "two time a number" is intended to mean "two numbers."
