Answer:
The distance between (-3, 2) and (0,3) is √10.
Step-by-step explanation:
As we go from (-3,2) to (0,3), x increases by 3 and y increases by 1.
Think of a triangle with base 3 and height 1. Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):
distance = √(3² + 1²) = √10
The distance between (-3, 2) and (0,3) is √10.
The equation for the area of a triangle is A= b*h /2. So, plug in your known variables, and you get 270in^2= b*30 /2. First you multiply by 2 to cancel out the division for 2, which gets you 540= b* 30. To get "b" by itself, divide both sides by 30, giving you <u>18=b</u>.
To check this, plug in your new known variable, as 270= 18* 30 /2. This will equal as 270=270, confirming 18in as the correct measurement.
The <em>quadratic</em> function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
<h3>How to analyze quadratic equations</h3>
In this question we have a graph of a <em>quadratic</em> equation translated to another place of a <em>Cartesian</em> plane, whose form coincides with the <em>vertex</em> form of the equation of the parabola, whose form is:
g(x) = C · (x - h)² - k (1)
Where:
- (h, k) - Vertex coordinates
- C - Vertex constant
By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.
x = 2
g(2) = (2 - 5)² + 1
g(2) = 10
x = 8
g(8) = (8 - 5)² + 1
g(8) = 10
The <em>quadratic</em> function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
To learn more on parabolae: brainly.com/question/21685473
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Answer:
12 which is on C
Step-by-step explanation:
use pathogoras theorem
a^2+b^2=c^2
16^2+b^2=20^2
256+b^2=400
b^2=400-256
b^2=144
b= square root of 144
b= 12
