No the figures aren’t similar. According to the Angle Angle Similarity Theorem- they should have the same angle degree.
Answer:
2.
Step-by-step explanation:
The line of best fit is a line through scatter plot of data points that best expresses the relationship between those points.
(hope this helps :P)
Break the problem into two parts: 1) the area of the this isosceles triangle whose hypotenuse is AB and 2) the area of the semicircle whose diameter is AB.
The triangle is isosceles because the lengths of the two shorter legs are the same (2 meters). Use the Pythagorean Theorem to find the length of the hypotenuse of this triangle. (AB)^2 = (2 m)^2 + (2 m)^2, or 8 m^2. Thus, AB = sqrt(8 m^2), or 2sqrt(2). This AB is also the base of the triangle. What is the area of the triangle?
Next, noting that the diameter AB of the semicircle is 2sqrt(2) and the radius is just sqrt(2), find the area of the semicircle. The area of a circle of radius r
is pi*r^2; here it's pi*(sqrt 2)^2, or pi*2, or 2pi.
Add the area of the triangle to this area of the semicircle (2pi) to find the total area of the figure.
Hint: the area of a triangle is (bh)/2, where h is the height, b is the base.
Our system of equations is:
y = -3x + 9
y = -x - 5
To solve this system of equations, we are going to use substitution. This means that we are going to substitute the second equation into the first equation since both are already solved for y in terms of x.
y = -3x + 9
-x - 5 = -3x + 9
Now, we must simplify by moving all of the constant terms to one side of the equation and all of the variable terms to the other side.
-x - 5 = -3x + 9
2x - 5 = 9
2x = 14
Finally, to undo the multiplication between the coefficient 2 and the variable x, we must divide both sides by 2 to get the variable x alone.
x = 7
Next, we must substitute in this value we have solved for x into one of the original equations to solve for the other variable, y.
y = -3x + 9
y = -3(7) + 9
To simplify, we must multiply through the parentheses and combine like terms by addition.
y = -21 + 9
y = -12
Therefore, your final answer is x = 7 and y = -12, or as an ordered pair (7, -12).
Hope this helps!
