Answer: SAS Similarity theorem.
Explanation.
SAS stands for Side - Angle - Side.
SAS theorem states that if two triangles have
corresponding angles that are congruent and corresponding sides
with identical ratios, then the triangles are similar.
And that is what the figure shows:
1) The angle at M is the same for both triangles.
2) The ratios of the sides are: 2/3 and 4 /6. Given that 2/3 = 4/6 you have that the two corresponding sides have identical ratios.
A. The ratio of lynx to mountain lions to wolverines is 2:3:1.
Thus, there are 2 lynx in the ratio. If there were 6 lynx, we would have to multiply all of the numbers in the ratio by 3 (because 6/2 = 3) to keep the ratio in the same proportion.
Therefore, because there is 1 wolverine in the ratio, and 1 * 3 = 3, if there were 6 lynx, there would be 3 wolverines.
b. We can use the same ideas that we had in part a to help us in part b.
There are 3 mountain lions in the ratio, but there are 15 mountain lions in the problem. Thus, the multiplier is 5, because 15/3=5.
Therefore, because there are 2 lynx in the ratio, and 2*5 = 10, if there were 15 mountain lions, there would be 10 lynx.
c. There is one wolverine in the ratio, but there are 10 wolverines in the problem. Thus, the multiplier is 10, because 10/1 = 10
Therefore, because there are 3 mountain lions in the ratio, and 3 * 10 = 30, if there were 10 wolverines in the park, then there would be 30 mountain lions.
d. The total number of lynx, mountain lions, and wolverines is 30.
To find out how many of each animal there should be, we must make an equation using the ratio and the variable x.
2x + 3x + 1x = 30
This equation means that the total number of animals together is 30, which is true. Now let's simplify by combining like terms.
6x = 30
Finally, we can simplify by dividing both sides by the coefficient of x, or 6.
x = 5
Thus, going back to our original equation, we know that the amount of lynx is 2x, mountain lions is 3x, and wolverines is 1x.
Lynx = 2x = 2(5) = 10 lynx
Mountain Lion = 3x = 3(5) = 15 mountain lions
Wolverines = 1x = 1(5) = 5 wolverines
Hope this helps! :)
Answer:
The area of the triangle is 
Step-by-step explanation:
Given:
Coordinates D (0, 0), E (1, 1)
Angle ∠DEF = 60°
△DEF is a Right triangle
To Find:
The area of the triangle
Solution:
The area of the triangle is = 
Here the base is Distance between D and E
calculation the distance using the distance formula, we get
DE = 
DE =
DE = 
DE = 
Base =
Height is DF
DF =
DF = 
DF = 
Now, the area of the triangle is
= 
=
=
=
Answer is 4 books per minute. 240 (books) divided by 60 (minutes in one hour) equals 4
Answer:
0.08
Step-by-step explanation:
