Analyze the photo below and answer the question that follows.
Monarch butterflies on a tree.
Photo by David Slater
The monarch butterflies shown in the image above live in Latin America’s __________ ecosystem.
A.
desert
B.
rainforest
C.
deciduous forest
D.
coniferous forest
Please select the best answer from the choices provided
A
B
C
D
The condition statements that must be met in order for three side lengths a, b, and c to create a triangle are:
a < b + c
a > |b - c|
(Note: The second condition is written as a > |b - c| because the difference between b and c can be positive or negative. Taking the absolute value ensures that the condition is met regardless of whether b is greater than or less than c.)
B. rainforest
The angles of a triangle measure 2x, 3x, and 4x. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle. (1 point)
Triangle Angle Sum Theorem states that the sum of the angle measures in any triangle is always 180 degrees.
Let's denote the angles as 2x, 3x, and 4x.
To find the smallest angle, we can set up the equation:
2x + 3x + 4x = 180
Combine like terms:
9x = 180
Divide both sides by 9:
x = 20
Now to find the measure of the smallest angle, we substitute x into the equation 2x:
2(20) = 40
Therefore, the measure of the smallest angle in this triangle is 40 degrees.
Complete the condition statements that must be met in order for three side lengths-a, b, and
c-to create a triangle. (1 point)
a b + c and a b - c
A right triangle has acute angles measuring 2x + 6 degrees and 3x - 26 degrees. Use the
Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.
In a right triangle, one of the angles is always a right angle, which measures 90 degrees. Let's denote the acute angles as 2x + 6 and 3x - 26.
Using the Triangle Angle Sum Theorem, we know that the sum of the angle measures in any triangle is always 180 degrees. Therefore, we can set up the equation:
2x + 6 + 3x - 26 + 90 = 180
Combine like terms:
5x - 20 + 90 = 180
Simplify:
5x + 70 = 180
Subtract 70 from both sides:
5x = 110
Divide both sides by 5:
x = 22
Now we can substitute x back into the angle measures to find their values:
Angle 1: 2x + 6
2(22) + 6 = 50 degrees
Angle 2: 3x - 26
3(22) - 26 = 40 degrees
Therefore, the measures of the missing angles in the right triangle are 40 degrees and 50 degrees.
Use the formula for the area of a triangle to determine the area of a triangle with base equal to 13 yards and height equal to 5 yards. (1 point)
18 square yards
65 square yards
32.5 square yards
27.5 square yards
The formula for the area of a triangle is A = (1/2) * base * height.
Given that the base is 13 yards and the height is 5 yards, we can plug these values into the formula:
A = (1/2) * 13 * 5
A = (1/2) * 65
A = 32.5
Therefore, the area of the triangle is 32.5 square yards.
If C = 12π, what is the area of the circle? (1 point)
36π
144π
24π
12π