Answer:
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The parent function y = sin(x) has the following:
- Amplitude (A) = 1
- Period = 2π
- Phase shift (C) = 0
- Vertical shift (D) = 0
- Mid-line: y = 0
From inspection of the given graph:
- Amplitude (A) = 1
- Phase shift (C) = 0
- Vertical shift (D) = +3 (as mid-line is y = 3)
Substituting the values into the standard form:
Therefore, the equation of the given trigonometric graph is:
<span>The congruency statement should be that which shows the congruency of the corresponding angle and the sides. In the rotation of the polygon, the angle A is congruent with angle A' still. The same is true for all the angles and sides. The congruency statement is therefore,
ABCD is congruent to A'B'C'D'
The answer to this item is letter A. </span>
Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
Answer:
35 calories
Step-by-step explanation:
create a proportion and solve.
30/150= 7/x
