<h3>
<u>Explanation</u></h3>
The structure or equation is similar to a quadratic function.
The value of a determines the slope of graph.
Tthe value of h determines the horizontal shift of graph.
The value of k determines the vertical shift of the graph.
From the given equation,
We can say that the graph shifts to the right 2 units and shifts down 7 units. Hence the vertex would be at x = 2 and y = -7. It can be written in coordinate form as (2,-7).
<h3>
<u>Answer</u></h3>
<u>
</u>
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer:
We must have two angles and a side.
A is the correct option.
Step-by-step explanation:
For any triangle ABC, the law of sine is given by
From this formula it is clear that in order to find the length of the side of the triangle, we must have two angles and a side.
Let us understand this by assuming that we need to find a (length of the side). From the formula, we have
Thus, to find the length a, we must have b, sin A and sin B.
Hence, o find the length of the side of the triangle, we must have two angles and a side.
Answer:
2n
Step-by-step explanation:
To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8.
Answer:
18
Step-by-step explanation:
