The statement that are true about the dilation are:
A. M'N' is 18 units.
D. The dilation is an enlargement.
F. Scale factor is 3.
<h3>What is Dilation?</h3>
Given that rectangle LMNP is dilated using the rule Dp.3, it means that rectangle LMNN is enlarged times 3 to get rectangle L'M'N'P'.
This means that the scale factor is 3.
We would have the following:
M'N' = 6 × 3 = 18 units.
Therefore, the statements that are true are:
A. M'N' is 18 units.
D. The dilation is an enlargement.
F. Scale factor is 3.
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<em>Complement</em> = 90-x
<em>Supplement</em>=180-x
180-x=4(90-x)+6
180-x=360-4x+6
3x=360-180+6
3x=186
x=186/3
x=62
The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3
<h3>The sinusoidal function</h3>
The minimum and the maximum of the function are
The amplitude (A) is calculated as:
A = 0.5 * (Maximum - Minimum)
So, we have:
A = 0.5 * (-5 + 1)
A = -2
The vertical shift (d) is calculated as:
d = 0.5 * (Maximum + Minimum)
So, we have:
d = 0.5 * (-5 - 1)
d = -3
The period (P) is calculated as:
P = 2π/B
From the graph,
B = 1
So, we have:
P = 2π/1
P = 2π
So, the amplitude is -2 and the period is 2π.
<h3>The equation of the sine function</h3>
In (a), we have:
A = -2
B = 1
d = -3
A sine function is represented as:
y = A sin(Bx + C) + D
So, we have:
y = -2sin(x + C) - 3
The graph passes through the point (0, -5)
So, we have
-5 = -2sin(0 + C) - 3
Solve for C, we have
C = 1.5
So, we have:
y = -2sin(x + 1.5) - 3
Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3
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