Answer:
Shift 4 units down: 
Stretching f(x) by 4 : 
Shift 4 units left: 
Compress by 1/4 units : 
Step-by-step explanation:
Given
Required
Match the transformations (See attachment)
<u>Shift 4 units down</u>
Shifting down a function is represented as:
In this case:
Substitute expression for f(x) and 4 for b in
<u>Stretching f(x) by 4 </u>
Stretching a function by some units is represented as:
In this case:
Substitute expression for f(x) and 4 for b in
<u>Shift 4 units left</u>
Shifting a function to the left is represented as:
In this case:
Substitute expression for f(x) and 4 for b in
Calculating f(x - 4)
Hence:
<u>Compress by 1/4 units </u>
This means that the function is stretched by 
Compressing a function is represented as:
In this case:
Substitute expression for f(x) and 4 for b in
Calculating f(4x)
Hence:
2.25/12.50 = 0.18. then turn 0.18 into a percentage by doing 0.18 x 100 = 18%. Therefore, he gave an 18% tip.
Answer:
Step-by-step explanation:
Discussion
You are working with the Cosine of the angle.
Hypotenuse = 12.5
Base = 3
Theta = ?
Solution
Cos(theta) = base / hypotenuse Substitute values
Cos(theta) = 3 / 12.5 Divide
Cos(theta) = 0.24 Tale the inverse cos
theta = cos-1(0.24)
theta = 76.11 degrees
That's 5 integers...
Logic tells me that a number divided by 5 should be equal to -3. -15/5 is in fact equal to -3.
Let's find 5 integers (two positive and three negative) when added up together equal -15.
-14, -3, -3, 2, 3.
[(-14)+(-3)+(-3)+2+3]/5 = (-15)/5 = -3
Mean = -3
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Now let's put these numbers in order, from lowest to highest - then pick out the middle value...
-14, -3, [-3], 2, 3
The median turns out to be -3.
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Let's look at the numbers once again...
-14, -3, -3, 2, 3
It turns out that -3 appears the most, therefore -3 is the mode too.
