The piece-wise linear functions can be written as follows:
.
.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
.
When x = 5, the function is constant at -5, hence:
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
.
More can be learned about linear functions at brainly.com/question/25537936
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Answer:
<h2>The height is 87.5 in</h2>
Step-by-step explanation:
We can solve the height of a square pyramid using the Pythagoras theorem, this is because the slant height the height and the section of the base form a right triangle
the slant height is equivalent to the hypotenuse
the height is equivalent to the opposite
while the base(half) is the adjacent
Given
the base of the pyramid= 
the adjacent is = 
the slant height (hypotenuse)= 
we know that Pythagoras theorem states that "The sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle) is equal to the square of the length of the hypotenuse ('c').
substituting we have
Answer: The prime numbers are 1, 2, 3, 5, 7.
5. 104
because 40+37= 77 and 180-77=104
6. 67
because 41+72=113 and 180-113=67
7. 15
add them together and subtract by 180
8. 44
add together and subtract 180
The shape of the distribution described the Left skewed.
<h3>What is left- skewed histogram?</h3>
A left skewed histogram is a histogram that attains a peak (which is the mode) towards the right side of the graph and has a “tail” towards the left side.
A histogram in which most of the data falls to the left of the graph's peak is known as a left-skewed histogram.
A left-skewed histogram is a type of histogram that is not symmetrical and in which the peak of the graph lies to the right of the middle value or the median.
Hence, considering the above definition the given histogram data falls on right side.
So, it is left skewed graph.
Learn more about left- skewed graph here:
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