Answer:
Step-by-step explanation:
A function is continuous at a point if and only if:
So, we have the piecewise function:
And we want to find the value of k such that the function is continuous.
First, find the left hand limit of f(x):
Since we're coming from the left, we'll use the first equation. Thus:
Direct substitution:
Simplify:
Subtract and divide:
So, what this tells us is that for the function to be continuous, the right hand limit as f(x) approaches 9 from the right <em>must</em> also be equal to 0.
Therefore:
Direct substitution:
Subtract 1 from both sides:
Divide both sides by -9:
Therefore, the value of k is 1/9.
So, our equation in the end is:
Answer:
120 cm^2.
Step-by-step explanation:
The area of one triangle = 1/2 * base * height
= 1/2 * 8 * 6
= 1/2 * 48
= 24 cm^2
So area of the pentagon = 5 * 24
= 120 cm^2.
Answer: x=35 and y=72.5
Step-by-step explanation:
Everything os 360, so x is 35 because it los like it has the same measure as the another 35, so if you substract 70 360=290 and 290/4 = 72.5
The direct relationship between the original distance and the resulting distance is y = 3 · x.
<h3>What is the relationship behind a given statement and graph?</h3>
In this problem we find the case of a direct relationship, that is, a linear relationship between two b. According to this case, the original distance (d), in yards, is directly proportional to the resulting distance (d'), in feet.
y = k · x
Where:
- x - Original distance, in yards.
- y - Resulting distance, in feet.
- k - Proportionality constant, in feet per yard.
If we know that x = 1 yd and y = 3 ft, then the proportionality constant is:
k = y / x
k = 3 ft / 1 yd
k = 3 ft / yd
The direct relationship is y = 3 · x.
To learn more on direct relationships: brainly.com/question/27989875
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Answer:
A= 16²
Step-by-step explanation:
A=s²
A= 4²
A= 16
(4² is the same as 4x4)