Hi I need help with this problem it called area quiz for 7th grade honors math class can you help
1 answer:
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It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers
Answer:
The length of line segment FG is equal to the length of F'G'
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
Step-by-step explanation:
Given
CDEFG and C'D'E'F'G
Translation: 7 units up and 5 units left
Solving (a): Segment FG and F'G'
When a shape is translated, the resulting image will have the same lengths as the original image (i.e, translation does not change measurements)
Hence:
Solving (b): Perimeter CDEFG and C'D'EF'G'
In (a), we established that lengths do not change during translation;
Hence:
The perimeter of the CDEFG and C'D'EF'G' will remain the same