For a function to be continuous at an x-value, say -17, you need to make sure two things line up:
The limit from the left equals the limit from the right.
This limit equals the functions value.
The left hand limit involves the first piece, f(x) = 20x + 1:
![\begin{aligned} \lim_{x \to -17^{-}} f(x) &= \lim_{x \to -17^{-}} (20x+1)\\[0.5em]&= 20(-17)+1\\[0.5em]&= -339\endaligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B-%7D%7D%20f%28x%29%20%26%3D%20%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B-%7D%7D%20%2820x%2B1%29%5C%5C%5B0.5em%5D%26%3D%20%20%2020%28-17%29%2B1%5C%5C%5B0.5em%5D%26%3D%20%20%20-339%5Cendaligned%7D)
The right hand limit invovles the second piece, f(x) = -10x^2:
![\begin{aligned} \lim_{x \to -17^{+}} f(x) &= \lim_{x \to -17^{+}} (-10x^2)\\[0.5em]&= -10\cdot (-17)^2\\[0.5em]&= -2890\endaligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B%2B%7D%7D%20f%28x%29%20%26%3D%20%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B%2B%7D%7D%20%28-10x%5E2%29%5C%5C%5B0.5em%5D%26%3D%20%20%20-10%5Ccdot%20%28-17%29%5E2%5C%5C%5B0.5em%5D%26%3D%20%20%20-2890%5Cendaligned%7D)
Since the two one-sided limits don't match, the function is not continuous at x=-17.
The answer to your question is 30
Answer:
If the roots of any equation are equal then it means that their Discriminant = 0
So, b²-4ac = 0
We have given the equation 2x² + kx + 2, where,
a = 2
b = k (we have to find the value)
c = 2
Then, b²-4ac=0
b² - 4(2)(2) = 0
b² - 16 = 0
b² = 16
√16 = 4
Hence the vue of k is 4.
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Step-by-step explanation:
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Answer:
B.
Step-by-step explanation:
So there are 16 grams initally. Then, the amount of water decreases by 3.5%.
So first we must find 3.5% of 16. 3.5% in decimal form is 0.035, since you divide 3.5 by 100. Then, when you multiply 0.035 by 16, you get 0.56. Since the solution decreased by that percentage, you must subtract 0.56 from 16, which is 15.44.
Then the amount of water decreases by 4.25%. That in decimal form is 0.0425. You multiply it by 15.44, and it comes out to 0.6562. You subtract that from 15.44, not 16, since some of the water has evaporated. So you get 14.7838.
0.4 least 38% is next then 5/8 is the greatest
