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.
Answer:
a) 236/100 = 2.36
b) 101/100 = 1.01
c) 814/100 = 8.14
Step-by-step explanation:
The divisor in each case is already a factor of 100, so multiply the numerator and denominator by the number that will make the denominator 100. Then add 100 times the integer to the numerator of the fraction.
a) 2 9/25 = (200 +9·4)/(25·4) = 236/100 = 2.36
b) 1 1/100 = (100 +1)/100 = 101/100 = 1.01
c) 8 7/50 = (800 +7·2)/(50·2) = 814/100 = 8.14
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Since each of these fractions has a denominator of 100, the decimal can be written by putting the least significant digit of the numerator in the hundredths place of the decimal number.
For example, for 236/100, putting 6 in the hundredths place puts 3 in the tenths place and 2 in the units place for a decimal number of 2.36.
Answer:
yes, 6÷1/3, which is 6×3 or 18
Step-by-step explanation:
Answer:
The answer is the temperature of the water (in degrees Fahrenheit) after Raul after Raul added the ice cubes is 72.3 + (-39.1)
Step-by-step explanation: