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 
It should be Additional because she adds on another rug right so you just add 2 /23 + 1 1/4 and you will get your answer hope this helps
! and if u subtract that means your removing 1 rug and that's not in the question. :D
The technique of matrix isolation involves condensing the substance to be studied with a large excess of inert gas (usually argon or nitrogen) at low temperature to form a rigid solid (the matrix). The early development of matrix isolation spectroscopy was directed primarily to the study of unstable molecules and free radicals. The ability to stabilise reactive species by trapping them in a rigid cage, thus inhibiting intermolecular interaction, is an important feature of matrix isolation. The low temperatures (typically 4-20K) also prevent the occurrence of any process with an activation energy of more than a few kJ mol-1. Apart from the stabilisation of reactive species, matrix isolation affords a number of advantages over more conventional spectroscopic techniques. The isolation of monomelic solute molecules in an inert environment reduces intermolecular interactions, resulting in a sharpening of the solute absorption compared with other condensed phases. The effect is, of course, particularly dramatic for substances that engage in hydrogen bonding. Although the technique was developed to inhibit intermolecular interactions, it has also proved of great value in studying these interactions in molecular complexes formed in matrices at higher concentrations than those required for true isolation.
-31 is a thing and it would be pronounced negative thirty-one hope that helps
Given equation: 3(x + 4) + 2 = 2 + 5(x – 4).
<em>First step is to distribute 3 on left side and 5 on right side of the equation,</em> we get
3x + 12 + 2 = 2 + 5x – 20
<em>Second step is combining like terms, 12+2=14 and 2-20=-18.</em>
We get
3x +14 = 5x -18.
<h3>Third step, we need to get rid 18 from right side and 3x from left side.</h3>
<em>Adding 18 on both sides and subtracting 3x from both sides</em>, gives
32 = 2x.
<h3>Fourth step , we need to get rid 2 from right side from 2x.</h3>
<em>We need to divide both sides by 2</em>, we get
16=x.
