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Ray Of Light [21]
2 years ago
5

For a function, each input(x) can only have ONE output (y). Is this a function?

Mathematics
1 answer:
cluponka [151]2 years ago
8 0

Answer C

Step-by-step explanation:

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Your mortgage is $135,400.00 at a 5.25% APR. If you pay $1,500.00 towards the mortgage each month, how much of your second month
Serjik [45]
For the answer to the question above, n the 1st month, the accrued interest is ___ (1/12) * .0525 * 135400 

subtract the interest from the payment to find the change in the principal for the 2nd month 

find the 2nd month's interest and subtract from the payment to find the amount applied to principal. Then that's it!
8 0
3 years ago
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How do you write an equation of a line that passes through (4,3) and has a slope of 2?
lana66690 [7]

Answer:

y = 2x - 5

Step-by-step explanation:

y-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We know the slope is 2, so all that's left is to find the y-intercept. To do this, for every 1 we subtract from x in (4,3), we take away 2 from y because the slope is two. We keep doing this until x is zero. The remaining y-value is the y-intercept.  

5 0
2 years ago
Read 2 more answers
For <img src="https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7D" id="TexFormula1" title="e^{-x^2/2}" alt="e^{-x^2/2}" align="absmiddl
nevsk [136]
I'm assuming you're talking about the indefinite integral

\displaystyle\int e^{-x^2/2}\,\mathrm dx

and that your question is whether the substitution u=\dfrac x{\sqrt2} would work. Well, let's check it out:

u=\dfrac x{\sqrt2}\implies\mathrm du=\dfrac{\mathrm dx}{\sqrt2}
\implies\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt2\int e^{-(\sqrt2\,u)^2/2}\,\mathrm du
=\displaystyle\sqrt2\int e^{-u^2}\,\mathrm du

which essentially brings us to back to where we started. (The substitution only served to remove the scale factor in the exponent.)

What if we tried u=\sqrt t next? Then \mathrm du=\dfrac{\mathrm dt}{2\sqrt t}, giving

=\displaystyle\frac1{\sqrt2}\int \frac{e^{-(\sqrt t)^2}}{\sqrt t}\,\mathrm dt=\frac1{\sqrt2}\int\frac{e^{-t}}{\sqrt t}\,\mathrm dt

Next you may be tempted to try to integrate this by parts, but that will get you nowhere.

So how to deal with this integral? The answer lies in what's called the "error function" defined as

\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt

By the fundamental theorem of calculus, taking the derivative of both sides yields

\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}

and so the antiderivative would be

\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt{\frac\pi2}\mathrm{erf}\left(\frac x{\sqrt2}\right)

The takeaway here is that a new function (i.e. not some combination of simpler functions like regular exponential, logarithmic, periodic, or polynomial functions) is needed to capture the antiderivative.
3 0
3 years ago
4(2k-3)+1=8k-11 help pls
Fofino [41]
4(2k - 3) + 1 = 8k - 11
8k - 12 + 1 = 8k - 11
8k - 11 = 8k - 11

So, these two equations equal to the same thing.
Glad I could help and gave a fantastic day!
8 0
2 years ago
A certain pet store has only cats and dogs. the ratio of the number of cats to the number of dogs in the pet store is 2:3. 1/4 o
svp [43]
The first thing we must do for this case is to define variables.
 We have then:
 x: number of cats
 y: number of dogs
 We write the system of equations:
 x / y = 2/3
 (1/4) x + (1/2) y = 48
 Solving the system we have:
 x = 48
 y = 72
 The total number of animals is:
 x + y = 48 + 72 = 120
 Answer:
 
The total number of animals in the pet store is:
 
120
8 0
3 years ago
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