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3 years ago

Solve this system. Write your answer as an ordered pair. -5x + y = -3 3x - 8y = 24

Mathematics

1 answer:

Ivanshal [37]3 years ago

7 0

Hello there, this is how we will solve your problem.\

here is the equation you gave us.

${\huge{\boxed{\mathbb{EQUATION}}}$

$\begin{bmatrix}-5x+y=-3\\ 3x-8y=24\end{bmatrix}$

we can isolate $x$ and say $x=\frac{-3-y}{5}$

Now here is our equation, $\begin{bmatrix}3\left(-\frac{-3-y}{5}\right)-8y=24\end{bmatrix}$ After we simplify it we get $\begin{bmatrix}\frac{9-37y}{5}=24\end{bmatrix}$ , solve this and we get that $y=-3$ , Before we said $x$ equals $-\frac{-3-y}{5}$ , So now we can plug in our value that $y$ equaled, and now we have $\frac{-3-(-3)}{5}$ . Two negatives equal a positive and we get that $x=0$ .

_________________

$y=-3$

$x=0$

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Aleks04 [339]

The answer is: $f^{-1} = 4x^2-3,\quad\text{for } x \leq 0$

The inverse of a function $f(x)$ is another function, $f^{-1}(x)$ , with the following property:

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In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, $f(x)=2x$ , and one that halves it: $f(x)= \frac{x}{2}$ . Their composition is clearly the identity function $f(x)=x$ , since you consider "twice the half of something", or "half the double of something".

In general, to invert a function $y=f(x)$ , you have to solve the expression for $x$ , writing an expression like $x = g(y)$ . If you manage to do so, then $g$ is the inverse of $f$ .

In your case, you have

$f(x) = y = -\frac{1}{2}\sqrt{x+3}$

Multiply both sides by $-2$ to get

$-2y = \sqrt{x+3}$

Square both sides to get

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Finally, subtract 3 from both sides to get

$x = 4y^2 - 3$

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

$f^{-1}(x) = 4x^2 - 3$

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain $b \in B$ such that there exists $a \in A : f(a)=b$ . So, we need the range of $f(x)$ .

We know that the range of $g(x)=\sqrt{x}$ is $[0,\infty)$ . When you transform it to $g(x)=\sqrt{x+3}$ you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times $-\frac{1}{2}$ you affect both extrema of the range, turning it into $(-\infty,0]$ , which you can simply write as $x \leq 0$

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Answer:

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Step-by-step explanation:

To find the sum of all the interior angles in a regular polygon, us this formula, where n is the number of sides: (n-2)*180

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Now we have the sum of all the angles. But we aren't done yet! We have to divide this value by the number of sides to find the measure of one angle.

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