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Brilliant_brown [7]
3 years ago
12

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 46°, a = 12, b = 11

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
6 0
*Hint: The Law of Sines is Sin A/a = Sin B/b = Sin C/c

In order to solve this equation, you will have to use this equation:

A= sin^(-1)[a sinB/b]
A= sin^ (-1) [12 (sin 46°) / 11]
A = sin^ (-1) [8.632077604/11]
A = sin ^(-1) [0.7847343276]
A = 51.69611349

Therefore, Sine A would be about 52°
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[Will mark as brainliest]
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:

f(f^{-1}(x)) = f^{-1}(f(x)) = x

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

4y^2 = x+3

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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2 years ago
Line r and m are parallel. Find the value of x.
vladimir2022 [97]

Answer:

Answer:

10x-3=7x+45 corresponding angle

10x-7x=45+3

3x=48

x=48/3=16

value of x is 16.

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2 years ago
A real estate agent earns 2.4% on the sale of a house priced at $89,950.
juin [17]

Answer:

$2158.8

Step-by-step explanation:

x/89,950= 2.4/100

89,950(2.4)= 215880

215880/100 gets you 2158.8. hope this helped

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Step-by-step explanation:

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v = w - 20

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