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iragen [17]
3 years ago
15

Find the center and the radius of the circle defined by the equation x^2-8x+y+12y+36=0

Mathematics
1 answer:
choli [55]3 years ago
3 0
Hello,
center is (4,-6)
radius=4
since
x^2-8x+y^2+12y+36=0\\

x^2-2*4x+16-16+y^2+2*6y+36=0\\

(x-4)^2+(y+6)^2=4^2




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Two pools are leaking, after 15 minutes pool A has leaked 2/3 gallon, after 20 minutes pool B has leaked 2/3 gallon. Which pool
shepuryov [24]

Answer:

Pool A.

Step-by-step explanation:

This can be solved through ratios. You would write it as \frac{gallons}{minutes} So, \frac{2/3}{15} for the first one, and \frac{2/3}{20} for the second. You might want to use a calculator for that part, but you could also change the gallons to cups, which gives you a much better number of 10.515. So, \frac{10.515}{15} = 0.701, and \frac{10.515}{20} = 0.52575 So, pool A is at a faster rate. If you want it in gallons per minute, it's by 0.01 (with the 1 repeating) gallons per minute. By cups, it's 0.17525 cups per minute.

(The reason I did not do this by cross multiplying and dividing ratios is because it gives you the exact same answer if you are finding it per one, as I am here with per one minute. You can do it this way, it just wastes a bit of time.)

6 0
3 years ago
Olivia goes shopping at the mall and buys a shirt that is on sale for 25% off. She also knows that the sales tax is 5%. If her f
Norma-Jean [14]

Answer:   The shirt originally cost 125 dollars.

Step-by-step explanation: The shirt on sale is 25% off. So first multiply 25 by 5 and you get 125. So 125 is the originall price. Her final cost is 25 dollars. Last step: 125 divided by 5 equals 25 dollars.

3 0
3 years ago
[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

4 0
3 years ago
3. Graph y=-4x² – 2 and its inverse. (1 point)
madam [21]

Function and its inverse was graphed.

<u>Step-by-step explanation:</u>

y = -4x²- 2

To find the inverse function of   y = -4x²- 2 we have to transform the formula to calculate  x in terms of y.

y = -4x²- 2

-4x² = y - 2

x = √(y-2) / -4

Now we can change the letters to follow the convention that  x is the independent variable and  y is the function's value:

y = √(x-2) / -4

Now we have to draw the graph as,

It was side by side that is LHS is the function and the RHS is its inverse.

6 0
3 years ago
What is the area of the triangle
Ludmilka [50]
Wouldn't the formula be a×b/2?
4 0
3 years ago
Read 2 more answers
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