Step-by-step explanation:
Let's say the coordinates of Q are (h, k).
The slope of PQ is perpendicular to the tangent line.
(k − 2) / (h − 2) = -⅓
3(k − 2) = -(h − 2)
3(k − 2) = 2 − h
Solving for h:
h = 2 − 3(k − 2)
h = 2 − 3k + 6
h = 8 − 3k
(2, 2) is a point on the circle, so:
(2 − h)² + (2 − k)² = r²
Substituting:
9 (k − 2)² + (2 − k)² = r²
10 (k − 2)² = r²
The equation of the circle is:
(x − 8 + 3k)² + (y − k)² = 10 (k − 2)²
Without more information, there are an infinite number of possible solutions. For example, if k = 1, the equation of the circle is:
(x − 5)² + (y − 1)² = 10
Answer :
It would be -15 and -3
<h3>
Answer: 10.68% decrease (choice F)</h3>
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Explanation:
A decrease of 23% means that you still retain 77% of the original value. This is because 23% + 77% = 100%. Or you could write it like this: 100% - 23% = 77%. The 77% then converts to the multiplier 0.77
An increase of 16% will involve the multiplier 1.16 in which we can think of it like 1.16 = 1 + 0.16 = 100% + 16%
Now we'll multiply those two decimal values mentioned:
0.77*1.16 = 0.8932
This result is smaller than 1, so we have a percent decrease of some sort. Subtract it from 1 to find the decimal form of the percent decrease
1 - 0.8932 = 0.1068
Lastly, move the decimal point 2 spots to the right:
0.1068 converts to 10.68%
We have a decrease of 10.68% overall when combining the initial 23% decrease followed by the 16% increase.
It turns out the order doesn't matter, and we could do the 16% increase first then the 23% decrease next. The key as to why the order doesn't matter all relies on the fact that multiplication can be done in any order. As you can probably guess, this process can be extended for as many percentage increases and/or decreases that you want.
<span>See examples for the method to solving literal equations for a given variable: Solve A = bh for b. Since h is multiplied times b, you must divide both sides by h in order to isolate b. Since (c+d) is divided by 2, you must first multiply both sides of the equation by 2</span>
You first need to cross multiply to get 8x+8=6x^2-6. Then make the function into 6x^2-8x-14=0 which can be simplified into 3x^2-4x-7=0 by dividing the equation by 2. Then you must split the middle(-4x) to get 3x^2+3x-7x-7=0. This simplifies to 3x(x+1)-7(x+1)=0 and then to (3x-7)(x+1)=0. From here you just solve for each root which you will find are x= -1 and 7/3
