<span>Proportional reasoning is one of the biggest math ideas students will develop over the junior years. It applies to almost all areas of the curriculum, and is considered a critical concept for success in secondary math. If this helped, please hit the thank you button :)
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<u>Given</u>:
Given that the circle is graphed with center (-1,1)
We need to determine the equation of the circle.
<u>Radius</u>:
To determine the radius of the circle, let us simply count the number of units between the center point to any point on the circle.
Hence, from the figure, it is obvious that there are 5 units between the center and any point on the circle.
Thus, radius of the circle is 5 units.
<u>Equation of the circle:</u>
The standard form for the equation of the circle is given by

where the center is (h,k) and radius is r.
Substituting the center (-1,1) and r = 5 in the above formula, we get;


Thus, the equation of the circle is 
For x = ay - bz:
Add bz to both sides:
ay = x + bz
Divide a on both sides:
y = (x + bz)/a
For xy + yz = 10:
Distribute y from the left side:
y * (x + z) = 10
Divide by x + z:
y = 10/(x + z)
For (ab - ac)/z = x:
Multiply by z on both sides:
ab - ac = xz
Take out a from the left side:
a * (b - c) = xz
Divide by b - c on both sides:
a = xz/(b - c)
Five pieces can be selected in 1287 ways
Step-by-step explanation:
When the selection has to be made without considering the order of selection, combinations are used.
The formula for combination is:

Here
Total candies = n = 13
Candies to be selected = r = 5
Putting the values in the formula

Five pieces can be selected in 1287 ways
Keywords: Combinations, selection
Learn more about combinations at:
#LearnwithBrainly