Recall that the general form of the equation of a circle centered at the origin is:

x² + y² = r²

We know that the radius of our circle is five. Therefore, we know that the equation for our circle is:

x² + y² = 5²

x² + y² = 25

Now, the question asks for the positive y-coordinate when x = 2.  To solve this, simply plug in for x:

2² + y² = 25

4 + y² = 25

y² = 21

y = ±√(21)

Since our answer will be positive, it must be √(21).

The equation for a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

We can eliminate (x+3) +(y+2) = 4 and (x+3)² + (y+2)² = 64. The first equation does not square the terms in parentheses, and the second refers to a center of (-3,-2) rather than (3,2).

Drawing the line y = -2 and a point at (3,2) for the center of the circle, we see that the only way the line could be tangent to the circle is if it touches the bottom-most part of the circle, directly under the center. The point of intersection will be (3,-2). From this, we can see that the distance from the center to this point of intersection is 4 units between (3,2) and (3,-2). This means the radius of the circle is 4.

Use the center point and the radius in the formula for a circle to find the final answer: (x - 3)² + (y - 2)² = 16

To solve the inequality, the first step is to add  to both sides:

The second step is to divide both sides by :

To graph the inequality, you draw a straight number line. Fill in the numbers from  to infinity. Infinity can be designated by a ray. Be sure to fill in the number , since the equation indicated greater than OR equal to.

The graph should look like:

If we plug the points  and  into each equation, we find that these points work only in the equation . This circle has a radius of  and is centered at .

The key here is to look for the line whose slope is the negative reciprocal of the original slope.

In this case,  is the negative reciprocal of .

Therefore, the equation of the line which is perpendicular to the original equation is:

The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.

The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of  .  

Alternatively, one could set up the equation,

  and factor, use the quadratic equation, or graph this on a calculator to find the root. 

If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,

.

In our case . So we need factors of  that when added together give us .

Thus the following factoring would solve this problem.

Then set each binomial equal to zero and solve for v.

Since we can't have a negative power our answer is .

The  inside the argument has the effect of shifting the graph  units to the left. This can be easily seen by graphing both the original and modified functions on a graphing calculator.  

To answer this question, we need to correctly identify where to plug in our given values and solve for .

Points on a graph are written in coordinate pairs. These pairs show the  value first and the  value second. So, for this data:

 means that  is the  value and  is the  value.

We must now plug in our  and  values into the original equation and solve. Therefore:

We can now begin to solve for  by adding up the right side and dividing the entire equation by .

Therefore, the value of  is .