You are given two of the three unknowns; plug I = 2.25 and r = 0.03 (the decimal equivalent of 3%) into the formula I = Pr:

2.25 = P(0.03)

Solve for P:

P = 75

By definition, the slope of any line is \(\frac{change\: in\: y}{change\: in\: x}\).

The question asks you to determine the slope from two points on the graph, so divide the change in y between the two points given by the change in x between the two points given:

\(\frac{y_{1} − y_{2}}{x_{1} − x_{2}}=\frac{5 − 3}{5 − 1}=\frac{2}{4}\)

²⁄₄ = ¹⁄₂

By definition, the slope of any line is \(\frac{change\: in\: y}{change\: in\: x}\).

The question gives the slope of the line as ²⁄₃, which means that for every positive change of 2 in y, there is a positive change in x of 3.

The question asks you to determine the x-intercept, or where y = 0. You are given a point on the line, (−2, 2).

Use the point-slope form of a line, y = mx + b, set y to 0, m to ²⁄₃, and solve for x:

(0 − 2) = ²⁄₃(x + 2)

−2 = ²⁄₃x + ⁴⁄₃

−⁶⁄₃ = ²⁄₃x + ⁴⁄₃

−\(\frac{10}{3}\) = ²⁄₃x, x = −5. The x-intercept is (−5,0).

Since you are given the radii of both circles, you can find the area of both circles.

The radius of the smaller circle is 2, so the area is π(2)², or 4π.

The radius of the larger circle is 6, so the area is π(6)² = 36π.

Since the smaller circle is removed from the larger circle, simply subtract the area of the smaller circle from the area of the larger circle: 36π − 4π = 32π.

This question is asking you to determine a weighted average. To answer the question, first calculate the total number of TVs:

(2 × 5), (3 × 20), (4 × 15), and (5 × 10).

Next, add these values together and divide by the total number of houses (50):

\(\frac{(2 × 5) + (3 × 20) + (4 × 15) + (5 × 10)}{50}\)

\(\frac{10 + 60 + 60 + 50}{50}=\frac{180}{50}=3.6\)

Find the slope by putting 2x − 3y = 6 into the slope-intercept form (y = mx + b where m is the slope):

−3y = −2x + 6

y = ²⁄₃x − 2. The slope is ²⁄₃.

The formula for a circle is (x − a)² + (y − b)² = r², where (a, b) is the center of the circle and r is the radius of the circle.

The question gives you the equation of the circle as (x − 2)² + (y + 1)² = 4.

So, a is 2 and b is −1.

The center of the circle, (a, b), is (2, −1).

By definition, an isosceles triangle has a hypotenuse, c, and two legs, a and b,that are congruent.

Use the measure of the hypotenuse given in the problem (12), and the Pythagorean theorem, a² + b² = c², to determine the length of one of the legs.

Remember that a = b:

a² + a² = 12²

2a² = 144

a² = 72

a = \(\sqrt{72}\)

The \(\sqrt{72}\) can be reduced to 6√2.

Here, you must first solve the inequality:

x² − 3 ≤ 13

x² ≤ 16

Because a negative number squared will yield a positive result, you must consider both the positive and negative values of x.

x ≤ 4 and x ≥ −4. The greatest real value of x is if x = 4.