To solve this problem, recall that \(\frac{n^{x}}{n^{y}}\) = n^x−y.

Since it is given in the problem that \(\frac{n^{x}}{n^{y}}\) = n², you can conclude that n^x−y = n² and thus x − y = 2.

The key to solving this problem is remembering that the triangle inequality states that no one side of a triangle can be greater than the sum of the other two sides.

Thus the third side of the triangle in the problem cannot be greater than the sum of the other two sides, 4.7 and 9, which is 13.7.

Of the answer choices, only 14 is too large to be a possible value for the third side of the triangle.

To find the distance between two points (x₁, y₁) and (x₂, y₂), you can use the distance formula, which is d =\(\sqrt{(x_{2} − x_{1})^{2} + (y_{2} − y_{1})^{2}}\). The length of the line segment that has endpoints (−3,4) and (5,−6) will equal the distance between points (−3,4) and

To solve this problem, you need to know that the equation of a circle with center (h,k) and radius r is (x−h)² +(y−k)² = r².
Therefore, the center of the circle in the problem,
(x − 3)² + (y + 3)² = 4, is (3,−3).

To find the solution set of x+2>−4, first solve for x by subtracting 2 from both sides.

The result is x > −6. Thus the solution set is {x : x > −6).

To find the slope of the line between any two points (x₁, y₁) and (x₂, y₂), you can use the equation \(\frac{(y_{2} − y_{1})}{(x_{2} − x_{1})}\).

Therefore, when you have the points (3,7) and (4,−8) it follows that the slope of the line joining these points is \(\frac{(−8 − 7)}{(4 − 3)}=\frac{-15}{1}\) , or −15.

If a rectangular parking lot has a length, l, that is 3 feet longer than its width, w, then l = 3+w, or w = l −3.

The area of a rectangle is equal to its length times it width, or A = lw. Since the area of this parking lot is 550, lw = 550. Substituting (l − 3) for
550 = l(l − 3) =
550 = l² − 3l
l² − 3l − 550 = 0.
To solve for l, factor the quadratic equation to get (l + 22)(l − 25) = 0, making l = −22 or l = 25.

Since negative values for length do not make sense in this context, the length is 25.

The diagonals of a rhombus intersect at their midpoints and form right angles as shown below.

Since the diagonals meet at their midpoints and form right angles, they form a right triangle with legs ¹²⁄₂ = 6 and ³²⁄₂= 16. To find the length of a side of the rhombus, you can simply use the Pythagorean Theorem and solve where the side of the rhombus, s, is the hypotenuse: s² = 6² + 16² = 292; s is approximately equal to 17.09.

For a certain quadratic equation ax² + bx + c = 0, if x = ^a⁄_b is a solution, then a possible factor would be (bx −a).

Since two solutions for ax² + bx + c = 0 are x = ³⁄₄ and x = −²⁄₅, then possible factors are (4x − 3) and (5x + 2).

The height, h, can be found using the Pythagorean Theorem (c² = a² + b²):
5² = 3² + h²
25 = 9 + h²
h² = 16, or h = 4.
Thus, when you multiply the base of the parallelogram by its height, the area of the parallelogram is 9 × 4 = 36.