The total square footage of mini storage units being rented in a city is graphed to forecast future demand. The scatter plot has

Let the three consecutive even integers representing the sides of triangle PQR be defined as x, (x + 2), and (x + 4). Given that the perimeter of triangle PQR equals 42 cm.

Answer: To remove fractions prior to solving, each term in the equation must be multiplied by .

Step-by-step explanation:

Consider the given expression:

It is essential to simplify this before attempting to solve it.

Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.

Break down the denominators into their prime components:

Select , as it possesses the greatest exponent. Thus:

Ultimately, to remove the fractions before solving, multiply both sides by 4:

Answer:

The 10th term in the geometric progression is 29.

Step-by-step explanation:

Given: In a geometric series, [T3 = 18] and [T6 = 486].

To find: The term [T10]?

Solution:

A geometric sequence takes the form [a, ar, ar^2,...]

Where, a represents the first term, and r denotes the common ratio.

The nth term is expressed as [Tn = a * r^(n-1)]

From the information provided: [T3 = a * r^2 = 18]

And [T6 = a * r^5 = 486]

By dividing the second equation by the first:

[(a * r^5) / (a * r^2)] = 486 / 18

[r^3 = 27]

Taking the cube root provides: r = 3.

Inserting r into one of the equations allows us to solve for a.

Substituting r gives: [T3 = a * r^2 = 18]

Thus, the first term is a = 2, and the common ratio is r = 3.

The 10th term in the geometric progression is computed as:

[T10 = a * r^(10-1)]

[Thus, T10 = 29.]

This is due to the distinct properties of logarithms in comparison to algebra. The expression log(3x - 1) is interpreted as log 3x divided by log 1. If we proceed with rearranging and solving for x, we arrive at: log(3x - 1) = log28, log 3x/log 1 = log 28, resulting in log 3x being equal to log 28 multiplied by log 1 which equals 0. Thus, 3x = 10⁰ = 1, leading to 3x = 1 and x = 1/3. Therefore, it follows that 3x - 1 equals 3(1/3) - 1 = 0.

Among the given options, number 3 is accurate. A line is classified as an undefined term since it represents something that lacks width or depth, yet it can extend infinitely in both directions, indicated by arrowheads.