If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

Answer:

The exact population of Vermont in 2008 could have been around 618,000

Step-by-step explanation:

* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

Therefore, 618,000 might represent the actual population of Vermont in 2008

Answer:

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

Step-by-step explanation:

Given:

Multiplication of 2x^2 – 3xy + y^2 and 2x – 4y

Multiplication refers to the product

(2x^2 – 3xy + y^2) (2x – 4y)

Expand the brackets

= 4x^3 - 8x^2y - 6x^2y + 12xy^2 + 2xy^2 - 4y^3

Combine like terms

= 4x^3 - 14x^2y + 14xy^2 - 4y^3

The result is

C. 4x^3 - 14x^2y + 14xy^2 - 4y^3

Quadratic equations find their application in various real-world scenarios such as: sports, bridges, projectile motion, the curvature of bananas, and so on.

Here are three images representing real-world instances of quadratics:

Example 1: A cyclist travels along a parabolic trajectory to leap over obstacles.

Example 2: A person throws a basketball towards the hoop, moving in a gently upward path described by a quadratic curve.

Example 3: A football player kicks the ball upward, which follows a quadratic path as it travels a distance.

Answer:

840

Step-by-step explanation:

As the arrangement matters, we apply the permutations formula to find the solution.

Permutations formula:

The count of possible arrangements of x items chosen from a total of n items is defined by this formula:

For this problem:

Jose occupies the first seat.

The other four can be arranged among the remaining 7 family members. Thus

Hence, the final answer is:

840

Answer:

A. C. E. F.

Which correspond to 2, 3, 5, and 6.

Step-by-step explanation:

Within geometry, exterior angles are defined as those angles formed between any side of a polygon and the extension of an adjacent side, as demonstrated in the diagram.

Observing the figure, angles 2 and 3 arise from a side of the triangle and a line extended from the following side. Likewise, angles 5 and 6 are created similarly. Thus, these four angles are classified as exterior angles.