The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 x2 + b over a ti

Answer: step 1. property of equality through addition

step 2. property of equality through subtraction

step 3. property of equality through division

Detailed explanation:

Answer:

  (1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

  s = ∛V

and the surface area is given by...

  A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

  r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

  r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

  r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

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Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

Response: 8n

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Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

Answer:

Step-by-step explanation:

A survey of 8225 Americans included age data collection.

The mean age was recorded as 42, whereas the median was noted as 37.

This indicates median < mean.

When the mean exceeds the median, it suggests the presence of right skewness in the data.

In a symmetrical distribution, mean and median align. If there is a discrepancy, the distribution is skewed.

Consequently, with the mean > median, the data is skewed to the right.