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On a set of steps, the first step from the base of the steps is labeled 111, the second is labeled 222, and so on. Each step has the same height. The table below shows the step number and step's height from the base of the steps.
Step number Height from the base (meters)
505050 101010
909090 181818
110110110 222222
Write an equation to describe the relationship between nnn, the step number, and hhh, the height from the base.

Sagot :

MrRoyal

The equation that describes the relationship between n, the step number, and h, the height from the base is [tex]\mathbf{h = 0.2n}[/tex]

The sets of step are given as:

Step number (n)       Height from the base (h)

        50                                 10

        90                                 18

        110                                 22

The above table represents a linear relationship.

So, we start by calculating the slope (m)

[tex]\mathbf{m = \frac{h_2 -h_1}{n_2 -n_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{18 - 10}{90 - 50}}[/tex]

[tex]\mathbf{m = \frac{8}{40}}[/tex]

Simplify

[tex]\mathbf{m = 0.2}[/tex]

The equation is then calculated as:

[tex]\mathbf{h = m(n -n_1) + h_1}[/tex]

So, we have:

[tex]\mathbf{h = 0.2(n -50) + 10}[/tex]

Expand

[tex]\mathbf{h = 0.2n -10 + 10}[/tex]

Evaluate like terms

[tex]\mathbf{h = 0.2n}[/tex]

Hence, the equation that describes the steps is [tex]\mathbf{h = 0.2n}[/tex]

Read more about linear equations at:

https://brainly.com/question/11897796

Answer:

h=0.2n

Step-by-step explanation:

I'm too lazy to do a step-by-step but this is correct on khan academy.

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