Sandia Aerial Tram Albuquerque boasts one of the longest aerial trams in the world. The
tram transports people up to Sandia Peak. The table shows the
elevation of the tram at various times during a particular ride.
Minutes into the Ride
2
5
9
14
Elevation in Feet
7069
7834
8854
10,129
a. Write an equation for a function (linear, quadratic,
or exponential) that models the relationship between
the elevation of the tram and the number of minutes
into the ride. Justify your choice.
b. What was the elevation of the tram at the
beginning of the ride?
c. If the ride took 15 minutes, what was the elevation
of the tram at the end of the ride?

Part 1: x ≥ 17/9

Part 2: x is greater than or equal to seventeen ninths.

Part 3: using x= 3 and 4 respectively, the solution was verified

The complete statement related to this found on (ID: 2020133) is stated below:

Use the inequality to answer Parts 1-3.

-3(x - 2) ≤ one third

Part 1: Solve the inequality. Leave answer in terms of a whole number or reduced improper fraction.

Part 2: Write a verbal statement describing the solution to the inequality.

Part 3: Verify your solution to the inequality using two elements of the solution set.

Use a word processing program or handwrite your responses to Parts 1-3. Turn in all three responses.

Step-by-step explanation:

Part 1) The inequality: -3(x - 2) ≤ one third

-3(x - 2) ≤ ⅓

Multiply through by 3

-3(3)(x-2) ≤ 3(⅓)

-9(x-2) ≤ 1

Expand the bracket

-9x + 18 ≤ 1

Collect like terms

-9x ≤ 1-18

-9x ≤ -17

Divide through by coefficient of x (-9)

-9x/-9 ≤ -17/-9

When you divide an expression in inequality by a negative sign, the inequality sign changes

x ≥ 17/9

Part 2) the verbal statement of the solution:

x is greater than or equal to seventeen ninths.

Part 3) We would verify the solution to the inequality using two elements of the solution set greater than 17/9.

17/9 = 1.89

Let's use x= 3 and x = 4. As they are greater than 17/9

-3(x - 2) ≤ ⅓

When x= 3

-3(3 - 2) ≤ ⅓

-3(1) ≤ ⅓

-3 ≤ ⅓

This satisfies the solution of the inequality

When x= 4

-3(4 - 2) ≤ ⅓

-3(2) ≤ ⅓

-6 ≤ ⅓

This satisfies the solution of the inequality