Question

1. use structure joni climbed 230 feet up a hill and then rappelled down 300 feet into a valley. a. write an addition expression to represent the situation. b. evaluate the expression to determine how far joni was from where she started. 2. the temperature at 8:00 a.m. on a winter day was - 2°f. by noon, the temperature had increased by 28°f. should you add or subtract the absolute values to find the temperature at noon? write and evaluate an absolute - value expression to find the temperature at noon. 3. math on the spot andreas income from a lemonade stand was $28. supply expenses were $9. write and evaluate an addition expression to find andreas profit or loss.

Explanation:

1.

Step1: Identify the movements as integers

Climbing up is a positive - direction movement and climbing down is a negative - direction movement. Joni climbed 230 feet up (represented as + 230) and 300 feet down (represented as - 300).
The addition expression is $230+( - 300)$.

Step2: Evaluate the expression

Using the rule of adding a positive and a negative integer $a+( - b)=a - b$, we have $230+( - 300)=230 - 300=-70$.

Step1: Set up the expression

The initial temperature is - 2°F and it increased by 28°F. To find the temperature at noon, we need to add the increase to the initial temperature. The expression is $-2 + 28$.

Step2: Evaluate the expression

When adding a negative and a positive integer, we can think of it as subtracting the absolute - value of the negative integer from the positive integer. $-2+28 = 28 - 2=26$.

Step1: Set up the profit - loss expression

Profit is calculated as income minus expenses. Income is $28$ and expenses are $9$. The addition expression to find the profit is $28+( - 9)$ (since subtracting a number is the same as adding its additive inverse).

Step2: Evaluate the expression

Using the rule of adding a positive and a negative integer $a+( - b)=a - b$, we have $28+( - 9)=28 - 9 = 19$.

Answer:

The addition expression is $230+( - 300)$ and the result is - 70, which means Joni ended up 70 feet below her starting point.

2.