John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations? (Hint: Draw a picture or use a number line.)

Question

Desmos Scientific Calculator

(1 point)
Responses

-43 feet
-43 feet

-205 feet
-205 feet

205 feet
205 feet

43 feet

Answer 1

To find the distance between the elevations of the bridge and the point where the rock sinks below the water's surface, we can visualize the situation as follows:

1. Elevation of the bridge: The bridge is 124 feet above the river's surface, so we can represent this as +124 feet.
2. Depth of the rock below the water: The rock sinks 81 feet below the water's surface. Since the water's surface is at 0 feet, sinking below it means we go into negative elevation. Therefore, the depth below the water is represented as -81 feet.

Now, to find the distance between these two points, we can calculate it as follows:

• Bridge elevation: +124 feet (above the river surface)
• Rock depth: -81 feet (below the water's surface)

The total difference in elevation between the bridge and the rock is calculated by:

\[ \text{Distance} = \text{Elevation of bridge} - \text{Depth of rock} \] \[ \text{Distance} = 124 - (-81) = 124 + 81 = 205 \text{ feet} \]

Thus, the distance between the elevations is 205 feet.

So the correct response is 205 feet.

Answer 2

Find the sum of -12 and -36.

Desmos Scientific Calculator

(1 point)
Responses

-24
-24

24
24

48
48

-48

Answer 3

To find the sum of -12 and -36, you add the two negative numbers together:

\[ -12 + (-36) = -12 - 36 = -48 \]

Therefore, the sum of -12 and -36 is -48.

The correct response is -48.