Eva sees a dolphin $3$ . $2$ meters below sea level and a bird $\frac{47}{10}$ meters above sea level. $\newline$ Which $2$ of the following expressions represents the vertical distance between the dolphin and the bird? $\newline$ Choose $2$ answers: $\newline$ (A) $\left|\frac{47}{10}+3.2\right|$ $\newline$ (B) $\left|-3.2-\frac{47}{10}\right|$ $\newline$ (C) $\left|3.2-\frac{47}{10}\right|$

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Algebra 1

Transformations of absolute value functions: translations and reflections

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Q. Eva sees a dolphin

3

2

meters below sea level and a bird

\frac{47}{10}

meters above sea level.

\newline

Which

2

of the following expressions represents the vertical distance between the dolphin and the bird?

\newline

Choose

2

answers:

\newline

(A)

\left|\frac{47}{10}+3.2\right|

\newline

(B)

\left|-3.2-\frac{47}{10}\right|

\newline

(C)

\left|3.2-\frac{47}{10}\right|

Convert to Decimal: To find the vertical distance between two points, we subtract the lower point's position from the higher point's position. The bird is above sea level, and the dolphin is below sea level, so we subtract the dolphin's position from the bird's position.
Subtract Positions: First, we need to convert the bird's position to a decimal to make the subtraction easier. The bird is $(\frac{47}{10})$ meters above sea level, which is $4.7$ meters.
Calculate Vertical Distance: Now, we subtract the dolphin's position from the bird's position. Since the dolphin is below sea level, its position is negative. So we have $4.7 - (-3.2) = 4.7 + 3.2$ .
Take Absolute Value: Performing the addition, we get $4.7 + 3.2 = 7.9$ meters. This is the vertical distance between the dolphin and the bird.
Check Given Options: The vertical distance is a positive value, so we need to take the absolute value of our expression to ensure it's positive. The correct expressions for the vertical distance are $|4.7 + 3.2|$ and $|-3.2 - 4.7|$ , which both simplify to $|7.9|$ .
Check Given Options: The vertical distance is a positive value, so we need to take the absolute value of our expression to ensure it's positive. The correct expressions for the vertical distance are $|4.7 + 3.2|$ and $|-3.2 - 4.7|$ , which both simplify to $|7.9|$ .Now, let's check the given options to see which ones match our correct expressions. Option A is $|(47/10) + 3.2|$ , which is correct because it simplifies to $|4.7 + 3.2|$ . Option B is $|-3.2 - (47/10)|$ , which simplifies to $|-3.2 - 4.7|$ , and is also correct. Option C is $|3.2 - (47/10)|$ , which simplifies to $|3.2 - 4.7|$ , and does not represent the vertical distance correctly because it would give a negative result before taking the absolute value.