Acarp is swimming approximately 8 1/4 feet beneath the water’s surface, and a sunfish is swimming approximately 3 1/2 feet beneath the water’s surface. which fish is swimming farther beneath the water’s surface?

The carp is swimming farther beneath the water's surface.

Step-by-step explanation:

The water surface is considered the number 0 in the number line. Positions below water's surface are considered negative.

The integer that represents the position of the carp is -8 1/4 feet or -8.25 feet.

The integer that represents the position of the sunfish is -3 1/2 feet or -3.5 feet.

In the number line we can see that carp postion is at the left most of the water surface, so the carp is swimming farther beneath the water's surface.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.