PLEASE HELP ME ASAP :( Solve for a.
= ✓ [?]
a
Enter the number that goes
beneath the radical symbol.
Enter

Answer that goes in the box = 28

Explanation:

We have a white triangle shown as the empty space between the green squares.

This right triangle has the following sides:

Use the Pythagorean Theorem to solve for 'a'

a^2 + b^2 = c^2

a^2 + 6^2 = 8^2

a^2 + 36 = 64

a^2 = 64 - 36 subtract 36 from both sides

a^2 = 28

a = sqrt(28) apply the square root to both sides

Optionally we can simplify like so

a = sqrt(28)

a = sqrt(4*7)

a = sqrt(4)*sqrt(7)

a = 2*sqrt(7)

But this would not fit the answer format your teacher has provided. So we'll stick to sqrt(28) as the final answer.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.