Harvey flew south 300 miles. He changed planes and then flew east 500 miles. If he travels a straight path back home, how many miles will he fly? Round to the nearest mile.

583 miles

Step-by-step explanation:

Let's draw this out (see attachment).

The straight line path creates the hypotenuse of a right triangle with legs of lengths 300 and 500. So, we use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 300 and b = 500. Then:

300² + 500² = c²

90000 + 250000 = c²

340000 = c²

c = √340000 ≈ 583.1 ≈ 583 mi

Thus, the answer is 583 miles.

~ an aesthetics lover

1.30

step-by-step explanation:

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.