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

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -