While flying a kite, 400 ft of string was let out. the string ,when pulled tight, formed a 40 angle with the ground .what was the approximate height of the kite

257 ft

Step-by-step explanation:

You know based upon soh that sin=opp/hyp

So drawing a right triangle with a hypotenuse of 400 ft and an angle of 40° with the ground, you can see that sin40=x/400

Multiply both sides to find your x value or height which is 257.

thats not a system of equations, that is a solution

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)