10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:
{y = -2 x - 2
{16 x + 6 = -2
in the second equation, look to solve for x:
{y = -2 x - 2
{16 x + 6 = -2
subtract 6 from both sides:
{y = -2 x - 2
{16 x = -8
divide both sides by 16:
{y = -2 x - 2
{x = -1/2
substitute x = -1/2 into the first equation:
{y = -1
{x = -1/2
collect results in alphabetical order:
answer: {x = -1/2 , y = -1
answered: Guest
(b) 240
step-by-step explanation:
first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.
pythagorean theorem formula:
a^2 + b^2 = c^2
(x - 20)^2 + (x - 40)^2 = x^2
x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2
x^2 -120x + 2000 = 0
(x - 100)(x - 20) = 0
x - 100 = 0 or x - 20 = 0
x = 100 or x = 20
we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.
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