Scott is using a 12 foot ramp to load furniture into the back of a moving truck. if the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck

A 12 feet ramp is used to load stuff into the truck which is at a height of 3.5 feet from ground.

The ramp forms a Right triangle with ground and height of truck.

In the Right triangle, hypotenuse is 12 feet and height is 3.5 feet. We need to find horizontal base of right triangle.

We can use Pythagorean theorem that is given by :-

(Hypotenuse)² = (Base)² + (Height)²

(12)² = (Base)² + (3.5)²

144 = (Base)² + 12.25

(Base)² = 144 - 12.25

(Base)² = 131.75

(Base) = √131.75

So, horizontal distance is 11.48 feet.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

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