If you place a 10-foot ladder against the top of a 6-foot building, how many feet will the bottom of the ladder be from the bottom of the building?

8 feet

Step-by-step explanation:

Draw a right triangle and label the sides using the given information. (Drawing below) Use pythagorean theorem to find the missing length:

a^2 + b^2 = c^2

(building)^2 + (missing piece)^2 = (ladder)^2

6^2 + x^2 = 10^2

36 + x^2 = 100. subtract 36

x^2 = 64. square root of both sides

x = 8

d. is the correct answer

step-by-step explanation:

{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