A painter leans an 18 foot ladder against the house so that the base of the ladder is 4 feet away from the wall. Approximately how far up the side of the house does the ladder reach?

17.5ft

Step-by-step explanation:

Use Pythagorean theorem

A^2 + B^2 = c^2 where c is the hypotenuse

The ladder leaning against the wall is the hypotenuse.

4^2 + b^2 = 18^2

16 + b^2 = 324

324-16 = b^2

308 = b^2

B = 17.5ft

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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