Arepairman leans the top of a 9ft ladder against the top of a stone wall. the base of the ladder is 5.5ft from the wall. about how tall is the wall? round to the nearest tenth of a foot.

Using the Pythagorean theorem:

a^2 + b^2 = c^2

a and b are the sides and c is the hypotenuse.

The length of the ladder would be the hypotenuse and the base away from the wall would be one side.

So now we have:

5.5^2 + b^2 = 9^2

Simplify:

30.25 + b^2 = 81

Subtract 30.25 from each side:

b^2 = 81 - 30.25

b^2 = 50.75

Take the square root of both sides:

b = √50.75

b = 7.123

Rounded to the nearest tenth of a foot = 7.1 feet.

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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step-by-step explanation:

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)