Jake plans to use a ramp to make it easier to move a piano out of the back of his truck. the back of the truck is 83 centimeters tall and the ramp is 158 centimeters long. what is the horizontal distance from the end of the ramp to the back of the truck?
round your answer to the nearest tenth of a centimeter.

134.4 centimeters

Step-by-step explanation:

This question is asking us for a missing leg on the triangle, lets call it x. Using the Pythagorean theorem (a²+b²=c²), we can figure out what value is missing (either a or b, they are interchangeable).

replace the values in the equation.

83²+x²=158²

get rid of the exponents.

6,889+ x² = 24,964.

subtract 6,889 from 24,964.

x²=18,075.

find the square root on both sides of the equation.

x=134.4432966.

I am assuming you want this rounded to the nearest tenth.

134.4 is your answer.

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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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