Triangle UVW is formed by the three squares G, H, and I: A right triangle UVW is shown. On the side UV of this triangle is a square. Inside the square is written Square G, Area equal to 81 square units. On the side VW of this triangle is another square. Inside the square is written Square H, Area equal to 144 square units. On the side UW of this triangle is another square. Inside the square is written Square I, Area equal to 225 square units. Which statement best explains the relationship between the sides of triangle UVW? (5 points) UV + VW = UW, because 81 + 144 = 225 (UV)2 + (VW)2 = (UW)2, because 152 + 92 = 122 (UV)2 + (VW)2 = (UW)2, because 81 + 144 = 225 UV + VW = UW, because 152 + 92 = 122

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.