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Theorem used: In any right triangle, if a and b are the legs and c is the length of the hypotenuse,...Given: The statement “The x-intercept of the line that passes through (−23,32) and the origin is...Given: The given statement is “f(c) is a relative maximum if (c,f(c)) is the highest point in some...Definitions used: The number i: The number i is defined such that i=−1 and i2=−1. To express roots...The statement is “The y intercepts of the graph of the function P(x)=5−2x3 is (5,0)”. Note that the...The following example disproves the given statement. Consider a logarithmic function y=log5x. Draw...The given statement is “If sinα>0 and cotα>0, then α is in the first quadrant”. Suppose that...Formula used: Basic trigonometric identities: sinx=1cscx, cscx=1sinxcosx=1secx,...In a triangle, if one measure is a side, then the other two possible measures are side and side,...

Given: The given statement is “For a system of two linear equations in two variables, if the graphs...Definitions used: 1) The standard equation of a parabola with vertex (h,k) and the vertical axis of...Given data: The given general term sequence is, 1,−2,3,−4,… (1) The nth term in the sequence is,...

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