Perl made the following conjecture.
the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8.

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You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.

Kevin's bank offered him a 4.5% interest rate for his mortgage. if he purchases 3 points, what will be his new rate?