Jean S.

Middle, High School, and College Professor

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Geometry

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Question:

Find the dimensions of the rectangle that has a length 3 meters more that its width and a perimeter equal in value to its area?

Jean S.

Answer:

Let L be the length and W be the width of the rectangle. L = W +3 Perimeter = 2L + 2W = 2(W +3) + 2W = 4W + 6 Area = L W = (W + 3) W = W^2 + 3W Area and perimeter are equal in value; hence W^2 + 3 W = 4W +6 Solve the above quadratic equation for W and substitute to find L W = 3 and L + 6

Statistics

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Question:

For the logical statement identify the converse, inverse, and contrapositive. If it rains, then school is closed.

Jean S.

Answer:

P= It rains Q= schools is closed: If p then q Converse: If q then p: If school is closed, then it is raining Inverse: Not p then not q: If it is not raining then school is not closed Contrapositive: If not q then not p: If school is not closed, then it is not raining

Algebra

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Question:

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Jean S.

Answer:

Multiply by the factors (-15x-10) + (-x+3)= (-16x-20)+13 Combine like terms (-16x -7) =(-16x-7) Both sides are equal so x equals all solutions

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