Exam 1: Preliminaries

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Refer to the following figure. Which points have negative y-coordinates? Refer to the following figure. Which points have negative y-coordinates?

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Factor the expression. Factor the expression.

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Find an equation of the circle with center at (a, a) and radius 3a.

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Use the intercept form of an equation of a line to find an equation of a line with the Use the intercept form of an equation of a line to find an equation of a line with the   -intercept 9 and the   -intercept 8. -intercept 9 and the Use the intercept form of an equation of a line to find an equation of a line with the   -intercept 9 and the   -intercept 8. -intercept 8.

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Find the real roots of the equation by factoring. Find the real roots of the equation by factoring.

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If the line passing through the points If the line passing through the points   and   is parallel to the line passing through the points   and   , what is the value of a? and If the line passing through the points   and   is parallel to the line passing through the points   and   , what is the value of a? is parallel to the line passing through the points If the line passing through the points   and   is parallel to the line passing through the points   and   , what is the value of a? and If the line passing through the points   and   is parallel to the line passing through the points   and   , what is the value of a? , what is the value of a?

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Perform the indicated operations and simplify the expression. Perform the indicated operations and simplify the expression.

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Find the coordinates of the points that are 5 units away from the origin and have a y-coordinate equal to -3.

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Factor the expression. Factor the expression.

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Rationalize the numerator of the expression. Rationalize the numerator of the expression.

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Find an equation of the line in general form that passes through the point (5, 2) and is perpendicular to the line 8x + 3y - 4 = 0.

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Use the fact that the Use the fact that the   to evaluate the expression without using a calculator.   Round the answer to the nearest thousandth. to evaluate the expression without using a calculator. Use the fact that the   to evaluate the expression without using a calculator.   Round the answer to the nearest thousandth. Round the answer to the nearest thousandth.

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Perform the indicated operations and simplify the expression. Perform the indicated operations and simplify the expression.

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Ivan wishes to determine which antenna he should purchase for his home. The TV store has supplied him with the information: Ivan wishes to determine which antenna he should purchase for his home. The TV store has supplied him with the information:   Ivan wishes to receive Channel 17 (VHF) that is located 20 mi east and 45 mi north of his home and Channel 38 (UHF) that is located 23 mi south and 33 mi west of his home. Which model will allow him to receive both channels at the least cost? (Assume that the terrain between Ivan's home and both broadcasting stations is flat.) Model __________ Ivan wishes to receive Channel 17 (VHF) that is located 20 mi east and 45 mi north of his home and Channel 38 (UHF) that is located 23 mi south and 33 mi west of his home. Which model will allow him to receive both channels at the least cost? (Assume that the terrain between Ivan's home and both broadcasting stations is flat.) Model __________

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Find the coordinates of the points that are Find the coordinates of the points that are   units away from the origin and have an x-coordinate equal to   . units away from the origin and have an x-coordinate equal to Find the coordinates of the points that are   units away from the origin and have an x-coordinate equal to   . .

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Determine whether the statement is true or false. Determine whether the statement is true or false.

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If a > b, then a - c < b - c.

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Factor the expression. Factor the expression.

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The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality   What is the largest diameter a ball bearing in the batch can have? Give your answer to two decimal places, if necessary. __________ inches What is the largest diameter a ball bearing in the batch can have? Give your answer to two decimal places, if necessary. __________ inches

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Find an equation of the line that is parallel to the x-axis and 7 units below it.

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