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Question;1.;Multiply;the first fraction by, and multiply;the second fraction by, to get;Since;the two fractions now have the same denominator, the numerators can be combined;This;fraction cannot be reduced any further.;2. The;quotient of two real numbers with different signs is;3. Simplify;the following expression;Move;the variables with the negative exponents to the opposite side of the fraction bar, and change those exponents;from negative to positive. This gives;Combine;like terms in the numerator and the denominator to get;Squaring;all of the terms in the numerator and the denominator then gives;4. Graph;the following equation;Substituting;x = 0 into the equation gives;The;point (0, 2) will be one point on the graph of this line.;Substituting;x = 3 into the equation gives;The;point (3, 4) will be another point on the line.;Plot;the two points and connect with a solid line. The graph looks like this;5. What;are the equation and slope of the y-axis?;The;y-axis is a vertical line, so its slope is;All;of the points on the y-axis have an x coordinate of 0, so the equation of the line is;6. Given;f(x) = 2x ? 8, find f(3).;Substitute;3 in place of x to get;7. Solve;the following inequality. Give each result in set notation and graph it;Dividing;through by 3 gives;Simplifying;then gives;The;solution in set notation is;The;graph looks like this;8. Solve;the following inequality. Write the solution in interval notation and graph it.;Convert;the inequality into a compound inequality;Subtracting;4 from each part gives;Dividing;through by 2 then gives;The;solution in interval notation is;The;graph of the solution set looks like this;9. Simplify;the following product.;Distributing;the -2t3u term through the parentheses gives;10. Simplify;the following expression fully;Multiplying the numerator and the;denominator by ab gives;Simplifying the terms then gives;11. Solve the equation 7(x + 5) = x ? 1;Distribute the coefficient of 7 on;the left side;Subtract x from both sides;Subtract 35 from both sides;Divide both sides by 6;12. Completely factor the following;expression: 16m4 ? 1.;This is the difference of two;squares, a2 ? b2, and can be factored as (a + b)(a ? b).;The last factor on the right side is;another difference of two squares, and can also be factored;The complete factorization is then;13. Write the numeral 0.0072 in scientific;notation.;Move the decimal three places to the;right, so that it follows the first non-zero digit;Then, since the decimal point was;moved three places to the right, add an exponent;of -3;14. Perform the indicated operation and;simplify completely.;The numerator of the first fraction;can be factored as;The denominator of the second;fraction can be factored as;Substituting these into the;expression gives;Cancelling the (x ? 5) terms from;the numerator and the denominator gives;Cancelling a y from the numerator and the denominator gives;Finally, dividing 6 by 2 leaves;15. Solve the following equation for r: d;= rt;Dividing both sides by t gives;16. Solve the system of equations given;below.;3x + y = 12;x ? y ? 2z = 10;2x + 3y + 5z = -7;Solving the first equation for y gives;Substituting this in place of y in;the second equation gives;Substituting for x and y in the;third equation gives;Substituting for x again then gives;Expanding terms and simplifying;gives;Multiplying through by 2 gives;With the value of z known, the value of x can be determined;Then;with the value of x known, the value;of y can be determined;17. Do the following two lines intersect?;Answer yes or no, together with the point of intersection;if any.;5x + 6y = -5.5;6x + 1.5y = -8.5;Rearranging the first equation into y = mx;+ b form gives;Rearranging the second equation into;the same form gives;The slope of the first line is -5/6.;The slope of the second line is -4. Since the;slopes of the two lines are;different, the two lines will intersect at some point.;Setting the right of each equation;equal gives;Multiplying;through by 12 then gives;Adding 11 to both sides gives;Substituting this into one of the;two equations for y gives;18. Compute the determinant;19. Compute the distance between the two;points and;20. Rationalize;the denominator of;To;rationalize the denominator, multiply both numerator and denominator by the conjugate of the denominator;Multiplying;the fractions and simplifying gives;21. The;volume (V) of a cylinder with radius;(r) and height (h) is given by V =?r2h.;Solve;this formula for r.

Paper#60865 | Written in 18-Jul-2015

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