91Ó°ÊÓ

For the following exercises, evaluate the expressions, writing the result as a simplified complex number. $$ \frac{4+i}{i}+\frac{3-4 i}{1-i} $$

Input the left-hand side of the inequality as a \(\mathrm{Y} 1\) graph in your graphing utility. Enter \(\mathrm{Y} 2=\) the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, 1:abs(. Find the points of intersection, recall ( \(2^{\text {nd }}\) CALC 5:intersection, 1st curve, enter, \(2^{\text {nd }}\) curve, enter, guess, enter). Copy a sketch of the graph and shade the \(x\) -axis for your solution set to the inequality. Write final answers in interval notation. $$ -\frac{1}{2}|x+2|<4 $$

For the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter \(\mathrm{Y} 2=\) the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, liabs ( Find the points of intersection, recall \((2^{\text { nd }}\) CALC 5:intersection, lst curve, enter, } \(2^{\text { nd }}\) curve, enter, guess, enter). Copy a sketch of the graph and shade the \(x\) -axis for your solution set to the inequality. Write final answers in interval notation. $$ -\frac{1}{2}|x+2|<4 $$

For the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter \(\mathrm{Y} 2=\) the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, liabs ( Find the points of intersection, recall \((2^{\text { nd }}\) CALC 5:intersection, lst curve, enter, } \(2^{\text { nd }}\) curve, enter, guess, enter). Copy a sketch of the graph and shade the \(x\) -axis for your solution set to the inequality. Write final answers in interval notation. $$ |4 x+1|-3>2 $$

Given these four points: \(A(1,3), B(-3,5), C(4,7)\) and \(D(5,-4),\) find the coordinates of the midpoint of line segments \(\overline{A B}\) and \(\overline{C D}\) .

Input the left-hand side of the inequality as a \(\mathrm{Y} 1\) graph in your graphing utility. Enter \(\mathrm{Y} 2=\) the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, 1:abs(. Find the points of intersection, recall ( \(2^{\text {nd }}\) CALC 5:intersection, 1st curve, enter, \(2^{\text {nd }}\) curve, enter, guess, enter). Copy a sketch of the graph and shade the \(x\) -axis for your solution set to the inequality. Write final answers in interval notation. $$ |4 x+1|-3>2 $$

A falling object travels a distance given by the formula \(d=5 t+16 t^{2} \mathrm{ft}\) , where \(t\) is measured in seconds. How long will it take for the object to traveled 74 \(\mathrm{ft}\) ?

Given these four points: \(A(1,3), B(-3,5), C(4,7)\) and \(D(5,-4),\) fi \(\mathrm{d}\) the coordinates of the midpoint of line segments \(\overline{A B}\) and \(\overline{C D}\).

If the profit equation for a small business selling \(x\) number of item one and \(y\) number of item two is \(p=3 x+4 y,\) find the \(y\) value when \(p=\$ 453\) and \(x=75\)

For the following exercises, evaluate the expressions, writing the result as a simplified complex number. $$ \frac{3+2 i}{1+2 i}-\frac{2-3 i}{3+i} $$