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Starting with the standard form of an equation \(A x+B y=C,\) solve this expression for \(y\) in terms of \(A, B, C,\) and \(x .\) Then put the expression in slope-intercept form.

A person has a garden that has a length 10 feet longer than the width. Set up a quadratic equation to find the dimensions of the garden if its area is 119 \(\mathrm{ft}^{2}\) . Solve the quadratic equation to find the length and width.

For the following exercises, use your graphing calculator to input the linear graphs in the \(\mathrm{Y}=\) graph menu. After graphing it, use the \(2^{\text { nd }}\) CALC button and l:value button, hit ENTER. At the lower part of the screen you will see 鈥渓eft bound?鈥� and a blinking cursor on the graph of the line. Move this cursor to the left of the \(x\)-intercept, hit ENTER. Now it says 鈥渞ight bound?鈥� Move the cursor to the right of the \(x\)-intercept, hit ENTER. Now it says 鈥済uess?鈥� Move your cursor to the left somewhere in between the left and right bound near the \(x\)-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the 鈥渮ero鈥� to the \(y\)-value. Use this to find the \(x\)-intercept. Note: With linear/straight line functions the zero is not really a 鈥済uess,鈥� but it is necessary to enter a 鈥済uess鈥� so it will search and find the exact \(x\)-intercept between your right and left boundaries. With other types of functions (more than one \(x\)-intercept), they may be irrational numbers so 鈥済uess鈥� is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. $$\mathrm{Y}_{1}=4 x-7$$

For the following exercises, evaluate the expressions, writing the result as a simplified complex number. $$ \frac{(1+3 i)(2-4 i)}{(1+2 i)} $$

Note: With linear/straight line functions the zero is not really a "guess," but it is necessary to enter a "guess" so it will search and find the exact \(x\) -intercept between your right and left boundaries. With other types of functions (more than one \(x\) -intercept), they may be irrational numbers so "guess" is more appropriate to give it the correct limits to find a very close approximation between the left nd right boundaries. $$ Y_{1}=4 x-7 $$

Abercrombie and Fitch stock had a price given as \(P=0.2 t^{2}-5.6 t+50.2,\) where \(t\) is the time in months from 1999 to \(2001 .(t=1 \text { is January } 1999) .\) Find the two months in which the price of the stock was \(\$ 30 .\)

The formula for the circumference of a circle is \(C=2 \pi r\) . Find the circumference of a circle with a diameter of 12 in. (diameter \(=2 r ) .\) Use the symbol \(\pi\) in your final answer.

Note: With linear/straight line functions the zero is not really a "guess," but it is necessary to enter a "guess" so it will search and find the exact \(x\) -intercept between your right and left boundaries. With other types of functions (more than one \(x\) -intercept), they may be irrational numbers so "guess" is more appropriate to give it the correct limits to find a very close approximation between the left nd right boundaries. \(\mathrm{Y}_{1}=\frac{3 x+5}{4}\) Round your answer to the nearest thousandth.

Suppose that an equation is given \(p=-2 x^{2}+280 x-1000,\) where \(x\) represents the number of items sold at an auction and \(p\) is the profit made by the business that ran the auction. How many items sold would make this profit a maximum? Solve this by graphing the expression in your graphing utility and finding the maximum using \(2^{\text { nd }}\) CALC maximum. To obtain a good window for the curve, set \(x[0,200]\) and \(y[0,10000].\)

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