91影视

Given that the following coordinates are the vertices of a rectangle, prove that this truly is a rectangle by showing the slopes of the sides that meet are perpendicular. \((-1,1),(2,0),(3,3),\) and \((0,4)\)

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. $$Y_{1}=\frac{3 x+5}{4} \text { Round your answer to the nearest thousandth.}$$

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 $$ |x+2|-5<2 $$

A formula for the normal systolic blood pressure for a man age \(A\) , measured in mm Hg, is given as \(P=0.006 A^{2}-0.02 A+120 .\) Find the age to the nearest year of a man whose normal blood pressure measures 125 mm Hg.

A man drove 10 \(\mathrm{mi}\) directly east from his home, made a left turn at an intersection, and then traveled 5 \(\mathrm{mi}\) north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

A man drove 10 mi directly east from his home, made a left urn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

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. $$ |x+2|-5 < 2 $$

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

The cost function for a certain company is \(C=60 x+300\) and the revenue is given by \(R=100 x-0.5 x^{2} .\) Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of \(x\) (production level) that will create a profit of \(\$ 300\) .

The slope for a wheelchair ramp for a home has to be \(\frac{1}{12} .\) If the vertical distance from the ground to the door bottom is 2.5 \(\mathrm{ft}\) , find the distance the ramp has to extend from the home in order to comply with the needed slope.