91Ó°ÊÓ

Solve: \(\sqrt{2 x+3}=2 x-3 .\) (Section 8.5, Example 4)

Find the distance between each pair of points. Express answers in simplified radical form and, if necessary, round to two decimal places. $$(-2 \sqrt{7}, 10) \text { and }(4 \sqrt{7}, 8)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$2+\sqrt{-4}=2-2 i$$

Find the distance between each pair of points. Express answers in simplified radical form and, if necessary, round to two decimal places. $$(-\sqrt{3}, 4 \sqrt{6}) \text { and }(2 \sqrt{3}, \sqrt{6})$$

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$ for the given values of \(a, b,\) and \(c .\) Where necessary, express answers in simplified radical form. \(a=2, b=9, c=-5\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 \pm 4 i}{2}=1 \pm 4 i$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I must have made an error when graphing this parabola because it is symmetric with respect to the \(y\) -axis

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$ for the given values of \(a, b,\) and \(c .\) Where necessary, express answers in simplified radical form. \(a=9, b=-12, c=4\)

The length of a rectangle is 3 meters longer than the width. If the area is 36 square meters, find the rectangle's dimensions. Round to the nearest tenth of a meter.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A horizontal line can intersect the graph of a function at more than one point.