Let the vector $\vec{u}=\langle 1,2\rangle$ and $\vec{v}=\langle 13,7\rangle$. Find $\vec{u}+\vec{v}$. Find the magnitude of the sum vector and its direction relative to east.

Use a calculator to approximate the given value to four decimal places. $\tan 23^{\circ}$

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. $10,49,50$

The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value. $t=757, s=595$

Solve the right triangle. Round decimals to the nearest tenth. Triangle EFD , EF = 2,FD= 6, $\angle F$= 90 $^{\circ}$

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. $17,144,145$

The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value. $r=35, t=37$

Use a calculator to approximate the given value to four decimal places. $\cos 36^{\circ}$

Draw vector $\overrightarrow{P Q}$ in a coordinate plane. Write the component form of the vector and find its magnitude. Round decimals to the nearest tenth. $P(-6,3), Q(6,-2)$

Sketch the figure that is described. Find the requested length. Round decimals to the nearest tenth. The diagonal of a square is 26 inches. Find the length of a side.

Solve the right triangle. Round decimals to the nearest tenth. Triangle EFD , EF = 7,FD= 7, $\angle F$= 90 $^{\circ}$

A segment has endpoints at A(6,-4) and B(12,9). Find the images of the segment under two dilations, one with scale factor $\frac{1}{3}$ and center $(0,0)$, and the other with scale factor $\frac{1}{2}$ and center $(0,0)$. Then tell whether the two image segments are parallel.

Solve the right triangle. Round decimals to the nearest tenth. Triangle EFD , EF = 20,FD= 21, $\angle F$= 90 $^{\circ}$

The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value. $s=20, t=101$