A brace for a shelf has the shape of a right triangle. Its hypotenuse is 12 inches long and the two legs are equal in length. How long are the legs of the triangle? The legs of the triangle both have a length of (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Find the center and radius of the circle represented by the equation below. \[ (x-4)^{2}+(y+9)^{2}=289 \] Answer Attempt 1 out of 5 Center: Radius:

Given \( \mathbf{v}=-9 \mathbf{i} \) and \( \mathbf{w}=-\mathbf{j} \) (a) find the dot product \( \mathbf{v} \cdot \mathbf{w} \) (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither.

Use the given vectors to find \( \mathbf{v} \cdot \mathbf{w} \) and \( \mathbf{v} \cdot \mathbf{v} \). \[ \begin{array}{l}\mathbf{v}=-7 \mathbf{i}-3 \mathbf{j}, \mathbf{w}=-9 \mathbf{i}-5 \mathbf{j} \\ \mathbf{v} \cdot \mathbf{w}=78 \text { (Simplify your answer.) } \\ \mathbf{v} \cdot \mathbf{v}=\square \text { (Simplify your answer.) }\end{array} \text { \$ } \]

Find the center and radius of the circle represented by the equation below. \[ (x-4)^{2}+(y-8)^{2}=25 \] Answer Attempt 1 out of 5 Center: \( (\square, \square \) Radius:

lengths is a right triangle. Justify your answe receive full credit. 14.60 feet, 80 feet, 100 feet