What is the value of y? Express your answer in simplest radical form. The right triangle has the right angle at the bottom left. The base is labeled 12, and the vertical leg on the left is labeled x. The hypotenuse, slanting from top left to bottom right, is labeled y. The angle at the bottom right is marked 30 degrees. All sides are outlined in bold black lines.

Fill in each missing reason.Given: Prove:  Two parallel appearing horizontal lines, each ending in double-headed arrows, extend left and right across the image. A diagonal line with arrowheads at both ends crosses the parallel lines from the upper right to the lower left. This intersection forms three clearly labeled angles. Angle 1 is located above the top parallel line on the left side of the diagonal. Angle 2 is above the bottom parallel line, also on the left side of the diagonal. Angle 3 lies opposite angle 2, positioned below the bottom parallel line on the right side of the diagonal. All lines are solid black. Statements Reasons a. Given b. [answer1] c. [answer2] d. [answer3]  

In order to walk to school from your house, you walk 0.8 mi north and 0.5 miles east. What is the direct distance from your house to school?

On a coordinate plane, a line segment has end points at and .  What is the midpoint? ( [answer0] , [answer1] )  

Find the value of x.  The triangle is oriented with its apex pointing upward. An exterior angle labeled 118 extends horizontally from the left vertex. The interior angle at the bottom right is labeled 54, and the interior angle at the top vertex is labeled x. All sides are drawn with bold black lines.

Which angles are alternate interior angles? “Two horizontal parallel appearing lines are intersected by two diagonal lines slanted to the left. This setup creates four intersection points, while each intersection forms four angles. The angles are numbered 1 through 16, which are labeled as follows: Top-left intersection: angles 1 (top-left), 2 (top-right), 5 (bottom-right), 6 (bottom-left) Top-right intersection: angles 3 (top-left), 4 (top-right), 7 (bottom-right), 8 (bottom-left) Bottom-left intersection: angles 9 (top-left), 10 (top-right), 13 (bottom-right), 14 (bottom-left) Bottom-right intersection: angles 11 (top-left), 12 (top-right), 15 bottom-right), 16 (bottom-left)”

The length of is shown. What other length can you determine for this diagram?  The slanted quadrilateral FGDE is outlined in black. Side GD is at the top, and side FE is at the bottom. Diagonals DF and GE intersect at a right angle, marked by a small square at the center of the left quadrant. Diagonal DF is divided into two equal segments by diagonal GE, indicated by tick marks. The side DE is labeled 12. Other sides and segments are unlabeled,

Select the image below that represents the construction of an angle bisector.

Write an equation for the line parallel to y = –3x + 4 that contains P(1, 4).

In the figure below, , , and . Which pair of angles are supplementary angles? “Four black straight lines are connected to form three distinct X-shaped intersections, creating a continuous zigzagging path across the image. At the leftmost intersection, four angles are formed. Angle 1 is on the left of the x-intersection. Angle 2 is at the top. Angle 3 is on the right, directly opposite angle 1. The angle at the bottom is unlabeled. The central intersection is created by one line extending from the upper left to the lower right and another line continuing from the lower right upward toward the third intersection. Angle 4 is labeled at the bottom of this intersection. The remaining three angles here are unlabeled. At the rightmost intersection, four angles are also formed. Angle 5 is at the top. Angle 6 is on the right side. The left and bottom angles are unlabeled. All labeled angles are marked with small numbers 1 through 6 placed within the corresponding wedge-shaped regions formed by the intersecting lines.”