Irrational Numbers and Geometric connections review

Multiply $$(\sqrt{20})(\sqrt{63})$$ .

Bill is planting a garden. He wants to plant tomatoes and green beans. The length and width of the garden is $$8\sqrt{12}$$ ft.

What is the perimeter of the garden in ft?

The sidewalks on both sides of Peach St. are parallel. One sidewalk can be modeled by

the equation 2x − y = −1 Which equation could model the other sidewalk?

A private plane and a jetliner both fly over a park that is at (−2, 2) on a map. The path of the jetliner follows the line $$y=\frac{1}{2}x+3$$ The private plane flies perpendicular to the jetliner. What is the equation in slope-intercept form of the line that represents the private plane’s flight path?

Triangle ABC has vertices with A(x, 2), B(-1, 2), and C(0, 4). Determine the value of x that would make triangle ABC a right triangle.

Three students, Jack, Mark, and Sue each make a claim about the sum of $$\sqrt{3}\ +\ \sqrt{9}$$ Each student's claim and their work to support their claim is shown below. Determine whether each student has provided correct reasoning to support their claim. Indicate whether each student's claim is Correct or Incorrect by selecting the hotspot in the respective box.

Simplify $$\sqrt[]{75}+\ \sqrt[]{12}$$ .