Algebra Two chords of a circle, $\overline{D E}$ and $\overline{F G}$, intersect at $C$ with segment lengths
$C D=3, C E=x+2, C F=6-x$, and $C G=5$. Write and solve an equation for $x$.

Physics Newton's Second Law says the force on an object is the net acceleration, which is a vector, multiplied by the mass. A block on a ramp is under the force of gravity at about $10 \mathrm{~m} / \mathrm{s}^2$ down and $a$ friction force of $4 \mathrm{~m} / \mathrm{s}^2$ up and $8 \mathrm{~m} / \mathrm{s}^2$ to the left. What is the net acceleration on the block?

Error Analysis Kaelie believes she has found a new trigonometric identity below based on $\sin ^2 \theta+\cos ^2 \theta=1$. Identify any errors she made and explain why she is wrong.

$$\begin{aligned} \sin ^2 \theta+\cos ^2 \theta & =1 \\ \sqrt{\sin ^2 \theta+\cos ^2 \theta} & =\sqrt{1} \\ \sin \theta+\cos \theta & =\pm 1 \end{aligned}$$

Multi-5tep Classify the polygon with vertices P(2,1), Q(7,-1), R(2,-3), and S(-3,-1), and find its perimeter. Give your answer in simplified radical form.

Error Analysis Donna wrote the matrix

$$\left[\begin{array}{ll}-3 & 1 \\ -3 & 1\end{array}\right]$$

for the translation three units left and one unit up. Explain Donna's error and correct the matrix.

A rectangular table has a length of 3 x-2, a width of 2 x+1, and an area of 2 x+28. Solve for x and provide a justification for each step.

If $\triangle A B C \cong \triangle D E F, A B=D E, B C=E F, \mathrm{~m} \angle A B C=(7 x-36)^{\circ}$, and $\mathrm{m} \angle D E F=(3 x+16)^{\circ}$, then what is $x$ ?

Express $\cos \theta \cdot \tan \theta$ in terms of $\sin \theta$.

Error Analysis Luka wrote the following as she was trying to prove that $\triangle R T F$ is equilateral. Find and correct any errors she made.

$$\begin{aligned} & T F=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{16}=4 \\ & F R=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{16}=4 \\ & T R=4 \end{aligned}$$

Mapping A map has a scale of 1:250. If a map represents a community center a square with an area of 100 square centimeters, what is the actual area of the community center, in square meters?

Formulate Determine a formula for the total surface area of a square pyramid with a side length of $s$ and a slant height of $I$.

Reflect the discussed figure across $\ell_1$, and then reflect the image across $\ell_2$.

Architecture A model of a pyramid for an art gallery has glass triangular lateral faces, each with a base of 3 feet and a height of 4 feet. The scale of the model is 2:41. How many square feet of glass will be needed for each triangular glass pane?

Analyze if the height of a cylinder is 31.4 centimeters, and the area of the cross section parallel to a circular face has the same area as the cross section perpendicular to the circular faces through a diameter of each face, what is the radius of the cylinder?