AF is a line segment and E is a point on it. From E, two rays EB and EC originate. Draw a diagram and then write what postulate, definition, or theorem justifies the statement about the diagram.

$m \angle A E B+m \angle B E F=180$

D is a point on A̅C̅ and E is a point on B̅C̅ of ΔABC such that D̅E̅ II A̅B̅. If CA = 35, DA = 10, and CE = 15, find EB.

Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solutions or infinitely many solutions.

$$3 x-2 y=-3$$

$$25 x+10 y=215$$

Complete the following sentences with the present tense of the verb vivir.

Mis abuelos __________________________ en Arecibo.

Write a system of equations that can be solved by multiplying one equation by -3 and then adding the two equations together.

If A is $2 \times 3, B$ is $3 \times 1, C$ is $2 \times 5, D$ is $4 \times 3, E$ is $3 \times 2$ and F is $2 \times 3,$ find the size and number of entries of each of the following. EB

A star explodes and loses half its mass. Its radius becomes half as large. Determine the new gravitational field strength on the surface of the star in terms of the original one.

Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

$$\left. \begin{array} { l } { 2 x - 2 y = 5 } \\ { y = x - 4 } \end{array} \right.$$

It is discovered that a diesel engine with a mass of 300 kg and an operating speed of 1800 rpm has a spinning unbalance of 1 kg-m. It will be put in place on the factory floor to serve as a source of backup power. The only type of isolator that is now available has a rigidity of 1 MN/m and a damping ratio of 5percent , and the maximum allowed force that can be transmitted to the floor is 8000 N. Investigate at possible solutions for the problem.

Select the correct answer and write it on the line provided.
Group A strep, also known as flesh-eating bacteria. causes .________________, __________________ (a)lupus erythematosus
(b)necrotizing fasciitis

Graph each function. Give the domain and range. $f(x)=2^{-x}$

A painter painted about half a room in half a day. Coley estimated the painter would paint 7 rooms in 7 days. Is Coley's estimate reasonable? Explain.

A 3-kg blob of putty moving at $10 \mathrm{~m} / \mathrm{s}$ hits a $2-\mathrm{kg}$ blob of putty at rest. Calculate the speed of the stuck-together blobs of putty immediately after the collision.

. True or False: The faster an asset is depreciated, the greater will be its after-tax present worth.