please help . A regional airport, community college, and city hall building are located at the vertices of a right triangle formed by three roads. The airport and the city hall are 10 miles apart. The distance between the airport and the community college is 8 miles, and the distance between the city hall and the community college is 6 miles. A service road will be constructed from the main entrance of the community college to the road that connects the airport and the city hall. What is the shortest possible length for the service road Round your answer to the nearest tenth.

Solve the system by the elimination method. 3x - 2y - 7 = 0 5x + y - 3 = 0 to eliminate y, the lcm is 2. which of the following is the resulting equations? 1.3x - 2y - 7 = 0 5x + y - 3 = 0 2.3x - 2y - 7 = 0 -10x - 2y + 6 = 0 3.3x - 2y - 7 = 0 10x + 2y - 6 = 0

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

In right ∆abc shown below, the midpoint of hypotenuse ac is located at d and segment bd is drawn. if ab = 12 and bc = 16, then explain why bd = 10. hint: consider what you know about the diagonals of a rectangle.