I know it's a lot of problems, but I don't have many points. I am not great with theorems, so if someone could explain 1, 2, 3, and 4 that would be great.

Agrocery store has 12 lb of trail mix that is 10% banana chips. the store's manager would like to add banana chips to bring the new mix up to 25% banana chips. write and solve a system of equations to find out how many pounds of banana chips manager needs to add.

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.

The length of triangle base is 26. a line, which is parallel to the base divides the triangle into two equal area parts. find the length of the segment between triangle legs.