What is the length of the missing side AB?

72.6 cm

Step-by-step explanation:

Since we know the two sides and one angle, we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and C is the angle corresponding to AB.

AB² = 38² + 83² - 2(38 × 83)Cos61

AB² = 1444 + 6889 - 2(3154)0.4848

AB² = 8333 - 3058.1184

AB² = 5274.8816

Taking square root of both sides, it becomes

AB = √5274.8816

AB = 72.6 rounded up to the nearest tenth

 Buying five of each type of plant costs 39, which is the lowest possible cost

Step-by-step explanation:

Linear programming is a method used to maximize or minimize a linear function of several variables like output or cost.

Given vertex is (5,39).

A botanist uses linear programming to find the vertex of the feasible region that results in the minimum value, in dollars, of the cost function.

Here,  vertex (5,39) means that  Buying five of each type of plant costs $39, which is the lowest possible cost.