Zachary is starting a business selling handmade necklaces. he has
decided to invest an initial amount of $31 for advertising, and materials
cost 56 for each necklace he makes. zachary can sell his creations for
537 per necklace. once he makes and sells a certain number of
necklaces, he will break even, with identical expenses and sales. how
many necklaces would that take? what would the total expenses and
sales be then?

answer:

photo math ur welcome

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).