Daren is opening a store that sells wooden mats. He invested $10 for marketing and raw materials cost $8 for each mat he makes. Daren can sell his mats for $9 per mat. He will break even once he makes and sells a certain number of mats, with identical expenses and sales. What would the total expenses and sales be then? How many mats would that take?

The total expenses and sales will be $90 and it would take 10 mats

Step-by-step explanation:

Equations

This problem can be solved by pure logical deduction, but we'll use equations instead.

Daren has a cost structure made of a fixed investment of $10 and a variable cost of $8 per mat he makes.

The total cost function can be written as:

C(x)=10+8x

Where x is the number of mats made.

Daren can sell the mats for $9 each. The revenue function is:

R(x)=9x

The number of sold mats needed to break even will occur when cost and revenue are the same:

10+8x=9x

Solving:

x=10 mats

The cost of 10 mats is:

C(10)=10+8*10=$90

The revenue for 10 mats is:

R(10)=9*10=90

The total expenses and sales will be $90 and it would take 10 mats

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.