Patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into small boxes. There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. a) How many cupcakes dud Patricia bake?
b) She sold all the small boxes and collected $189. How much did she sell each small box for?

The answer is given below

Step-by-step explanation:

a)

Let us assume Patricia baked x number of cakes. She put half of the cupcakes (i.e x/2) equally into 6 big boxes.

6 big boxes contained cakes, therefore 1 big box would contain cakes.

Let us assume she put the other half into 14 small boxes, therefore each small box would contain cakes.

There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. That is:

Therefore Patricia baked 84 cup cakes

b)

She sold all the small boxes and collected $189, i.e she sold 14 small box for $189. Each small box = $189/14 = $13.5

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180