The demand function for a certain product, p=d(q), is linear, where p is the price per item in dollars and q is the quantity demanded. if p increases by 8$, market research shows that q drops by two items. in addition, 50 items are purchased if the price is 250. find a formula for q as a function

Step-by-step explanation:

Given:

is a linear model for demand function

where represents the price per item in dollars and  is the quantity demanded.

With increase in by $8 there is a decrease in by 2 items.

For items purchased the price .

To find   as a function of which is  

Since its a linear model, so we can find rate of change or slope of line from the given data.

Slope

So, the function can be written as:

where is the initial value or the y-intercept.

Using the point

Adding 62.5 both sides.

∴

So,

what is the graph

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.