6.) a kennel owner has 168 feet of fencing with which
to enclose a rectangular region. he wants to subdivide
this region into three smaller rectangles of equal
length. if the total area to be enclosed 832 ft-, what are
the possible dimensions of the region?

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular region

y ----> the width of the rectangular region

we know that

The perimeter of a rectangle is equal to

Remember that

A kennel owner wants to subdivide  this region into three smaller rectangles of equal  length

so

we also have to take into account the divisions

we have

simplify

-----> -----> equation A

The total area to be enclosed is 832 ft^2

The area is equal to

so

----> equation B

substitute equation A in equation B

Solve the quadratic equation by graphing

The solution are y1=16 ft, y2=26 ft

see the attached figure

For

For

therefore

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft

the weight of the object inside the box!

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get