Alright. It seems like the triangle that has the 45 degree angle with angles c & d is an isosceles triangle which meas two sides are equal.
If that is true, angle d would be 45. Add 45 and 45 together to get 90, which is angle c. The angle right across from c, a, will be 90 as well. Add 90 and 45 to get 135 and then do 180 - 135 to get angle b. Angle b should equal 45 as well. So adding each of the angles together, 90 + 45 + 90 + 45 = 360

Your final answer is 360.

8 0

3 years ago

a gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sel

adell [148]

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

= 24000 - 750x + 2400x - 75x²

= 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

⇒1650 - 150x = 0

⇒150x = 1650

⇒x = 1650/150

⇒x = 11

∴ we get

Price per Wind chime = $ 150 + 15(11)

= $ 150 + 165

= $ 315

So,

The price per wind chime that will maximize revenue = $ 315

3 0

3 years ago