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irga5000 [103]
3 years ago
5

Pleaseee will make brainlist :(

Mathematics
1 answer:
Vlada [557]3 years ago
4 0

Answer:

x^2 -20x + 100

Step-by-step explanation:

How this works is that you multiply each number by every other number, so.

(x+a)(x+b) so you do x times x since the parenthesis multiplies them together. Then you do x times b.

Then you do a times x since a is the next number in the first pair. then you do a times b.

(* is the sign for multiplication for the sake of simplifying it and to be easier than doing something like x x x where you are multiplying x together with x.)

So in the expression (x + a)(x + b) you are basically doing

x * x            +         x * b           +        a * x        +          a * b

In your case, a is = to -10 and b is equal to -10

So your expression would be

x * x    +   x * -10    +    -10 * x     +    -10 * -10

so x times x is x^2 and x times -10 is -10x     You are doing -10 * x twice so it is -20x and -10 times -10 is 100

So the final equation would be x^2 plus -20x plus 100 or

x^2 + (-20x)  + 100

which is

x^2 -20x + 100

Hope this helps!

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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)

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                                    = $ 315

So,

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

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