The lengths of two sides of a triangle are 20 cm and 32 cm.
Explain why the third side of the triangle can or cannot have a length of 10 cm

No

Step-by-step explanation:

By the Triangle Inequality Theorem, for sides a, b, and c of a triangle:

a + b > c

a + c > b

b + c > a

Here, we already have two sides of lengths 20 and 32. We want to see if the third side can be 10 cm. Suppose a = 32, b = 20, and c = 10. According to the Triangle Inequality Theorem:

20 + 32 >? 10  ⇒  52 > 10       that's good

32 + 10 >? 20  ⇒  42 > 20       that's also good

20 + 10 >? 32  ⇒  30 > 32       this is false

So, the third side cannot be 10 because that would violate the theorem.

Hope this helps!

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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