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Yuri [45]
3 years ago
15

Hank’s teacher asked him to verify that the product (y – 3)(y2 + 3y + 9) is a difference of cubes. He used the distributive prop

erty to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3 + 3y2 + ay – 3y2 – ay – 27. What is the value of a in the polynomial?
Mathematics
2 answers:
kicyunya [14]3 years ago
7 0

Answer:

a = 9

Step-by-step explanation:

expand (y - 3)(y² + 3y + 9)

= y³ + 3y² + 9y - 3y² - 9y - 27

compare the coefficients of like terms with

y³ + 3y² + ay - 3y² - ay - 27

ay = 9y and - ay = - 9y ⇒ a = 9


Viktor [21]3 years ago
4 0

Answer:

C.

Step-by-step explanation:

edg.

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He sold his entire stock for  $10000.

Let the number of shirts be x.
Let the number of ties be     y.

The shirt is at 3 for $100. Therefore, a shirt would cost   $(100/3)
The tie cost $20 each.

Therefore, Multiplying by the number of shirts and ties:

100x / 3    +  20y  =  10000 .............(i).

If he had sold half the shirts and two-thirds the ties, the equation becomes:
100/3 * (x/2)  +  20 * (2y / 3) =  6000
50x / 3          +    40y / 3        = 6000 ..............(ii)

Multiply equation (ii) by 2.

2*(50x / 3          +    40y / 3 )      = 2* 6000
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Equation (i)  Minus (iii) . Inorder to eliminate x.

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Substituting into equation (i).
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100x / 3      =  10000 - 6000
100x / 3      =  4000
x  =  4000 * 3 / 100
x = 120.

So he actually sold 120 shirts and 300 ties. Cheers.
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