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3 years ago

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Perform the following multiplicationa) 9xy ( x²y – xy²)b) 7 p²q² (9 pq - 9 p²q²)

1 answer:

erastova [34]3 years ago

6 0

Answer:

hsjishsvdndkssjxbbxjsiaiajbxbxbsjsisis

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mr. ken's class is collecting empty water bottles. they started with 17 water bottles on day 1. on day 3, they had 30 water bott

Oxana [17]

They had 23 and 38 water bottles on day 2 and day 4 respectively. Also, there will be 68 water bottles on day 7.

<u><em>Explanation</em></u>

Suppose, the equation representing the number of bottles is $y= ax^2 +bx+c$ , where $x$ is the number of days.

There are 17 water bottles on day 1, 30 water bottles on day 3 and 47 water bottles on day 5

So, the three points in the form of (x, y) are: (1, 17) , (3, 30) and (5, 47)

Plugging these three points into the above equation, we will get .....

$17=a(1)^2 + b(1) +c\\ a+b+c=17 ............................ (1)\\ \\ 30=a(3)^2+b(3)+c\\ 9a+3b+c=30 ......................... (2) \\ \\ 47=a(5)^2+b(5)+c\\ 25a+5b+c=47 ......................... (3)$

Subtracting equation (1) from equation (2) , we will get .....

$8a+2b=13 ..................... (4)$

Subtracting equation (2) from equation (3) , we will get .....

$16a+2b=17 ...................... (5)$

Now, subtracting equation (4) from equation (5) , we will get ......

$16a -8a = 17-13\\ \\ 8a= 4\\ \\ a=\frac{4}{8}= 0.5$

Substituting this $a= 0.5$ into equation (4) ........

$8(0.5)+2b=13\\ \\ 4+2b=13\\ \\ 2b=9\\ \\ b=\frac{9}{2}=4.5$

Again, substituting $a=0.5$ and $b=4.5$ into equation (1) , we will get ......

$0.5+4.5+c=17\\ \\ 5+c=17\\ \\ c=17-5 =12$

So, <u>the equation will be now</u>: $y= 0.5x^2 +4.5x+12$

For finding the number of bottles on day 2 , day 4 and day 7 , we need to plug $x=2 , 4, 7$ respectively into the above equation.

For $x= 2$ , $y= 0.5(2)^2 +4.5(2)+12 = 2+9+12= 23$

For $x= 4$ , $y= 0.5(4)^2 +4.5(4)+12 = 8+18+12= 38$

For $x= 7$ , $y= 0.5(7)^2 +4.5(7)+12 = 24.5+31.5+12= 68$

So, they had 23 water bottles on day 2 and 38 water bottles on day 4

Also, there will be 68 water bottles on day 7

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10 ≤ -2 ( 3 + 4b )

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