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Rom4ik [11]
3 years ago
11

Can some help me, please? ​

Mathematics
1 answer:
kkurt [141]3 years ago
5 0

Since value of k is same for y/x for all values in the table so, y varies directly with x

And equation is: y=-2.25\,x

Step-by-step explanation:

We need to find if y varies directly with x from the values given in the table.

If y varies directly with x then we have the equation:

y=k\,x

where k is constant of proportionality

or we can write

\frac{y}{x}=k

If k is same for all values of x and y when (y/x=k) then we can say that y varies directly with x.

if x = -20 and y=45 then k is:

\frac{45}{-20}=-2.25

So, value of k is -2.25

if x = 1 and y=-2.25 then k is:

\frac{-2.25}{1}=-2.25

So, value of k is -2.25

if x = 12 and y=-27 then k is:

\frac{-27}{12}=-2.25

So, value of k is -2.25

Since value of k is same for y/x for all values in the table so, y varies directly with x

And equation is: y=-2.25\,x

Keywords: Direct Relationship

Learn more about Direct Relationship at:

  • brainly.com/question/10708697
  • brainly.com/question/2678748

#learnwithBrainly

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What is the 4th term of the expanded binomial (2x – 3y)^6
san4es73 [151]

Answer:

The 4th term of the expanded binomial is -4320x^3y^3

Step-by-step explanation:

Considering:

$ (x+y)^n = \sum_{k=0}^{n} \binom{n}{k}  x^{n-k}y^k$

$ (2x-3y)^6 = \sum_{k=0}^{6} \binom{6}{k}  (2x)^{6-k}(-3y)^k$

Now, you gotta calculate for every value of k

$ (2x-3y)^6 = \binom{6}{0}  (2x)^{6-0}(-3y)^0     +       \binom{6}{1}  (2x)^{6-1}(-3y)^1     +      \binom{6}{2}  (2x)^{6-2}(-3y)^2   +   \\ $

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I will not write every product, but just solve following the steps:

For k=0

$\binom{6}{0}  (2x)^{6-0}(-3y)^0$

$\frac{6!}{(6-0)!(0!)}   (2x)^{6-0}(-3y)^0$

$ \frac{6!}{6!} \left(2x\right)^{6-0}\cdot 1$

$1\cdot \:1\cdot \left(2x\right)^{6-0}$

$2^6x^6$

64x^6

(2x-3y)^6=64x^6-576x^5y+2160x^4y^2-4320x^3y^3+4860x^2y^4-2916xy^5+729y^6

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