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Alex777 [14]
3 years ago
14

Which expression is a factor of 3xy + 2x − 18y − 12?

Mathematics
2 answers:
trapecia [35]3 years ago
6 0
X(3y+2)-6(3y+2)
(x-6)(3y+2)
so the answer is 2+3y
cluponka [151]3 years ago
3 0

Answer:  The correct option is (C) 2 + 3y.  

Step-by-step explanation: We are given to select the expression that is a factor of the following expression :

E=3xy+2x-18y-12.

To select the correct factor, first we need to factorize the given expression.

The factorization is as follows :

E\\\\=3xy+2x-18y-12\\\\=x(3y+2)-6(3y+2)\\\\=(x-6)(3y+2)\\\\=(x-6)(2+3y).

Thus, the required factors of the given expression are (x - 6) and (3y + 2).

The correct option is (C) 2 + 3y.  

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Answer:

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3 0
3 years ago
Read 2 more answers
Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b
trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) \cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}

( 2 ) \sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}

These two identities makes sin(π / 10) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and cos(π / 10) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}.

Therefore cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}. Substitute,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right]

And now simplify this expression to receive our answer,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right] = -\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i,

-\frac{3\sqrt{5+\sqrt{5}}}{4} = -2.01749\dots and \:\frac{3\sqrt{3-\sqrt{5}}}{4} = 0.65552\dots

= -2.01749+0.65552i

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}, cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}

We know that 6\sqrt{5+\sqrt{5}} = 16.13996\dots and -\:6\sqrt{3-\sqrt{5}} = -5.24419\dots . Therefore,

Solution : 16.13996 - 5.24419i

Which rounds to about option b.

7 0
3 years ago
Please help, thank you
solmaris [256]

Answer:

1.

8x + 6y = 28

9x + 3y = 39

Set to equal y.

8x + 6y = 28

6y = -8x + 28

y = -8/6x + 28/6

y = -4/3x + 14/3

9x + 3y = 39

3y = -9x + 39

y = -9/3x + 39/3

y = -3x + 13

Set equal to each other.

-4/3x + 14/3 = -3x + 13

Combine like terms.

5/3x = 25/3

Multiply by 3/5

x = 5

Plug x in.

y = -3(5) + 13

y = -15 + 13

y = -2

(5, -2)

2.

-2x - 9y = -3

-7x - 9y= -33

Set equal to y.

-2x - 9y = -3

-9y = 2x - 3

y = -2/9x + 3/9

y = -2/9x + 1/3

-7x - 9y= -33

-9y = 7x - 33

y = -7/9x + 33/9

y = -7/9x + 11/3

Set equal to each other

-2/9x + 1/3 = -2/9x + 1/3

0 = 0

infinitely many solutions

8 0
2 years ago
1.325 to the nearest hundreths
12345 [234]
Its 1.33 because you round up if its 5 or greater
4 0
3 years ago
Read 2 more answers
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