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2 years ago

Simplify the expression: -9n + -2n

Mathematics

1 answer:

Andreas93 [3]2 years ago

7 0

Answer:

-11n

Step-by-step explanation:

You have to combine like terms

BRAINLIEST PLEASEE

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Which of the following functions are homomorphisms?

Vikentia [17]

Part A:

Given $f:Z \rightarrow Z,$ defined by $f(x)=-x$

$f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y$

but

$f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy$

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.

Part B:

Given $f:Z_2 \rightarrow Z_2,$ defined by $f(x)=-x$

Note that in $Z_2$ , -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular $f(x)=x$

$f(x+y)=x+y \\ \\ f(x)+f(y)=x+y$

and

$f(xy)=xy \\ \\ f(x)\cdot f(y)=xy$

Therefore, the function is a homomorphism.

Part C:

Given $g:Q\rightarrow Q$ , defined by $g(x)= \frac{1}{x^2+1}$

$g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1}$

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.

Part D:

Given $h:R\rightarrow M(R)$ , defined by $h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)$

$h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)$

but

$h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)$

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.

Part E:

Given $f:Z_{12}\rightarrow Z_4$ , defined by $\left([x_{12}]\right)=[x_4]$ , where $[u_n]$ denotes the lass of the integer $u$ in $Z_n$ .

Then, for any $[a_{12}],[b_{12}]\in Z_{12}$ , we have

$f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)$

and

$f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)$

Therefore, the function is a homomorphism.

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2 years ago

Use the graph to write a linear function that relates y to x.

allsm [11]

Answer:

um we need the photo sry

Step-by-step explanation:

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2 years ago

Use the function Y=2x^2+3x+7 to answer the following questions

zalisa [80]

Answer:

What are the questions?

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2 years ago

Round 246,539 to the nearest ten thousand and to the nearest hundred thousand

svetlana [45]

Answer:

Nearest ten thousand: 250,000 Nearest hundred thousand: 200,000

Step-by-step explanation:

For the nearest ten thousand, look at that place which is the 4 then look at the number next to it. Its a 6. That 6 is closer to ten than it is to 0 so you round up to the next number which is 250,000. For the hundred thousand place do the same thing. Look at the number next to it which is 4 which is closer to 0 than 10 so you round down to 200,000.

7 0

2 years ago

Evaluate -5x^2 − 8x + 1 when x = -3.

Yakvenalex [24]

Hello.

Answer: 70

New equation: −5(−3^2)−(8)(−3)+1

How to get the answer:

(−5)(−9)−(8)(−3)+1

=45−(8)(−3)+1

=45−(−24)+1

=69+1

=70

Have a nice day

7 0

2 years ago

Simplify the expression: -9n + -2n￼

Simplify the expression: -9n + -2n