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2 years ago

How to solve a system algerbreticially

Mathematics

1 answer:

Neko [114]2 years ago

8 0

Y=x+5
y=6

the first equation tells you that y equals x plus 5, and the second tells you that y equals 6.

that means x+5 would equal 6, because they both equal y.

x+5=6
x=1

to find y, simply grab one of the two equations and plug in the value of x, which is 1.

y=x+5
y=(1)+5
y=6

Answers:
x=1 and y=6

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Find the lowest common denominator for the following fractions.

Marat540 [252]

Your answer is 6 because 6 is the smallest number that is divisible by both 2 and 3

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2 years ago

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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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3 years ago

The scale on a map shows that 10 kilometers is represented by 4 centimeters. Which proportion can be used to find the actual dis

Illusion [34]

10/4=x/20
Your answer will be x=50 kilometers

3 0

3 years ago

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The graph of the function f(x) = (x + 2)(x - 4) is shown.

hoa [83]

Answer:

B) All real values of 'x' where -2 < x< 4

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given function f(x) = (x +2 ) ( x-4)

(x+2)(x-4) =0

⇒ x +2 =0 and x-4=0

⇒ x =-2 and x=4

From graph

Given parabola lies between the x=-2 and x =4

∴ All real values of 'x' lies between x=-2 and x =4

All real values of 'x' lies -2 < x< 4

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2 years ago

In 1992, the countries Chad and Denmark each had population of about 5.2 million. However,

irinina [24]

9514 1404 393

Answer:

5,339,479

Step-by-step explanation:

The populations in millions of the different countries can be represented by the equations ...

c = 5.2(1.025^t)

d = 5.2(1.001^t)

We want to find d when c = 10. Solving for t when c=10, we have ...

10 = 5.2(1.025^t)

10/5.2 = 1.025^t

log(10/5.2) = t×log(1.025)

t = log(10/5.2)/log(1.025)

Then the value of d for that value of t is ...

d = 5.2(1.001^(log(10/5.2)/log(1.025)) ≈ 5.3394789

The population of Denmark is about 5,339,479 when the population of Chad is 10 million.

_____

If we round the number of years to 26.5 before computing the population of Denmark, we get 5,339,571 -- about 92 more people. Ordinarily, one would not round intermediate results.

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2 years ago