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Rina8888 [55]
3 years ago
7

Does coordinate m or n represent a greater number​

Mathematics
1 answer:
AlexFokin [52]3 years ago
5 0

Answer:

m

Step-by-step explanation:

If all points are plotted on a graph, we'd see that (3, 5) and (10, 5), would be on the same horizontal level. Both points have the same y coordinate of 5.

Invariably, (0, 1) would be on the same horizontal level with (m, n). The coordinate of n, which is the y value on the y-axis would be same as 1.

The coordinate of m, which is the x-value on the x-axis would certainly be greater than 1.

Therefore, coordinate m represents a greater number.

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<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

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\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right

===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}

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y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D

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