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worty [1.4K]
3 years ago
14

There are two different maps of ohio. The scale on the first map is 1 cm to 10 km. The distance from cleveland to clncinnati is

40 cm. The scale on the second map is 1 to 50 km what is the distance from cleveland to cincinnati on the second map explain your reasoning
Mathematics
1 answer:
aev [14]3 years ago
5 0

Answer: Distance from Cleveland to Cincinnati on the second map is 8 km.

Step-by-step explanation:

Since we have given that

The scale on the first map is

1\ cm:10\ km

That means

1\ cm=10\ km

Distance from Cleveland to Clncinnati = 40 cm

So,

1\ cm=10\ km\\\\40\ cm=10\times 40\ km\\\\40\ cm=400\ km

Similarly, Scale on the second map is given by

1\ cm:50\ km\\\\i.e.\\\\1\ cm=50\ km

So, our 400 km in second map will be

\frac{400}{50}\ km=8\ km

Hence, Distance from Cleveland to Cincinnati on the second map is 8 km.

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3<em>x</em> - 4<em>y</em> = 32

To solve by elimination, multiply the top equation by 3 and the bottom equation by 2.

3(-2<em>x</em> + 6<em>y</em> = -38) --> -6<em>x</em> + 18<em>y</em> = -114

2(3<em>x</em> - 4<em>y</em> = 32) --> 6<em>x</em> - 8<em>y</em> = 64

Add the equations.

-6<em>x </em>+ 18<em>y</em> = -114

6<em>x</em> - 8<em>y</em> = 64

+_____________

0 + 10<em>y</em> = -50

10<em>y</em> = -50

<em>y</em> = -5

Substitute -5 for y into one of the original equations to find x.

3<em>x</em> - 4<em>y</em> = 32

3<em>x</em> - 4(-5) = 32

3<em>x</em> + 20 = 32

3<em>x</em> = 12

<em>x</em> = 4

Check work by plugging the <em>x</em>- and <em>y</em>-values into both of the original equations.

-2<em>x</em> + 6<em>y</em> = -38

-2(4) + 6(-5) = -38

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38 = 38


3<em>x</em> - 4<em>y</em> = 32

3(4) - 4(-5) = 32

12 + 20 = 32

32 = 32

Answer:

<em>x</em> = 4 and <em>y</em> = -5; (4, -5).

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