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4 years ago

Given the equation 4x − 26 = 2x − 4, which order of operations completely solves for x?

1 answer:

6 0

4x - 26 = 2x - 4....subtract 2x from both sides
4x - 2x - 26 = -4...add 26 to both sides
4x - 2x = -4 + 26...combine terms
2x = 22...divide both sides by 2
x = 22/2 = 11

OR
4x - 26 = 2x - 4.....subtract 4x from both sides
-26 = 2x - 4x - 4....add 4 to both sides
-26 + 4 = 2x - 4x...combine terms
-22 = -2x....divide both sides by -2
-22/-2 = x
11 = x

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The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further from the lighthouse. The new bearing is 25°

djverab [1.8K]

Answer:

The distance between the ship at N 25°E and the lighthouse would be 7.26 miles.

Step-by-step explanation:

The question is incomplete. The complete question should be

The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further towards the south. The new bearing is N 25°E. What is the distance between the lighthouse and the ship at the new location?

Given the initial bearing of a lighthouse from the ship is N 37° E. So, $\angle ABN$ is 37°. We can see from the diagram that $\angle ABC$ would be $180-37=$ 143°.

Also, the new bearing is N 25°E. So, $\angle BCA$ would be 25°.

Now we can find $\angle BAC$ . As the sum of the internal angle of a triangle is 180°.

$\angle ABC+\angle BCA+\angle BAC=180\\143+25+\angle BAC=180\\\angle BAC=180-143-25\\\angle BAC=12$

Also, it was given that ship sails 2.5 miles from N 37° E to N 25°E. We can see from the diagram that this distance would be our BC.

And let us assume the distance between the lighthouse and the ship at N 25°E is $AC=x$

We can apply the sine rule now.

$\frac{x}{sin(143)}=\frac{2.5}{sin(12)}\\ \\x=\frac{2.5}{sin(12)}\times sin(143)\\\\x=\frac{2.5}{0.207}\times 0.601\\ \\x=7.26\ miles$

So, the distance between the ship at N 25°E and the lighthouse is 7.26 miles.

3 0

3 years ago

Alberto ran 45 kilometer on Monday. On Tuesday, he runs 910 of the distance he ran on Monday. How far did he run on Tuesday? Ent

Digiron [165]

Answer:

85.95 km

Step-by-step explanation:

Given that,

Alberto ran 45 kilometers on Monday.

On Tuesday, he runs 91% of the distance he ran on Monday.

We need to find how far did he run on Tuesday. It can be given by :

$T=45+45\times \dfrac{91}{100}\\\\=85.95\ km$

So, he run 85.95 km on Tuesday.

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3 years ago

A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 3 miles to the roa

patriot [66]

53+3(D) = L

53 + 3(38) =L

53 +114 = L

167=L

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3 years ago

Pleas help me ASAP thank you :)

RoseWind [281]

Answer:

Step-by-step explanation:

it says 11

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3 years ago

Is one flag a translation image of the other, or a rotation image? EXPLAIN

S_A_V [24]

The flags are a translation. Both flags are located at different origins, so it couldn't be a rotation. Both flags have the colors in the same place ( black on the bottom, white on the top) so one flag was moved up or down from the other flag, which is a translation.

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3 years ago

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