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MA_775_DIABLO [31]
2 years ago
11

the line y=ax-1 is parallel to the line by-(a+1)x=2. These two lines have the same distance to the origin. find a and b

Mathematics
1 answer:
Levart [38]2 years ago
6 0

By using the parallel condition and the fact that the distance to the origin is the same, we will see that a = 1 and b = 2.

<h3>How to find the values of a and b?</h3>

First, remember that two lines are parallel if have the same slope and different y-intercept.

In this case, we know that

y = a*x - 1

b*y - (a + 1)*x = 2

Are parallel, if we write both of them in the slope-intercept form, we get:

y = a*x - 1

y = (a + 1)*x/b + 2/b

Note that because both of the lines are parallel, the slopes must be equal, then we have that:

(a + 1)/b = a

Then if we know that the distance of both lines to the origin is the same, we have that:

|-1/(√(a^2 + 1))| = | (2/b)/(√(((a + 1)/b)^2 + 1))|

Because the slopes are equal the denominators are equal, this means that:

|-1| = |2/b|

And the y-intercepts must be different, this means that:

b = 2

now we can solve:

(a + 1)/b = a

(a + 1)/2 = a

a + 1 = 2a

1 = 2a - a = a

a = 1 and b = 2.

If you want to learn more about linear equations, you can read:

brainly.com/question/1884491

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Check the explanation

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3 0
3 years ago
1500 soldiers arrive at a training camp. A few soldiers desert the camp. The drill sergeants divide the remaining soldiers into
iren [92.7K]

Answer:

The number of deserters is 34.

Step-by-step explanation:

We have to calculate the number of desertors in a group of 1500 soldiers.

The sergeant divides in groups of different numbers and count the lefts over.

If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.

If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.

If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.

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The number 1,645.6 expressed in scientific notation equals
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Step-by-step explanation:

<u>Step 1:  Convert to Scientific Notation</u>

<u />1645.6 is in standard notation

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given the graph function below which of the following ordered pairs are found on the inverse function
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Answer:

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Graph of function has been given in the figure.

Coordinates of the points lying on this graph will be

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Therefore, Option A. will be the answer.

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