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3 years ago

Slope of segment DE is -2 and slope of segment AC is -2 whAT is the justification for this statement?

1 answer:

5 0

Answer:
slope formula

Explanation:
1- Slope of DE:
Assume point D is (x1, y1) and point E is (x2, y2). To get the slope of DE, we will substitute with the given points in the following formula:
slope of DE = (y2-y1) / (x2-x1) = -2

1- Slope of AC:
Assume point A is (x1, y1) and point C is (x2, y2). To get the slope of AC, we will substitute with the given points in the following formula:
slope of AC = (y2-y1) / (x2-x1) = -2

3- Therefore, the easiest way to get the slope of any line is by using the slope formula.

4- Note that since the two slopes are equal, this means that the two lines are parallel.

Hope this helps :)

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Nadusha1986 [10]

The GCF is the largest number that both will divide into. Eight is the larger of the two, but 52 is not divisible by 8. The next highest value is 4. 8÷4=2 and 52÷4=13. Therefore, the GCF is 4.

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3 years ago

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Step-by-step explanation:

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3 years ago

Read 2 more answers

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.

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3 years ago

In a given right triangle, If 0 º < x < 90 º and cos x = √ 3 / 2, then sin x = ?

nordsb [41]

Answer:

1/2

Step-by-step explanation:

The "Pythagorean relation" between trig functions can be used to find the sine.

<h3>Pythagorean relation</h3>

The relation between sine and cosine is the identity ...

sin(x)² +cos(x)² = 1

This can be solved for sin(x) in terms of cos(x):

sin(x) = √(1 -cos(x)²)

<h3>Application</h3>

For the present case, using the given cosine value, we find ...

sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)

sin(x) = 1/2

<em>Additional comment</em>

The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...

sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)

A calculator can always be used to verify the result.

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1 year ago

Solve for Unknown: x/10=43/46.

sergey [27]

Answer:

Step-by-step explanation:

x= 430/46

x=9.35 approximately 9( nearest whole number)

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2 years ago