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3 years ago

Are the graphs of the lines in the pair parallel? Explain. y = 3/7x + 11 –3x + 7y = 13

Mathematics

2 answers:

Kitty [74]3 years ago

6 0

Yes because both line have a slope of .857/2

Kobotan [32]3 years ago

5 0

Yes they will be parallel. Now you try to solve it.

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Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to

bekas [8.4K]

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

cos B= (a^2 + c^2 - b^2)/2ac

cos C = (a^2 + b^2 - c^2)/2ab

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s^2 + s^2 - s^2)/(2s×s)

cos A = (s^2 )/(2s^2)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s^2 + s^2 - s^2)/(2s×s)

cos C = (s^2 )/(2s^2)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here: brainly.com/question/2866347

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3 0

2 years ago

At the movie theatre, child admission is $5.20 and adult admission is $9.00 . On Saturday, 156 tickets were sold for a total sal

stiks02 [169]

We can solve this by using systems of equations.

Let's find our first formula, how much money was made using the tickets.

$5.20x + 9y = 1027.80$

Here x is how many child tickets we sold and y is how many adult tickets we sold. Now that we have defined that, we can make another formula for the total tickets sold!

$x + y = 156$ since we sold 156 tickets that could be any combination of child and adult tickets.

Let's solve this system. I'm going to use <em>substitution</em> so I'm going to take our second formula and subtract both sides by x to get $y = 156 - x$ .

Now I will plug this in the first equation for y to get You plug it in for y to get $5.20x + 9 (156-x) = 1027.8.$

From this you can solve for x to get $x = 99$ .

Since $x + y = 156$

$99 + y = 156$

$y = 57$

There were 99 child tickets and 57 adult tickets.

3 0

3 years ago

Write an equation that represents the

Schach [20]

Answer:

Our free fall calculator can find the velocity of a falling object and the height it ... accelerating by 9.80665 m/s (approximately equal to 32.17405 ft/s ) every second.

Step-by-step explanation:

3 0

3 years ago

What is the slope of the line through the points (1,5) and (-2,-4)?

olasank [31]

Answer:

slope = 3

Step-by-step explanation:

Use the coordinates of the points to determine the slope.