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2 years ago

Write equations for the horizontal and vertical lines passing through the point (8,5)

Mathematics

1 answer:

almond37 [142]2 years ago

7 0

Answers:

Horizontal Line: y = 5

Vertical Line: x = 8

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Explanation:

All horizontal lines are of the form y = k, for some constant k. We want the horizontal line to pass through (8,5), meaning every point on this horizontal line must have y coordinate 5. Therefore, y = 5 is the equation of the horizontal line. Two such points on this line are (1, 5) and (8, 5). All that matters is the y coordinate is 5. The x coordinate can be anything you want. The slope of any horizontal line is 0.

Flipping things around, all vertical lines will have the x coordinate of each point be the same value. Draw a vertical line through (8,5) and note how each point has x coordinate of 8. Two such points are (8,1) and (8,5). Therefore, the equation of the vertical line is x = 8. The y coordinate can be any value you want. The slope of any vertical line is undefined. Unlike the horizontal line, we cannot write this equation in slope intercept form (namely because the slope isn't defined).

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Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5

jolli1 [7]

To solve the the question we proceed as follows:

From trigonometric laws

$(cos x)^2+(sin x)^2=1$

$sin (x-y)=sin$ $x$ $sin$ $y-sin$ $y$ $cos$ $x$

$cos (x-y)=cos$ $x$ $cos$ $y+sin$ $x$ $xin$ $y$

si $x=\frac{8}{17}$

$cos$ $x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}$

$cos$ $y=\frac{3}{5}$

$sin$ $x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}$

thus

$tan (x-y)=[sin (x-y)]/[cos (x-y)]$

=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]

plugging in the values we obtain:

$[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]$

simplifying

$[24/85-60/85]/[45/85+32/85]$

$=-\frac{36}{77}$

6 0

1 year ago

Eight times the difference of a number and seventeen is thirty"?

ladessa [460]

"The number" is first, do an example, to find out how, like pick any number under 17. Let's do 14. Their difference is 3. 8*3=24. that;s not quite 30. We have to find a number to equal 30, let's pick 15 and 17. Their difference is 2. 2*8=16. Not quite. Now, check the multiplication table for 8. Do any of them equal 30? No. So now you can see that the answer is going to have a decimal place. Divide 30 by 8. That equals to 3.75. Now do 17 minus 3.75. That is 13.25. The difference between 13.25 and 17 is 3.25. Now, do 8*3.75. That is 26. Oops. I am not in high school, but keep going like that and YOU'LL FIND IT! I BELIEVE IN YOU!

5 0

3 years ago

The population of a school is 800 students and is increasing at a rare 2% per year use an exponential function to find the popul

tiny-mole [99]

The answer is 800 + 144 which is 944

6 0

3 years ago

A paper has an area of 624 square centimeters. What is the papers area in square inches using the following conversion: 1 square

kompoz [17]

Answer:

96 square inch

Step-by-step explanation:

=6.5 cm^2 = 1 in^2

So,

=624 cm^2 / 6.5 cm^2

= 96 in^2

6 0

2 years ago

Please help asap, it would be much appreciated!! :) Thank you so much!!

LiRa [457]

Statement 1 is false.

While it is true that some of the y-values have more than one corresponding x-value, this does not make the relation not a function. It would not be a function if some of the <em>x-values</em> had more than one corresponding y-values.

Statement 2 is true.

The domain of a function is all the x-values it encompasses. This function starts at 3 and ends at 8.

Statement 3 is false.

The range of a function is all the y-values it encompasses. This includes all the y-coordinates, but it does not express the range properly. The range is [6, 10].

Hope this helps!!

5 0

2 years ago