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san4es73 [151]
3 years ago
6

A line passes through (1,1) , (-2,4) , and (6,n) . Find the value of n.

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
8 0
General\ formula\ for\ line:\\y=ax+b\\\\ Passes\ through\ (1,1)\ (-2,4)\\\\\left \{ {{1=1a+b\ |\cdot2} \atop {4=-2a+b}} \right. \\\\ \left \{ {{2=2a+2b} \atop {4=-2a+b}} \right. \\+-----\\\\6=3b\ \ |:3\\b=2\\\\1=a+2\\1-2=a\\a=-1\\\\y=-x+2\\\\Passes\ through\ (6,n):\\\\n=-6+2\\\\\boxed{n=-4}
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Solve each system by substitution<br><br> 2x - 3y = -1<br> X + 4y = -6
lord [1]

Answer:

(- 2, - 1 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = - 1 → (1)

x + 4y = - 6 → (2)

Rearrange (2) expressing x in terms of y by subtracting 4y from both sides

x = - 6 - 4y → (3)

Substitute x = - 6 - 4y into (1)

2(- 6 - 4y) - 3y = - 1 ← distribute and simplify left side

- 12 - 8y - 3y = - 1

- 12 - 11y = - 1 ( add 12 to both sides )

- 11y = 11 ( divide both sides by - 11 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = - 6 - 4(- 1) = - 6 + 4 = - 2

Solution is (- 2, - 1 )

3 0
3 years ago
if 5.25 MB have been downloaded and 2.25 MB are left. what percent of the application has already been downloaded?
ollegr [7]
5.25 + 2.25 = 7.50 MB

x/100 x (7.50) = 5.25
7.50x/100 = 5.25
7.50x = 5.25(100)
7.50x = 525
x = 525/7.50
x = 70
Hence, 70% of the application has already been downloaded. 


6 0
3 years ago
Which of the following is NOT a variation of a Pythagorean identity?​
Ipatiy [6.2K]

The expression that is not a variation of the Pythagorean identity is the third option.

<h3>What is the Pythagorean identity?</h3>

The Pythagorean identity can be written as:

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

For example, if we subtract cos^2(x) on both sides we get the second option:

sin^2(x) = 1 - cos^2(x)

Which is a variation.

Now, let's divide both sides by cos^2(x).

sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1

Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.

Concluding, the correct option is the third one.

If you want to learn more about the Pythagorean identity, you can read:

brainly.com/question/24287773

3 0
2 years ago
All four sided polygons are quadrilaterals
Sati [7]
This is a true statement (:
3 0
3 years ago
Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the ce
dexar [7]

If the center of town is the origin then 4 blocks west and 1 block south would be 4 blocks to the left and 1 block down or (-4, -1) house 3 block east and 2 blocks north would be 3 blocks to the right and 2 blocks up or (3, 2) use the distance formula to find the distance between two points. That's all I know! hope this helps!~ just remember to use the distance formula to find the distance between two points.

5 0
3 years ago
Read 2 more answers
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