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Ede4ka [16]
3 years ago
10

Solve the following system of equations for all three variables.

Mathematics
1 answer:
Semenov [28]3 years ago
5 0

Answer:

x=2, z=4, y=-6

Step-by-step explanation:

Add

<u>-9x-y+2z= -4</u>

<u>-6x+y+5z= 2</u>

-9x-6x is -15x

-y+y is 0

2z+5z is 7z

-4+2 is -2

So the equation now looks like this: -15x+7z=-2

Subtract

<u>-6x+y+5z= 2</u>

<u>-4x+y+5z= 6</u>

So the equation will look like this:

<u>-6x+y+5z= 2</u>

<u>-(-4x+y+5z= 6)</u>

-6x+4x is -2x

y-y is 0

5z-5z is 0

2-6 is -4

So the equation now looks like this: <u>-2x=-4</u>

You can find x by dividing -2 on both sides:

<u>x=2 </u>

So 2 is x

Now you can substitute x into 2

-15(2)+7z=-2

-30+7z=-2

7z=28

Divide 7 on both sides:

<u>z=4</u>

So now you can substitute z into 4 (For any of the three equation)

-4(2)+y+5(4)=6

-8+y+20=6

20 minus 8 is 12

y+12=6

Subtract 12 on both sides:

y=-6

So the answers are

x=2, z=4, y=-6

Hope this helps!

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Answer:

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Step-by-step explanation:

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Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16
ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: a^2+b^2=c^2

Thus:

\sqrt{a^2+b^2}=c

Option A:

\sqrt{8^2+15^2}=17 → 17 = 17 OK!

Option B:

\sqrt{6^2+8^2}  = 10 → 10 ≠ 12 NO

Option C:

\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex] → \sqrt{202} ≠ 21 NO

Option D:

\sqrt{4^2+13^2} = \sqrt{185} → \sqrt{185} ≠ 16 NO

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3 years ago
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nalin [4]

Answer:

The second one

Step-by-step explanation:

because i did that question and it was right trust me

4 0
2 years ago
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HELP ME PLEASE!!! A Kite flying in the air has a 12 feet line attached to it. It's line is pulled and cast an 11 feet shadow. Fi
ZanzabumX [31]

Step-by-step explanation:

By Pythagoras' theorem,

12^2 = 11^2 + height^2

height = ±√12^2 - 11^2 (rej -ve value since height > 0)

height = 16.279 (5sf) = 16.3 (nearest tenth place)

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5 0
3 years ago
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