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4 years ago

Can someone help me with this 2x+4y+3z=6 x-2y+z=-5 -x-3y-2z=-7 solve for x,y,z

Mathematics

1 answer:

Flauer [41]4 years ago

3 0

Answer:

x = -7 2/3, y = 1 1/3 and z = 5 1/3.

Step-by-step explanation:

2x+4y+3z=6 ..... 1

x-2y+z=-5 ...... 2

-x-3y-2z=-7 .......3

Add equations 2 and 3 to eliminate x:

-5y - z = -12 .....4

Multiply equation 2 by - 2:

-2x + 4y - 2z = 10

Add this to equation 1:

8y + z = 16 ........ 5

Now add equation 4 to equation 5:

3y = 4

y = 4/3 = 1 1/3.

Now find z by substituting for y in equation 4:

-5(4/3) - z = -12

z = 12 - 20/3

z = 36/3 - 20/3 = 16/3 = 5 1/3.

Finally, we find x by substituting for y and z in equation 1:

2x + 4*4/3 + 3*16/3 = 6

2x = 6 - 16/3 - 16

2x = 18/3 - 16/3 - 48/3 = -46/3

x = 23/3 = 7 2/3.

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A die is rolled 20 times. given that three of the rolls came up 1, five came up 2, four came up 3, two came up 4, three came up

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Solution:

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3 years ago

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Answer:

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algol [13]

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Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

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V=x(12-2x)(18-2x)

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$x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}$

which yields:

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we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

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