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andriy [413]
3 years ago
6

Solve the following three variable system.

Mathematics
1 answer:
Ket [755]3 years ago
6 0
1)\ \ \ 2x + 3y + 4z = 9\\2)\ \ \ -x + 2y - z = 0\\3)\ \ \ -2x + 4y + z = 3\\===================================\\3)\ \ \ -2x + 4y + z = 3\ \ \ \Rightarrow\ \ \ z=2x-4y+3\\\\1)\ \ \ 2x + 3y + 4z = 9\ \ \ \Rightarrow\ \ \ 2x + 3y + 4(2x-4y+3) = 9\\2x+3y+8x-16y+12=9\\10x-13y=-3\\\\2)\ \ \ -x + 2y - z = 0\ \ \ \Rightarrow\ \ \ -x+2y-(2x-4y+3)=0\\-x+2y-2x+4y-3=0\\-3x+6y=3\ /:(-3)\\x-2y=-1\ \ \ \Rightarrow\ \ \ x=2y-1\\\\

1)\ \ \ 10x-13y=-3 \ \ \ \Rightarrow\ \ \ 10(2y-1)-13y=-3\\20y-10-13y=-3\\7y=7\ /:7\ \ \ \Rightarrow\ \ \ y=1\\\\2)\ \ \ x=2y-1\ \ \ \Rightarrow\ \ \ x=2\cdot2-1=1\\\\3)\ \ \ z=2x-4y+3\ \ \ \Rightarrow\ \ \ z=2\cdot1-4\cdot1+3=2-4+3=1\\\\Ans.\ x=y=z=1
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Answer:

b

Step-by-step explanation: B

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3 years ago
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For the expression 6 − y + 3, determine the coefficient for the variable term.
sergij07 [2.7K]

<span>6 − y + 3 

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5 0
4 years ago
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A
dsp73

Answer:

We are given the path, y=-3x-6

The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.

Thus, the slope of the given line is -3.

As, we have that the incipient path is perpendicular to the given path.

And, we ken that, 'Product of slopes of perpendicular lines is -1'.

Since, the incipient path passes through the point (-3,3). Superseding the values in the general form, we get,

b= 3+1

b= 4.

Step-by-step explanation:

4 0
3 years ago
Dons signature coffee blend is 60% dark roast and 40% light roast. He has 10 kg of blend A, which is 80% dark roast and 20% ligh
astraxan [27]

Answer

Find out the how many kilograms of blend A will don need to use to make 10 kg of his signature blend .

To proof

As given

Dons signature coffee blend is 60% dark roast and 40% light roast.

He has 10 kg

60 % is written in the decimal form

= \frac{60}{100}

= 0.6

40 % is written in the decimal form

= \frac{40}{100}

= 0.4

Now 60% dark roast of  10 kg = 0.6 ×10

                                                 = 6 kg

Now 40% of  10 kg = 0.4 × 10

                               = 4 kg

As given

He has 10 kg of blend A, which is 80% dark roast and 20% light roast  i.e 80% of the 6kg is dark roast and 20% of the  4kg is light roast .

80% is written in the decimal form

= \frac{80}{100}

= 0.8

80% of the 6kg is dark roast = 0.8 × 6

                                                = 4.8 kg

20% is written in the decimal form

= \frac{20}{100}

= 0.2

20% of the 4kg is light roast = 0.2 × 4

                                               = .8kg

Total kilograms of blend A will don need to use to make 10 kg of his signature blend =  4.8 kg + .8 kg

                          = 5.6 kg

Hence proved




 


8 0
3 years ago
what if connors distance of 3 kilometers represented only 2/10 of the total distance of the race what would the distance of the
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Answer:

24 kilometres.

Step-by-step explanation:

10/10=Total Distance of the Race

3 kilometres =2/10

24 kilometres=10/10

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