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ElenaW [278]
3 years ago
11

Solve the system of equations using any method. 2X – Y + Z = – 2, 6X + 3Y – 4Z = 8, – 3X + 2Y +3Z = – 6

Mathematics
1 answer:
krok68 [10]3 years ago
6 0

Answer:

Z = - 2, Y = 0, X = 0

Step-by-step explanation:

2X – Y + Z = – 2

6X + 3Y – 4Z = 8

– 3X + 2Y +3Z = – 6

isolate "X" in the first equation

2X - Y + Z = - 2 => isolate "2X"

2X = - 2 - Z + Y => divide either side by 2

X = - 1 - Z/2 + Y/2

substitute this value of X in the second two equations (applying the substitution method here)

6(- 1 - Z/2 + Y/2) + 3Y - 4Z = 8,

6Y - 7Z - 6 = 8

- 3(- 1 - Z/2 + Y/2) + 2Y +3Z = - 6,

Y + 9Z + 6/2 = - 6

isolate Y in the second equation (6Y - 7Z - 6 = 8) and substitute in the third equation (Y + 9Z + 6/2 = - 6)

6Y - 7Z - 6 = 8 => isolate 6Y

6Y = 14 + 7Z => divide either side by 6

Y = 7Z + 14/6 => substitute in second equation

7Z + 14/6 + 9Z + 6/2 = - 6 => solve for Z

61Z + 50/12 = - 6, Z = - 2

substitute the value of Z into the equations "Y = 7Z + 14/6" and using the value of Y and Z, substitute into "X = - 1 - Z/2 + Y/2"

Y = (7(- 2) + 14)/6 = 0 / 6

= 0

X = - 1 - (- 2)/2 + 0/2 = - 1 - (-1) + 0

= - 1 + 1 + 0 = 0

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Find the area of polygon​
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Answer:

87 cm²

Step-by-step explanation:

there is 1 triangle and 1 rectangle in the diagram. so you have to find the area of the both polygons and sum up to find the total area of polygon

area of triangle formula:

\frac{1}{2}  \times base \times height

1) area of triangle AED

base = 12 cm

height = 4.5 cm

area:

\frac{1}{2}  \times 12 \times 4.5 = 27 {cm}^{2}

area of rectangle formula:

length \times height

2) area of rectangle ABCD

length = 12cm

height = 5 cm

area:

12 \times 5 = 60 \: cm {}^{2}

3) area of whole polygon

= area of triangle AED + area of rectangle ABCD

= 27 cm² + 60 cm²

= 87 cm²

7 0
2 years ago
5x-25=-10<br><br> Please HELP
solong [7]

Answer:

We simplify the equation to the form, which is simple to understand  

5x+25=10

We move all terms containing x to the left and all other terms to the right.  

+5x=+10-25

We simplify left and right side of the equation.  

+5x=-15

or this is another way

Simplifying

5x = 25 + -10

Combine like terms: 25 + -10 = 15

5x = 15

Solving

5x = 15

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 3

Simplifying

x = 3

We divide both sides of the equation by 5 to get x.  

x=-3

3 0
3 years ago
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katen-ka-za [31]

Answer:

20 in³

Step-by-step explanation:

Volume of 300 pages:

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When the no. of pages change, only the thickness of the book changes:

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5 0
3 years ago
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Please help me to figure out this question. Thanks
Marta_Voda [28]

Answer:

a) 5 : 7

b) 25 black keys

c) 100 black keys will appear.

Step-by-step explanation:

a) From the picture,

There are 5 black keys and 7 white keys.

Therefore, the ratio of black keys to white keys are = 5 : 7 = 5/7

b) If the pattern continues, 25 black keys will be appeared on a portable full-sized keyboard.

Explanation -

From part A, we get the ratio of black keys to white keys = 5 : 7. Therefore,

If there are 7 white keys, there are 5 black keys

If there are 1 white keys, there are 5/7 black keys

If there are 35 white keys, there are (5*35)/7 black keys

= 25 black keys.

c) If there are 240 keys, the black keys will appear -

We get, the ratio of black keys to white keys = 5 : 7

The summation of the black keys and white keys = (5 + 7) = 12.

Therefore, if there are 240 keys, the black keys will be

= (5/12) x 240

= (5 x 240)/12

= 100

Therefore, there are 100 black keys.

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