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Kamila [148]
3 years ago
14

X-y+z=-4 3x+2y-z=5 -2x+3y-z=15 How do I solve this?

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
5 0
1)\ \ \ x-y+z=-4\ \ \ \Rightarrow\ \ \ z=-4-x+y\\\\2)\ \ \ 3x+2y-z=5 \\.\ \ \ \  \Rightarrow\ \ 3x+2y-(-4-x+y)=5 \\.\ \ \ \  \Rightarrow\ \ 3x+2y+4+x-y=5 \\.\ \ \ \  \Rightarrow\ \ 4x+y=1\\\\3)\ \ \ -2x+3y-z=15\\.\ \ \ \  \Rightarrow\ \ -2x+3y-(-4-x+y)=15\\.\ \ \ \  \Rightarrow\ \ -2x+3y+4+x-y=15\\.\ \ \ \  \Rightarrow\ \ -x+2y=11\\--------------------\\

z=-4-x+y\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ and\\ \left \{ {{4x+y=1\ \ \ \ } \atop {-x+2y=11\ /\cdot4}} \right. \\\\\left \{ {{4x+y=1\ \ \ \ } \atop {-4x+8y=44}} \right. \\-------\\y+8y=1+44\\9y=45\ /:9\\y=5\\\\-x+2y=11\ \ \ \Rightarrow\ \ \ x=2y-11\ \ \ \Rightarrow\ \ \ x=2\cdot5-11=-1\\\\z=-4-x+y=-4-(-1)+5=-4+1+5=2\\\\Ans.\ x=-1\ \ \ and\ \ \ y=5\ \ \ and\ \ \ z=2
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ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex  form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

5 0
3 years ago
Lisa has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area
Amiraneli [1.4K]
I would use the formula, area = length x width
7 0
3 years ago
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Amy bought a bag of chips for 0.75, a sandwhich for 5.50, a bottle of water for 1.60. How much does amy have left from 10.
ch4aika [34]

Answer:

Amy would have 2.15 left

Step-by-step explanation:

To find out how much she has left, subtract the cost of the items from 10.

10 - 0.75 - 5.50 - 1.60 = 2.15

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3 years ago
The supplement of an angle is 3 times the complement of an angle.
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Let’s says that x is the measure of the angle. X and it’s supplement are equal to 180. X and it’s complement are equal to 90. The supplement is s and the complement is c. S is times c which is the same as 3c.

3c + x = 180

C+x = 90
X = 90 - c

3c + 90 - c = 180
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The complement of. 45 degree angle is 45 degrees.

The angle is 45 degrees.
6 0
3 years ago
Plz explain.
slega [8]
Idk, why does the world need problems like this, not like everyone is going to grow up to be a math teacher.
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