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4 years ago

25 points!

1 answer:

7 0

Pick 2 pairs of equations then use addition and subtraction to eliminate the same variable from both pairs of equations then it is left with 2 variables
Pick two pairs
4x - 3y + z = - 102x + y + 3z = 0
eliminate the same variable from each system
4x - 3y + z = - 10
2x + y + 3z = 0

4x - 3y + z = - 10
-4x - 2y - 6z = 0

-5y - 5z = - 10

2x + y + 3z = 0
- x + 2y - 5z = 17

2x + y + 3z = 0
-2x + 4y - 10z = 34

5y - 7z = 34
Solve the system of the two new equations:
-5y - 5z = - 10
5y - 7z = 34

-12z = 24
which is , z = - 2

-5y - 5(- 2) = - 10
-5y = - 20
wich is , y = 4
substitute into one of the original equations
- x + 2y - 5z = 17
- x + 2(4) - 5(- 2) = 17
- x + 18 = 17
- x = - 1
x = 1
which is , (x, y, z) = (1, 4, - 2)
Does 2(1) + 4 + 3(- 2) = 0 ? Yes

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Dilate the the triangle, scale factor = 3 (positive 3, ignore the

HACTEHA [7]

Answer:

The rule of dilation is $P'(x,y) = 3\cdot P(x,y)$ .

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

$P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0,0)$ , $k = 3$ , $A(x,y) = (-7,-6)$ , $B(x,y) = (-5,-2)$ and $C(x,y) =(-1,-5)$ , then dilated points of triangle ABC are, respectively:

$A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]$ (2)

$A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]$

$A'(x,y) = (-21, -18)$

$B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]$ (3)

$B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]$

$B'(x,y) = (-15,-10)$

$C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]$ (4)

$C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]$

$C'(x,y) = (-3,-15)$

The rule of dilation is:

$P'(x,y) = 3\cdot P(x,y)$ (5)

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

7 0

3 years ago

Find the equation of the line passing through the given points. Use function notation to write the equation, (-2,8) and (-6,20)

bekas [8.4K]

First you gotta find the slope
$\frac{20 - 8}{ - 6 - ( - 2)} = \frac{12}{ - 4} = - 3$
Then you can put it into point slope form using either of the points
$y - 20 = - 3(x + 6) \\ y - 20 = - 3x - 18 \\ y = - 3x + 2$

7 0

3 years ago

Please help me!! Will mark as the brainliest!!

Alexxx [7]

Answer:

Step-by-step explanation:

Use the number line and count how many numbers from 7 until you get to -3

4 0

3 years ago

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Solve the equation x2 + 5 = 0

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