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3 years ago

PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER

Mathematics

2 answers:

IgorC [24]3 years ago

4 0

$\left\{\begin{array}{ccc}-3x-y+z=6\\-3x-y+3z=0\\x-3z=3&|\text{add 3z to both sides}\end{array}\right\\\\x=3+3z\\\\\text{Substitute it to the first and the second equation:}\\\\\left\{\begin{array}{ccc}-3(3+3z)-y+z=6\\-3(3+3z)-y+3z=0\end{array}\right\\\\\text{use distributive property}\\\\\left\{\begin{array}{ccc}-9-9z-y+z=6&|\text{add 9 to both sides}\\-9-9z-y+3z=0&|\text{add 9 to both sides}\end{array}\right\\\\\text{combine like terms}$

$\left\{\begin{array}{ccc}-8z-y=15\\-6z-y=9&|\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-8z-y=15\\6z+y=-9\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-2z=6\qquad\text{divide both sides by (-2)}\\.\qquad\boxed{z=-3}\\\\\text{Put the value of z to the second equation:}\\\\6(-3)+y=-9\\-18+y=-9\qquad\text{add 18 to both sides}\\\boxed{y=9}\\\\\text{Put the value of z to the equation}\ x=3+3z:\\\\x=3+3(-3)\\x=3-9\\\boxed{x=-6}$

$Answer:\ \boxed{x=-6,\ y=9,\ z=-3\to(-6,\ 9,\ -3)}$

mash [69]3 years ago

3 0

Answer:

(-6,9,-3)

Step-by-step explanation:

-3x -y +z=6

-3x-y+3z =0

x-3z =3

Multiply the second equation by -1

-1 *(-3x-y+3z) =0*-1

3x +y -3z =0

Add this to the first equation

-3x -y +z=6

3x +y -3z =0

----------------------

0 + 0 + -2z = 6

Divide by -2

-2z/-2 = 6/-2

z = 6/-2

z=-3

Take the third equation to find x

x-3z=3

x-3(-3) = 3

x+9=3

Subtract 9 from each side

x+9-9 =3-9

x=-6

Now we need to find y

3x +y -3z =0

3(-6) +y -3(-3) =0

-18 +y +9=0

-9+y =0

Add 9 to each side

-9+9+y = 0+9

y=9

(-6,9,-3)

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11Alexandr11 [23.1K]

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A. x-intercepts: (4,0),(-2,0)

C. Vertex: (1,-9)

Step-by-step explanation:

We have been given factored form of a quadratic equation $y=(x-4)(x+2)$ . We are asked to find vertex and x-intercepts of our given equation.

We know that x-intercepts of a graph are those points at which graph touches or crosses x-axis and y-coordinates of x-intercepts are always zero.

So we will substitute $y=0$ in our given equation to find the x-intercepts.

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Since y-coordinates of x-intercepts will be 0, therefore, x-intercepts of the graph will be (4,0), (-2,0) and option A is the correct choice.

To find the vertex of the parabola, we will expand our given expression using FOIL.

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$x^2-2x-8$

We will use formula $\frac{-b}{2a}$ to find the x-coordinate of vertex of parabola, where, a and b represents the coefficient of $x^2\text{ and }x$ respectively.