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3 years ago

What is the solution to the system of equations graphed below? y = x - 2 y = 4x - 5

1 answer:

6 0

There are 3 available methods - Substitution , Elimination and Matrix.

The substitution method is used to eliminate one of the variables by replacement.

The elimination method is used for solving linear systems.

A Matrix is an array of numbers.

Lets use Substitution to solve this system.

$x-2=4x-5$

$-2=4x-5-x$

$-2=(4x-x)-5

 
$

$-2=3x-5$

$-2+5=3x$

$3=3x$

$3=3x / 3$

$x=1$

Now substitute $x=1$

$y=x-2$

$y=1-2

 
$

$y=-1

$

Hence - $x=1
 
y=-1$

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the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to retu

Snowcat [4.5K]

It takes 4.3 seconds for the rocket to return to earth.

The equation is:
$0=-9.8t^2+v_0t+h_0$
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:

$0=-9.8t^2+42t$

We will use the quadratic formula to solve this. The quadratic formula is:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Plugging in our information we have:
$t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)}
\\
\\=\frac{-42\pm \sqrt{1764-0}}{-19.6}
\\
\\=\frac{-42\pm \sqrt{1764}}{-19.6}
\\
\\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6}
\\
\\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6}
\\
\\=4.3\text{ or }0$

x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

8 0

3 years ago

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