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3 years ago

Why might you want to use the commutative property to change the integers

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

To keep the equation equal. what you do on one side should be done to the other.

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

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Brooke plays on her schools softball team. Last season she was at bat 500 times and made a safe hit 28% of the time. How is 28%

Gre4nikov [31]

Answer:

28/100

Step-by-step explanation:

5 0

3 years ago

Numbers expressed using exponents are called .

N76 [4]

Answer:

numbers expressed using exponents are called powers

4 0

2 years ago

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Help me find x on either one of these problems please!

mash [69]

In the problem with the white circle, x=100, in the problem with the blue circle, x might equal 165, but I'm not entirely certain. But I am certain about the first one.

3 0

3 years ago

During a movie, Tanvi ate 4/5 of a handful of snack mix, and Wyatt ate 2/5 of a handful. How much more did Tanvi eat?

skelet666 [1.2K]

2/5 more i believe!
basically just subtract 4/5 and 2/5 and you get 2/5
feel free to mark brainliest, hope this helps!

4 0

3 years ago

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