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3 years ago

30 points and will give brainliest

Mathematics

1 answer:

djyliett [7]3 years ago

4 0

The correct answers are B. (0,3) and C. (2,3/16)

Hope I helped.

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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

Read 2 more answers

Which property is shown? 4/5+ -<br> 4/5=0

TEA [102]

This looks like the additive inverse property, because when you add something to its negative counterpart (or its additive inverse), you get 0 as a sum.

Another example would be 2+ (-2) = 0. -2 is the additive inverse for 2.

7 0

2 years ago

What is the relationship between 9.125×10−3 and 9.125×102 ? Select from the drop-down menus to correctly complete the statement.

JulsSmile [24]

Given $9.125\times10^{-3}$ and $9.125\times10^{2}$

$9.125\times10^{2}=9.125\times10^{-3+5} \\ \\ =9.125\times10^{-3}\times10^5=9.125\times10^{-3}\times100000$

Therefore, $9.125\times10^{-3}$ is 100,000 times less than $9.125\times10^{2}$ .

8 0

3 years ago

Read 2 more answers

What is the square root of 83 to the nearest tenth?

Ymorist [56]

Knowing the squareroot of 81 is 9, we can easily know that square root of 83 is close to 9.

9 to the closest tenth is 10.

Hope I helped :)

8 0

3 years ago

Use rounding or compatible number to estimate the difference 287- 162

Nookie1986 [14]

Okay so i subtract and then i got my number 125 as the total answer

5 0

3 years ago