2x + 12 = 18 - X<br> A. X= 3<br> B. X = 10<br> C. x = 6<br> D. X= 2

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

A volleyball reaches its maximum of 13 feet, 3 seconds after it is served. What quadratic formula could model the height of the

Katena32 [7]

Answer:

$H=-(t-3)^2+13$

Step-by-step explanation:

The path covered by the volleyball will be a downward parabola with the vertex being the highest point of the ball.

A general form of a downward parabola is given as:

$y=-a(x-h)^2+k$

Where $(h,k)$ is the vertex of the parabola and 'a' is a constant.

Now, let 'h' be the vertical height and 't' be the time taken.

So, the equation would be of the form:

$H=-a(t-h)^2+k$

Now, as per question:

h = 2 seconds, k = 13 feet.

$H=-a(t-3)^2+13$

Now, taking a = 1. So, the formula that can be used is:

$H=-(t-3)^2+13$

7 0

2 years ago

Please help! ! Timed !******

lord [1]

Answer:

(fоg)(x) = x

Step-by-step explanation:

f(x) = (x-1)/3

g(x)=3x+1

(fоg)(x) = f(g(x)) = ((3x+1)-1) / 3 = 3x / 3 = x

3 0

2 years ago

Brenda is planning her birthday party. She wants to have 10.82 liters of punch, 6.5 gallons of ice cream 3.9 pounds of fudge and

faltersainse [42]

The answer is 0.4328 liters hope this helped!

6 0

2 years ago

PLZ HELP FAST!!! WILL MARK THE BRAINLIEST -Which of the following is an equivalent form of the compound inequality −33 > −3x

Mazyrski [523]

Answer:

The answer is A

Step-by-step explanation:

4 0

2 years ago

2x + 12 = 18 - X A. X= 3 B. X = 10 C. x = 6 D. X= 2