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3 years ago

The table given shows some x

Mathematics

1 answer:

Zigmanuir [339]3 years ago

8 0

Answer:

D and F

Step-by-step explanation:

r: m=-2 y=1 y = -2x + 1

s: m=2 y=1 y = 2x + 1

t: m=1/2 y=1 y = 1/2x + 1

slope of r x slope of t = -2 x 1/2 = -1 (r and t is perpendicular)

all 3line have the same y intercept (0,1), they are not possible to be parallel

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A machine produces 576 units in 18 hours at this rate how many will it produce in 28 hours

olga2289 [7]

Answer: 896

Step-by-step explanation:

Let's use a rule of three here.

$\frac{576}{x}=\frac{18}{28}$

Solve for x;

$x=\frac{576*28}{18}$

$x=896$

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3 years ago

Brandi needs to wrap a birthday present for her friend's party. Each side length is 16.7 in. What is the minimum amount of paper

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3 years ago

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:

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

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3 years ago

Read 2 more answers

What is the distance -4 and 7 on a number line?

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11 spaces :) 7 minus 11 is -4

3 0

4 years ago

the graph shows the number of people in an amusement park at different times where our 0 represents 9 a.m. if this trend continu

NNADVOKAT [17]

Answer:

can we see the graph?

Step-by-step explanation:

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3 years ago