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3 years ago

Ted jogged a total of 11.2 miles in 4 days. He jogged the same distance each day

Mathematics

1 answer:

marta [7]3 years ago

3 0

Answer:

Part A: 2.8 miles

Part B: 16.8 miles

Step-by-step explanation:

First, solve for how many miles Ted jogged in 1 day:

Variable x = number of miles

11.2/4 = x/1

Cross multiply

11.2 × 1 = 4 × x

11.2 = 4x

Divide both sides by 4

2.8 = x

He jogged 2.8 miles every day.

To find how many miles Ted would jog in 6 days, simply multiply his miles per day by the number of days he will jog:

2.8 miles × 6 days = 16.8 miles in 6 days

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What is 0.45 expressed as a decimal with a line over 5

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3 years ago

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R(x) = -0.21x^3 + x^2 - 8.1x - 3 for x= -1 and x = 2

Minchanka [31]

Answer:

r(-1) = 6.31 and r(2) = -16.88

Step-by-step explanation:

* Lets read the problem and solve it

- Evaluate means find the value, so evaluate r(x) means find the value

of it at the given values of x

∵ r(x) = -0.21x³ + x² - 8.1x - 3

∵ x = -1 and x = 2

- Then find r(-1) by substitute x by -1 and find r(2) by substitute x by 2

# At x = -1

∴ r(-1) = -0.21(-1)³ + (-1)² - 8.1(-1) - 3

∴ r(-1) = -0.21(-1) + (1) - 8.1(-1) - 3

∴ r(-1) = 0.21 + 1 + 8.1 - 3

∴ r(-1) = 6.31

# At x = 2

∴ r(2) = -0.21(2)³ + (2)² - 8.1(2) - 3

∴ r(2) = -0.21(8) + (4) - 8.1(2) - 3

∴ r(2) = -1.68 + 4 - 16.2 - 3

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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

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