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olga55 [171]
3 years ago
15

your bathtub is 2 feet wide, 6 1/2 feet long, and 2 feet, 9 inches deep when full how many cubic feet of water do you need to fi

ll your bathtub?
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
4 0

Answer:

35.75

Step-by-step explanation:

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Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?
lakkis [162]
Given a circle described by the equation:
y^2+x^2=100
and a function g(x) given by the table
\begin{center}
\begin{tabular}{ |c |c |c }
 x & g(x) \\
 -1 & -22 \\
 0 & -20  \\
1 & -18   
\end{tabular}
\end{center}

The function g(x) describes a straight line with the equation:
\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}  \\  \\  \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)}  \\  \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1}  \\  \\ y+22=2(x+1)=2x+2 \\  \\ y=2x-20

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
y^2+x^2=100 \\  \\ (2x-20)^2+x^2=100 \\  \\ 4x^2-80x+400+x^2=100 \\  \\ 5x^2-80x+300=0 \\  \\ x^2-16x+60=0 \\  \\ (x-6)(x-10)=0 \\  \\ x-6=0 \ or \ x-10=0 \\  \\ x=6 \ or \ x=10

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).
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86= 10x + 26, what is x?
pashok25 [27]

Answer:

60 = 10x \\ x = 6

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A car travels 240 kilometers in 2 1/2 hours what is its speed
Oksanka [162]

Answer:

v = 96 km/h

Step-by-step explanation:

Data:

d = 240 km

t = 2.5 h

speed = d/t

speed = 240/2.5 = 96 km/h

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