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Viefleur [7K]
3 years ago
12

a dog weighs 8 times as many as his cat. together the two pets weigh 54 pounds. how much does the dog weigh?

Mathematics
2 answers:
Savatey [412]3 years ago
4 0
The cat would weigh 6.75 pounds because 54( the total weight)divided by 8( the dog's weight) equals 6.75( the cat's weight) 
Anna [14]3 years ago
3 0
54/9=6
the dog weighs 6*8 is 48 pounds
and the cat weighs 6 pounds
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Sergeu [11.5K]

Answer should be: 2 + 2i

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Find the value of x so that the figures have the same area.<br><br> 25ft, x-6 ft<br><br> x ft, 15ft
levacccp [35]
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3 0
3 years ago
A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int
Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}

By expanding the previous equation:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0

Since there is no accumulation within the tank, expression is simplified to this:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}, where c(0) = 0 \frac{pounds}{gallon}.

\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}

The solution of this equation is:

c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})

The salt concentration after 8 minutes is:

c(8) = 0.166 \frac{pounds}{gallon}

The instantaneous amount of salt in the tank is:

m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds

3 0
3 years ago
Write an equation of each line in standard form with integer coefficients.<br> 4. y = 2.4x + 1.8
Nadusha1986 [10]

Answer:

<h2>12x - 20y = -9</h2>

Step-by-step explanation:

The standard form of an equation of a line:

Ax+By=C

We have

4y=2.4x+1.8

Convert

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40y=24x+18          <em>subtract 24x from both sides</em>

-24x+40y=18            <em>change the signs</em>

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3 years ago
3 2/7 fraction that have the same value
zimovet [89]
46/14. Hoped this helped!
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3 years ago
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