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Anton [14]
3 years ago
13

309 / 17 equals plz need help

Mathematics
1 answer:
MaRussiya [10]3 years ago
8 0
309/17 equals about 18.176 but it’s a rounded answer/decimal.
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Pls help fast 27/d=4 1/2 i need to find d
zvonat [6]

Answer:

121 1/2

Step-by-step explanation:

27/d = 4.5

*27       *27

d = 121.5

d = 121 1/2

6 0
2 years ago
Read 2 more answers
Solving a Two-Step Matrix Equation<br> Solve the equation:
Cloud [144]

Answer:

\boxed {x_{1} = 3}

\boxed {x_{2} = -4}

Step-by-step explanation:

Solve the following equation:

\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right]

-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:

-First equation:

3x_{1} + 2x_{2} + 1 = 2

-Second equation:

5x_{1} + 5x_{2} + 2 = -3

-Choose one of the two following equations, which I choose the first one, then you solve for x_{1} by isolating

3x_{1} + 2x_{2} + 1 = 2

-Subtract 1 to both sides:

3x_{1} + 2x_{2} + 1 - 1 = 2 - 1

3x_{1} + 2x_{2} = 1

-Subtract 2x_{2} to both sides:

3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1

3x_{1} = -2x_{2} + 1

-Divide both sides by 3:

3x_{1} = -2x_{2} + 1

x_{1} = \frac{1}{3} (-2x_{2} + 1)

-Multiply -2x_{2} + 1 by \frac{1}{3}:

x_{1} = \frac{1}{3} (-2x_{2} + 1)

x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}

-Substitute -\frac{2x_{2} + 1}{3} for x_{1} in the second equation, which is 5x_{1} + 5x_{2} + 2 = -3:

5x_{1} + 5x_{2} + 2 = -3

5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3

Multiply -\frac{2x_{2} + 1}{3} by 5:

5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3

-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3

-Combine like terms:

-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3

\frac{5}{3}x_{2} + \frac{11}{3} = -3

-Subtract \frac{11}{3} to both sides:

\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}

\frac{5}{3}x_{2} = -\frac{20}{3}

-Multiply both sides by \frac{5}{3}:

\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}

\boxed {x_{2} = -4}

-After you have the value of x_2, substitute for x_{2} onto this equation, which is x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}:

x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}

x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}

-Multiply -\frac{2}{3} and -4:

x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}

x_{1} = \frac{8 + 1}{3}

-Since both \frac{1}{3} and \frac{8}{3} have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:

x_{1} = \frac{8 + 1}{3}

x_{1} = \frac{9}{3}

\boxed {x_{1} = 3}

5 0
3 years ago
King High School has asked Marcy to paint some murals around the school, and Marcy is thrilled! Her mural in the main office wil
34kurt

Answer:

She used  cans of 2 and 1/2white paint.

Step-by-step explanation:

3 0
3 years ago
Your swimming pool containing 60,000 gal of water has been contaminated by 6 kg of a nontoxic dye that leaves a swimmer's skin a
Paul [167]

[a] Dye is removed from the pool at a rate of

(250 gal/min) * (<em>q</em>/60,000 g/gal) = -<em>q</em>/240 g/gal

where <em>q</em> denotes the amount of dye in the pool at time <em>t</em>. Clean water is pumped back into the pool, so no dye is being re-added.

So the net rate of change of the amount of dye in the pool is given by the differential equation,

\dfrac{\mathrm dq}{\mathrm dt}=-\dfrac{q(t)}{240}

with the intial value, <em>q</em>(0) = 6000 g (or 6 kg).

[b] The ODE above is separable as

\dfrac{\mathrm dq}q=-\dfrac{\mathrm dt}{240}

Integrate both sides to get

\ln|q|=-\dfrac t{240}+C

e^{\ln|q|}=e^{-t/240+C}

\implies q(t)=e^{-t/240+C}=e^{-t/240}e^C=Ce^{-t/240}

Now plug in the initial condition:

6000=Ce^0\implies C=6000

so the particular solution to the IVP is

q(t)=6000e^{-t/240}

[c] The acceptable concentration of the dy is 0.03 g/gal, which in a pool containing 60,000 gal of water corresponds to

(0.03 g/gal) * (60,000 gal) = 1800 g = 1.8 kg

of dye. Find the time <em>t</em> when this occurs:

1800=6000e^{-t/240}\implies0.3=e^{-t/240}

\implies\ln0.3=-\dfrac t{240}

\implies t=-240\ln0.3\approx288.953

so the amount of dye in the pool is within the acceptable tolerance after about 289 min have passes, or about 4.82 hrs. So no, the filtration system is not up to the task.

8 0
3 years ago
Read 2 more answers
Casey took 25 test in 135 days at this rate how many days will it take her to take 10 more test?
Dominik [7]
It will take 54 days for her to take 10 more tests :)
3 0
3 years ago
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