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2 years ago

Solve the system of equations - 6x + 5y = 0 and -5x + 5y = -5 by combining

Mathematics

1 answer:

Anna [14]2 years ago

7 0

9514 1404 393

Answer:

(x, y) = (-5, -6)

Step-by-step explanation:

The coefficients of y are the same, so we can eliminate y by subtracting one equation from the other. Here, we choose to subtract the first from the second, so that the coefficient of x ends up positive.

(-5x +5y) -(-6x +5y) = (-5) -(0)

x = -5 . . . . . . simplify

-6(-5) +5y = 0 . . . . . . substitute x into the first equation

6 +y = 0 . . . . . . . . . . divide by 5

y = -6 . . . . . . subtract 6

The solution to the system of equations is (x, y) = (-5, -6).

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Answer:

Step-by-step explanation:

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Now we cross multiply:

$100\cdot12=1200\\\\1200\div60=20$

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2 years ago

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Answer:

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2 years ago

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solmaris [256]

Answer:

The initial mass of the sample was 16 mg.

The mass after 5 weeks will be about 0.0372 mg.

Step-by-step explanation:

We can write an exponential function to model the situation.

Let the initial amount be A. The standard exponential function is given by:

$P(t)=A(r)^t$

Where r is the rate of growth/decay.

Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:

$\displaystyle P(t)=A\Big(\frac{1}{2}\Big)^{t/4}$

After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.

Therefore, when x = 12, P(x) = 2. By substitution:

$\displaystyle 2=A\Big(\frac{1}{2}\Big)^{12/4}$

Solve for A. Simplify:

$\displaystyle 2=A\Big(\frac{1}{2}\Big)^3$

Simplify:

$\displaystyle 2=A\Big(\frac{1}{8}\Big)$

Thus, the initial mass of the sample was:

$A=16\text{ mg}$

5 weeks is equivalent to 35 days. Therefore, we can find P(35):

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2 years ago

Solve the following equation:<br> 1/3(y - 2) -5/6 (y + 1) =3/ 4(0 - 3) - 2

Evgesh-ka [11]

Answer:

11/5

Step-by-step explanation:

If you need help with more problems like this you can use m a t h w a y. (remove the spaces) :)

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2 years ago

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TEA [102]

Answer:

w = -7z/2

Step-by-step explanation:

We need to solve for w in terms of z.

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5w + 9z = 2z + 3w

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5w - 3w = 2z - 9z

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2 years ago

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