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1 year ago

2x+9y=27 x-3y=-24 It’s substitution

Mathematics

1 answer:

harkovskaia [24]1 year ago

7 0

Answer:

x = -9, y = 5

Step-by-step explanation:

Since we need to solve this system of linear equations by substitution, let's transform the second equation into the form, x = ay + b. We start off with x - 3y = -24, subtract 3y from both sides, and we get x = 3y - 24. Then, substitute the expression 3y - 24 for y in 2x + 9y = 27.

2(3y - 24) + 9y = 27 Substitute 3y - 24 for x.

6y - 48 + 9y = 27 Distribute 2.

15y = 75 Add & subtract to combine the like terms.

y = 5 Divide by 15.

Now that we have the value of y, we can find x by substituting 5 for y in any of the equations. Let's use 2x + 9y = 27 for example.

2x + 9(5) = 27 Substitute 5 for y.

2x + 45 = 27 Multiply.

2x = -18 Subtract.

x = -9 Divide by 2.

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krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

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