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2 years ago

What is the solution to this system of equations?

Mathematics

1 answer:

mixas84 [53]2 years ago

5 0

Answer:

(-2,4)

Step-by-step explanation:

The solution is the point at which the two lines intersect, (-2,4). That point is the only one that satisfies (works) in both equations:

y = x + 6

4 = -2 + 6

and

y = -0.5x + 3

4 = -0.5(-2) + 3

4 = 1 + 3

====

You can also solve it algebraically:

y = x + 6

y = -0.5x + 3

-0.5x + 3 = x + 6 [Use the value of y from the second equation in the first equation]

-1.5x = 3

x = -2

Use this is y = -2 + 6:

y = 4

(-2,4)

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1 year ago

What is the area of the trapezoid shown below?

Olin [163]

Answer:

78 sqr units

Step-by-step explanation:

Use the Pythagorean Theorem to help find the base opposite the two.

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3 years ago

Read 2 more answers

Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

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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3 years ago