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3 years ago

12

To create an image, Figure D is going to be reflected across the y-axis, rotated 180° around the point indicated in the figure,

and translated vertically across the x-axis. What must be true about Figure D and its image?

1 answer:

uranmaximum [27]3 years ago

8 0

The image and pre-image are congruent

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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

5 0

3 years ago

Some landlords ask for a special deposit before renting out an apartment. Which is the most likely purpose of a special deposit?

qaws [65]

Definitely A because it is the only one that makes sense

3 0

3 years ago

Read 2 more answers

Triangles ABC and DEF are similar. Find the lengths of AB and EF. Right triangles A B C and D E F. Side A B is 5 x, side B C is

Doss [256]

Answer:

Ummm...

Step-by-step explanation:

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2 years ago

Three adults and four children must pay $94 for their tickets

Sliva [168]

13.42 dollars EACH if all the tickets cost the same

8 0

3 years ago

Find mAC<br><br> Help me please

aleksandrvk [35]

Answer:

130 degrees

Step-by-step explanation:

arc CA is 50 since the angle is 50 and then you would subtract from 180 since it is half the circle which leaves you with C, or 130 degrees.

5 0

2 years ago