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3 years ago

How many transformations are found in each function f(x)=-2(x+3)^2-4

Mathematics

1 answer:

patriot [66]3 years ago

6 0

a reflexion across the x axis

vertical stretch by a factor of 2

a horizontal shift 3 units left

a vertical shift 4 units down

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sasho [114]

#8: $900. (I found this answer by multiplying 3000 and 0.3 by the way)
#9: 160 miles. I found this answer by multiplying 80 by two, since two halves/50% make a whole or 100%.

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3 years ago

Solve the inequality:<br> 5 (2h+8) < 60

sashaice [31]

Answer:

5 (2h+8) < 60

10h+40<60

10h<20

h<2

Your Welcome

BIFFY OUT!!!

5 0

3 years ago

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

Which graph represents the function f(x)=−3x+7

zepelin [54]

It's be a line that crosses the y-axis at (0,7) and has a slope of -3 or -3/1.

4 0

3 years ago

The perimeter of the rectangle is 20\text{ cm}20 cm20, start text, space, c, m, end text. One side is 6\,\text{cm}6cm6, start te

Tamiku [17]

Answer: The lenght of the missing side is 4 cm

Step-by-step explanation:

The correct question is:

<em>The perimeter of the rectangle is 20cm . One side is 6cm. What is the length of the missing side?</em>

So, to answer it we have to apply the next formula:

Perimeter of a rectangle = 2 width + 2 length

Replacing with the values given: (assuming that the side given is the length of the rectangle)

20 = 2(6) + 2x

Solving for x:

20 =12 +2x

20-12 =2x

8 =2x

8/2 =x

4=x

The length of the missing side is 4 cm

Feel free to ask for more if needed or if you did not understand something.

3 0

3 years ago

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