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3 years ago

Which of the following is 3 units lower than y = 4x2 – 8x + 2, but opens in the same direction and has the same shape?

Mathematics

1 answer:

olga_2 [115]3 years ago

6 0

Simplify the function $y=4x^2-8x+2$ in the following way:

$y=4x^2-8x+2=4x^2-8x+4-4+2=4(x^2-2x+1)-2=4(x-1)^2-2.$

If you have to translate the graph of the function 3 units lower (down), then

$y=4(x-1)^2-2-3=4(x-1)^2-5.$

The graph of obtained function opens in the same direction as the graph of the function $y=4(x-1)^2-2.$

Answer: $y=4(x-1)^2-5.$

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Answer:

B. g(x)= -x² - 4

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Step-by-step explanation:

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Since, The vertex of parabola g is on point (0 ,-4) then we have to subtract 4.

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3 years ago

Read 2 more answers

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium d

nikitadnepr [17]

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

$P(t)=Ce^{kt}$

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

$P(t)=Ce^{kt}$

For t=0, we have:

$P(0)=Ce^0=C=58$

If we use the duplication time, we have:

$P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08$

Then, we have the model as:

$P(t)=58e^{2.08t}$

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

$RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k$

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

$P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644$

The rate of growth can be calculated as dP/dt and is:

$dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)$

For t=8, the rate of growth is:

$dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140$

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

$P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81$

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3 years ago

Which strategy would not correctly solve this story problem? Luke buys a muffin and glass of juice each Monday for breakfast. Ea

svetlana [45]

Answer:

The answer is D.

Step-by-step explanation:

Each Monday, Luke spends $5 ($3 for the muffin, $2 for the juice). To figure out how much he spends in 6 weeks, you multiply $5 by 6. Hope this helps! :)

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3 years ago