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Anit [1.1K]
3 years ago
12

Two angles are supplementary. if the larger angle is 3 degrees more than twice the smaller angle then how big is each angle. wri

te an expression for each angle. write the equation for this situation. solve the equation. find the size of each angle.
Mathematics
1 answer:
Margaret [11]3 years ago
4 0
Two angles are supplementary when they <span>add up to 180 degrees.

x = </span><span>smaller angle
</span>2x+3 =<span> larger angle

x + 2x + 3 = 180
3x = 180 - 3
3x = 177
x = 177/3
x = 59</span>°   ← smaller angle

2x + 3 = 2*59 + 3 = 121°  ← larger angle
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3 years ago
A population of protozoa develops with a constant relative growth rate of 0.4964 per member per day. On day zero the population
vodka [1.7K]

Answer:

The population size after eight days is about 265

Step-by-step explanation:

This is an example of an exponential growth model. A quantity <em>y</em> that grows or decays at a rate proportional to its size fits in an equation of the form

\frac{dy}{dt}=ky

where k is a positive constant. Its solutions have the form

y=y_{0}e^{kt},

where y_{0} =y(0) is the initial value of y.

The population size can be calculated by using the below formula:

P(t)=P(0)e^{kt} where P(0) is the population on day zero.

Let t be the time in days,

We know from the information given that:

  • k = 0.4964 per member per day and
  • The day zero (t = 0) the population size is 5 (P(0) = 5)

To find the population size after eight days

Substitute P(0) = 5, k=0.4964 in P(t)=P(0)e^{kt}

Then

P(t)=5e^{0.4964\cdot t}

Now we calculate P(t) when t = 8 days

P(8) = 5e^{0.4964\cdot 8}\\P(8) = 5e^{3.9712}\\e^{3.9712}=53.04815\dots \\P(8) = 5 \cdot 53.04815\dots\\P(8) = 265.24075\dots \approx 265

Therefore the population size after eight days is about 265

8 0
3 years ago
Which of the following could be the graph of this equation?
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Answer: OPTION C.

Step-by-step explanation:

Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.

For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).

Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.

Therefore, you need to search the option that shown the graph wich contains the point (1,-3).

Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).

This is the graph of the option C.

8 0
3 years ago
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