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3 years ago

What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

Mathematics

1 answer:

uysha [10]3 years ago

5 0

Answer:

y = 1/5 x + 12/5

Step-by-step explanation:

We are looking for the equation of a line.

We satart with the slope-intercept form of the equation of a line.

y = mx + b

We need to find m, the slope, and b, the y-intercept.

The given line is y = 1/5 x - 3.

Its slope is 1/5.

Parallel lines have equal slopes, so the slope we need is also 1/5.

Now we have for our line

y = 1/5 x + b

Now we find b.

We are given a point on the line, (-2, 2). Using the slope we already know, plug in (-2, 2) in the equation and solve for b.

2 = 1/5 * (-2) + b

10 = -2 + 5b

12 = 5b

b = 12/5

Now that we know the y-intercept, we can write the equation of the line.

y = 1/5 x + 12/5

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<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are $10(1.8)^{168}$ bacteria in 1 week</h3>

<em><u>Solution:</u></em>

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

<em><u>The increasing function is given as:</u></em>

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

$r = 80 \5 = \frac{80}{100} = 0.8$

<em><u>Determine how many will be in 5 hours</u></em>

Substitute t = 5

$y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96$

y = 189

Thus, there are 189 bacteria in 5 hours

<em><u>Determine how many will be in 1 day ?</u></em>

1 day = 24 hours

Substitute t = 24

$y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588$

Thus, there are 13382588 bacteria in 1 day

<em><u>Determine how many will be in 1 week</u></em>

1 week = 168

Substitute t = 168

$y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}$

Thus there are $10(1.8)^{168}$ bacteria in 1 week

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Step-by-step explanation:

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Rina8888 [55]

<em><u>Note: The complete question, along with the graph, is attached below.</u></em>

Answer:

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Step-by-step explanation:

Given the function

$f\left(x\right)=a\left(b^x\right)$

From the attached graph, it is clear that

at x = 0,

$f\left(0\right)=a\left(b^0\right)$

$\:f\left(0\right)\:=\:a\:\times \:1$ ∵ $b^0=1$

$f\left(0\right)=a$

Thus

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From the attached figure, it is clear that

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$f\left(0\right)=a$

3 = a ∵ $f\left(0\right)=y=3$

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