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3 years ago

A line passes through the point A(n,4) and B(8,6) and is parallel to y=2x-5. what is the value of n

Mathematics

1 answer:

NARA [144]3 years ago

8 0

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

We have the line y = 2x - 5.

The parallel lines have the same slope. Therefore we have y = 2x + b.

Put the coordinates of the point B(8, 6) to the equation:

6 = 2(8) + b

6 = 16 + b subtract 16 from both sides

-10 = b → b = -10

The equation of a line: y = 2x - 10.

Put the coordinates of the point A(n, 4) to the equation:

4 = 2(n) - 10 add 10 to both sides

14 = 2n divide both sides by 2

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3 years ago

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4 years ago

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ra1l [238]

Using exponential functions, it is found that:

a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

b) The patient could have ingest 231 milligrams of caffeine.

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.
r is the decay rate, as a decimal.

In this problem:

Caffeine metabolize at a rate of 13% per hour, hence $r = 0.13$ .

Then:

$A(t) = A(0)(1 - r)^t$

$A(t) = A(0)(1 - 0.13)^t$

$A(t) = A(0)(0.87)^t$

Item a:

The coffee cup contains 150 milligrams of caffeine, hence $A(0) = 150$ .

At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).

$A(t) = A(0)(0.87)^t$

$A(8) = 150(0.87)^8$

$A(8) = 49.2$

Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

Item b:

This A(0), considering A(11) = 50, hence:

$50 = A(0)(0.87)^{11}$

$A(0) = \frac{50}{(0.87)^{11}}$

$A(0) = 231$

The patient could have ingest 231 milligrams of caffeine.

A similar problem is given at brainly.com/question/25537936

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2 years ago

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