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lutik1710 [3]
2 years ago
15

Write an equation of the line that passes through (−1,3) and is parallel to the line y=2x+2.

Mathematics
1 answer:
MA_775_DIABLO [31]2 years ago
4 0

The equation of the line that passes through (−1,3) and is parallel to the line y = 2x + 2 in slope intercept form is y = 2x + 5

<h3><u>Solution</u>:</h3>

Given that line passes through (-1, 3) and parallel to line y = 2x + 2

We have to find the equation of the line

Let us first find the slope of the line

<em><u>The slope intercept form of line is given as:</u></em>

y = mx + c  ---- eqn 1

where "m" is the slope of the line and "c" is the y-intercept

Comparing the given line equation y = 2x + 2 with y = mx + c,

We get slope "m" = 2

The slope of parallel lines are equal

Hence slope of the line which is parallel to y = 2x + 2 is also 2

Now let us find the equation of line with slope "m" = 2 and passes through point (-1, 3)

Substitute (x, y) = (-1, 3) in eqn 1 to find value of "c"

3 = 2(-1) + c

3 = -2 + c

c = 5

Now substitute "c" = 5 and m = 2 in eqn 1 to get equation of required line

y = 2x + 5

Thus the equation of line in slope intercept form is y = 2x + 5

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2 Richard and Jason each begin filling pools at the same time.
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The quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.

<h3>What are gallons?</h3>

A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.

It is given in the question that:-

Richard fills his pool at a rate of 6 gallons per minute.

Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.

After 20 minutes the amount of liquid in the tank will be:-

For Richard = 6 gallons per minute. x  20  minutes= 120 gallons

For Jason= 2 gallons per minute  x  20  =40 gallons

Jason has 200 gallons already in the tank

So it will become = 200+24=240 gallons.

Hence  quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.

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2 years ago
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The number of bacteria growing in an incubation culture increases with time according to n left parenthesis t right parenthesis
Anon25 [30]
For this case we have the following function:
 n (t) = 2400 * (5) ^ t 
 For n (t) = 60000 we have:
 60000 = 2400 * (5) ^ t
 We clear the value of t.
 For this we use the logarithm:
 (5) ^ t = 60000/2400
 log5 ((5) ^ t) = log5 (60000/2400)
 t = log5 (60000/2400)
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5 0
3 years ago
Find the first five terms of the sequence given the following recursive formula:
forsale [732]

Answer:

The first five terms are;

-3,-7,11,-29,69

Step-by-step explanation:

The recursive definition of the sequence is

a_1=-3,, a_2=-7 and a_n=a_{n-2}-2a_{n-1}.

When n=3, we obtain;

a_3=a_{3-2}-2a_{3-1}.

\implies a_3=a_{1}-2a_{2}.

\implies a_3=-3-2(-7).

\implies a_3=11.

When n=4

\implies a_4=a_{2}-2a_{3}.

\implies a_4=-7-2(11)=-29.

When n=5

\implies a_5=a_{3}-2a_{4}.

\implies a_4=11-2(-29)=69.

Therefore the first five terms are;

-3,-7,11,-29,69

5 0
3 years ago
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