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2 years ago

What is the equation in point−slope form of the line passing through (−3, −4) and (0, 2)?

Mathematics

1 answer:

Nana76 [90]2 years ago

4 0

Answer:

y = 2x + 2

Step-by-step explanation:

To find the slope we do (Y1 - Y2)/(X1-X2) aka rise over run

So, m = (-4 - 2) / (-3 - 0)

m = 2

Now we have y = 2x +b

Notice one of our points is (0,2)

Since the x value of that point is 0, it is the y intercept.

In the slope intercept form b = y-intercept

Therefore b = 2

So, y = 2x + 2

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

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2 years ago

What is the measure of

Alona [7]

Yeh provide more info

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2 years ago

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Kisachek [45]

Answer:

2, 4, 6, and 8, respectively

Step-by-step explanation:

The rule says that 2 times the x value, which we are given, equals to y, which we must find. So all we hve to do is multiply each of the given x values by two to get the y value.

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Dahasolnce [82]

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(3/4)*x

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2 years ago

The table below shows the population of a town over x years. A 2-column table with 5 rows. The first column is labeled years wit

mel-nik [20]

Answer:

10,346.0(1.1)^x

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Step-by-step explanation:

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2 years ago

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