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2 years ago

What is the slope of the line that is perpendicular to the line that goes through the two points (-8, 3) and (4, 27)?

Mathematics

1 answer:

Mademuasel [1]2 years ago

8 0

Answer:

-1/2 or -0.5

negative half

Step-by-step explanation:

slope of regular line= (y1-y2) / (x1-x2)

(27-3) / (4 - -8)

24 / (4+8)

24 / 12 = 2

the slope of a perpendicular line is the negative reciprocal

the negative reciprocal of positive 2/1 (2 as a fraction) is:

negative half: -1/2 or -0.5

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The the intensity I of light (in lumens) in a certain lake at a depth of x feet is given by log(1/12) = -0.00235x. What is the i

ch4aika [34]

Answer:

11.45 lumens

Step-by-step explanation:

We are given that

$log(I/12)=-0.00235x$

Where x=Depth

I=Intensity of light

We have to find the intensity of the light at a depth of 20 feet.

Substitute the value of x

$log(I/12)=-0.00235\times 20$

$log(I/12)=-0.047$

$\frac{I}{12}=e^{-0.047}$

$I=12e^{-0.047}$

$I=11.45 Lumens$

Hence, the intensity of the light (in lumens) at a depth of 20 feet=11.45 lumens

4 0

3 years ago

Which set of numbers is most reasonable to use to describe the area of your kitchen floor

elixir [45]

Square feet or Square meters (depending on if you live in the USA or UK)

8 0

3 years ago

10Hello, can you help me with this? How much is 5 raised to 5?

vesna_86 [32]

Answer:

A 5 by 5 Power in Trust is a clause that lets the beneficiary make withdrawals from the trust on a yearly basis. The beneficiary can cash out $5,000 or 5% of the trust's so-called fair market ...

Step-by-step explanation:

5^5

=5*5*5*5*5

=5^5

=3125

6 0

3 years ago

The sum of the first ten terms of a linear sequence is 145. the sum of the next ten term is 445. find the sum of the first four

chubhunter [2.5K]

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

$S_n =\frac{n}{2}(2a+(n-1)d)$

The sum of the first ten terms of a linear sequence is 145

⇒ $S_{10} =\frac{10}{2}(2a+(10-1)d)$

⇒ 145 = 5 (2a+9d)

⇒ $\frac{145}{5} =2a+9d$

⇒ 29 = 2a + 9d ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ $S_{20} =\frac{20}{2}(2a+(20-1)d)$

⇒ 590 = 10 (2a + 19d)

⇒ $\frac{590}{10}=2a+19d$

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = $\frac{30}{10}$

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = $\frac{2}{2}$

⇒ a = 1

Thus, sum of first four terms is

⇒ $S_4 =\frac{4}{2}(2(1)+(4-1)(3))$

⇒ $S_4 =2(2+(3)(3))$

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

Learn more about sum of sequence of n terms here

brainly.com/question/20385181

#SPJ4

6 0

1 year ago

The school you want to go to has an acceptance rate of 15%. That means that 15% of the students who apply to the school get in.

lisov135 [29]

12,000 Students Applied...

To find the answer, consider that for every 1000 students that apply, 150 students are accepted.

Divide 1800 by 150 and you get 12....which can be translated to 12,000 students

4 0

3 years ago