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salantis [7]
3 years ago
9

Write in point slope form of the line that passes through the points (3,-1) and (6,-2)

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
8 0

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-(-1)}{6-3}\implies \cfrac{-2+1}{3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=-\cfrac{1}{3}(x-3)\implies y+1=-\cfrac{1}{3}(x-3)

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For every 20 penguins at the North Pole there are 9 polar bears. If you encountered 27 polar bears, how many penguins would you
cluponka [151]

Answer:

60 penguins

Step-by-step explanation:

We need to find out how many times 9, the number of polar bears for every 20 penguins, was multiplied by, so that we can multiply 20 penguins by the same amount.

27/9 = 3

20*3 = 60

5 0
2 years ago
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You roll a six-sided die. Find the probability of each of the following scenarios
romanna [79]

Answer:

a) 1/2

b) 5/6

c) 2/3

Step-by-step explanation:

a)

Rolling a number greater than 3 means you can roll a 4, 5, or 6, which contains rolling a 6. So, the probability is (1+1+1)/6=3/6=\boxed{1/2}

b)

Rolling a number less than 5 means you can roll a 1, 2, 3, or 4, but because you could also roll an even number, so you could also roll a 6.

So, the probability is (1+1+1+1+1)/6=\boxed{5/6}

c)

Rolling a 4 or an odd number means you can roll a 1, 3, 5, or 4. So, the probability is (1+1+1+1)/6=4/6=\boxed{2/3}

6 0
2 years ago
John invests a sum of money in a
nexus9112 [7]

Answer: 0.000007638035

Step-by-step explanation:

We can use the formula for compound interest to solve this.

Now, the formula goes thus:

A = P ( 1 + r/n)^nt

Where A is the amount compounded, P is the initial amount I.e the principal, r is the rate in % , t is the time while n is the number of times the interest is compounded per time I.e how many times per year.

From the question, we get the following parameters, A = $1912.41 , P = ? , t = 15 years, r = 2.63% and n = 1 of course.

Now, we substitute these into the formula

1912.41 = P ( 1 + 2.63) ^ 15

1912.41 = P ( 3.63) ^ 15

1912.41 = P ( 250,379,850)

P = 1912.41 ÷ 250,379,850

P = 0.000007638035

Looks pretty funny an answer right?

6 0
2 years ago
Help ASAP, really stuck
SpyIntel [72]

The total length of the wire needed to make this shape is 162cm

<h3>Perimeter of a triangle</h3>

The perimeter of a triangle is the sum of the external side of the triangle.

Given the following parameters

Length of one side of the outside shape = 24cm

The side length of the smaller triangle = 24/4 = 6cm

The perimeter of the smallest triangle  3(6) = 18cm

The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm

Total length of wire needed. = 3(24) + 3(18) + 36

Total length of wire needed = 72 + 54 + 36

Total length of wire needed = 162cm

Hence the total length of the wire needed to make this shape is 162cm

Learn more on perimeter of triangle here: brainly.com/question/24382052

#SPJ1

6 0
1 year ago
How to find restrictions for x??<br> 3. F(x)=2 sqrt x-4
stealth61 [152]

Answer:

  1. none
  2. none
  3. x ≥ 4

Step-by-step explanation:

The restrictions placed on the independent variable in a function are those necessary to ensure that the function is defined for all allowed values of that variable.

In the graphs of problems 1) and 2), we see that the functions are defined for all values of x, so there are no restrictions.

__

3. For the function ...

  f(x)=2\sqrt{x-4}

the value under the radical cannot be negative. The square root function is not defined for negative values, so the restriction is ...

  x -4 ≥ 0

  x ≥ 4 . . . . . . . add 4 to both sides of the inequality

4 0
2 years ago
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