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3 years ago

The length between (3, 8) and (-2, -4) is ______?

Mathematics

2 answers:

Mumz [18]3 years ago

4 0

Answer:

4,4

Step-by-step explanation:

vlada-n [284]3 years ago

4 0

Answer:
13 units

Explanation:
The formula used to find the distance between two points is known as the distance formula. The distance formula states that d = √((x₂ - x₁)² + (y₂ - y₁)²).

Let’s find the variables. Given that the points are (3, 8) and (-2, -4), we can say that

x₁ = 3
y₁ = 8
x₂ = -2
y₂ = -4

Let’s substitute these values into the distance formula.

d = √((-2 - 3)² + (-4 - 8)²)

Let’s simplify this.

-2 - 3 is -5, and -4 - 8 is -12.

d = √((-5)² + (-12)²)

(-5)² is 25, and (-12)² is 144.

d = √(25 + 144)

25 + 144 is 169.

d = √169

√169 is 13.

d = 13

Since d = 13, we know that the distance between the points (3, 8) and (-2, -4) is 13 units.

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117. Sami opens an account and deposits $100 into it at the end of each month. The account earns 2% per year compounded monthly.

Sergio [31]

Answer:

The explicit function is:

$S_{n} =Pz^{n-1} +C(\frac{z^{n-1}-1}{z-1} )$

where

$z=(1+\frac{0.02}{12})$

and we calculate S12:

$S_{12} = $1211.06$

Step-by-step explanation:

Expanding a few steps of the compound interest:

$S_{1}=100\\S_{2}=S_{1}(1+\frac{0.02}{12})+100\\S_{3}=S_{2}(1+\frac{0.02}{12})+100\\...\\S_{n}=S_{n-1}(1+\frac{0.02}{12})+100$

We can write:

$(1+\frac{0.02}{12})=z$

$100=C$ for deposits

Then, expanding the previous equations would yield:

$S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C$

This is a geometric series form, which can be simplified to:

$S_{n}=C(\frac{z^{n}-1}{z-1} )$

plugin in the values for the 12 month gives:

$S_{12}=100(\frac{(1+\frac{0.02}{12})^{12} -1}{\frac{0.02}{12}})=1211.0613$

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3 years ago

Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below

user100 [1]

Answer:

5/9

Step-by-step explanation:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favourable outcomes of either a multiple of 3 or an even number are

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

That is we have 20 favourable outcomes

Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=

total number of outcomes

favourable outcomes

Therefore, after substituting the values we get

probability=\frac{20}{36}probability=

After simplification we will get

probability=\frac{5}{9}probability=

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3 years ago

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Answer:

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