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Snowcat [4.5K]
3 years ago
13

Write an equation in standard form for the line that passes through the given points.

Mathematics
1 answer:
Natasha2012 [34]3 years ago
3 0

Answer:

The equation of the line in standard form is 3x+2y=12

Step-by-step explanation:

we know that

The equation of the line in standard form is

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have the points

(0,6) and (4.0)

substitute the values

m=\frac{0-6}{4-0}

m=\frac{-6}{4}

m=-\frac{3}{2}

step 2

Find the equation of the line in slope intercept form

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept

we have

m=-\frac{3}{2}

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem the y-intercept is given

The y-intercept is the point (0,6)

so

b=6

substitute

y=-\frac{3}{2}x+6

step 3

Convert to standard form

Multiply by 2 both sides to remove the fraction

2y=-3x+12

Adds 3x both sides

3x+2y=12

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On equal intervals, the y-values of a quadratic function have a common _________
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Answer:

  second difference

Step-by-step explanation:

The differences of the y-values will differ by a common amount.

<u>Example</u>:

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  differences of these differences are 8 and 8, a common value.

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Question about a rational expression
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-9=6/v

You have to multiply v both sides because
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2 years ago
A. Describe the connection of the pattern of outcomes to Pascal’s triangle.
pychu [463]

Answer:

The answer to the question is;

A. The pattern of outcomes of 0 heads, 1 head, 2 heads ... n heads when arranged in the Pascal's triangle is given by the row of the triangles with the lowest at the edges and highest  outcome in the middle potion of the rows in the Pascal's triangle.

B. The number of total possible outcomes in a row n is 2ⁿ.

Step-by-step explanation:

To solve the question, we note that.

Pascal's triangle is an important sequence of numbers formed by starting with 1 at the top of the triangle followed by 1s on the outer edges of the triangle and the numbers directly below two adjacent numbers is the sum of the two adjacent numbers.

In probability theory, such as in throwing a coin,  Pascal's triangle indicates the number of possible heads obtained when n number of coins is thrown, that is, 0 heads, 1 head 2 heads etc. as follows

Number of coins                          Possible head outcome             Total outcome

0 coin                                                      1                                                 1

1 coin                                                      1  1                                               2

2 coins                                                  1  2 1                                             4

3 coins                                                 1  3  3 1                                          8

4 coins                                               1  4  6 4  1                                       16

The above triangle means that when

0 coin is flipped, the number of 0 heads is  1

1 coin  is flipped, the number of 0 heads is 1 (T) and 1 head is 1 (H)

2 coins are flipped, the number of 0 heads is 1, (TT), 1 head is 2 (TH), (HT) and 2 heads is 1 (HH)

3 coins are flipped 0 heads = 1 (TTT), 1 head = 3, (TTH), (THT), (HTT), the number of 2 heads = 3, (HHT), (HTH), (TTH) and the number of 3 heads = 1, (HHH).

B. The pattern in the number of total possible outcomes is

1, 2, 4, 8, 16 which is =2 raised to the power of the number of coin tossed for a particular row as follows

Number of coin tossed = 0  = 2⁰ = 1 = Total possible outcome

Number of coin tossed = 1  =  2¹ =  2 = Total possible outcomes

Number of coin tossed = 2  = 2² = 4 = Total possible outcomes

Number of coin tossed = 3  = 2³ = 8 = Total possible outcomes

Number of coin tossed = 4  = 2⁴ = 16 = Total possible outcomes

Therefore total number of possible outcome = 2ⁿ where n = number of coins tossed.

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