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julsineya [31]
3 years ago
8

Equation of the line (-6,5) and (8,14) in standard form

Mathematics
1 answer:
blsea [12.9K]3 years ago
4 0

Answer:

\huge\boxed{9x-14y=-70}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

We have two points (-6, 5) and (8, 14).

Substitute:

m=\dfrac{14-5}{8-(-6)}=\dfrac{9}{14}\\\\y-5=\dfrac{9}{14}(x-(-6))\\\\y-5=\dfrac{9}{14}(x+6)

Thew standard form of an equation of a line:

Ax+By=C

transform:

y-5=\dfrac{9}{14}(x+6)\qquad|\text{multiply both sides by 14}\\\\14y-14\cdot5=14\!\!\!\!\!\diagup^1\cdot\dfrac{9}{14\!\!\!\!\!\diagup_1}(x+6)\\\\14y-70=9(x+6)\\\\14y-70=9x+54\qquad|\text{subtract}\ 9x\ \text{from both sides}\\\\-9x+14y-70=54\qquad|\text{add 70 to both sides}\\\\-9x+14y=70\qquad|\text{change the signs}\\\\9x-14y=-70

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Answer:

Note that both relations and functions have domains and ranges. The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.

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3 years ago
A large pizza has a diameter of 14 inches. A medium pizza has a diameter of 10 inches. How much larger is the area of the large
Arte-miy333 [17]

Answer:

The bigger pizza has a diameter of 14 inches, or a radius of 14 / 2 = 7 inches.

The smaller pizza has a diameter of 12 inches, or a radius of 12 / 2 = 6 inches.

Step-by-step explanation:

The area of a circle is πR2 where R is the radius.

The difference in the size of the pizzas is  

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= π(7 inches)2 - π(6 inches)2 = = 49π inches2 - 36π inches2 = 13π inches2  

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An elevator containing five people can stop at any of seven floors. What is the probability that no two people exit at the same
elena-s [515]

Answer:

Approximately 0.15 (360 / 2401.) (Assume that the choices of the 5 passengers are independent. Also assume that the probability that a passenger chooses a particular floor is the same for all 7 floors.)

Step-by-step explanation:

If there is no requirement that no two passengers exit at the same floor, each of these 5 passenger could choose from any one of the 7 floors. There would be a total of 7 \times 7 \times 7 \times 7 \times 7 = 7^{5} unique ways for these 5\! passengers to exit the elevator.

Assume that no two passengers are allowed to exit at the same floor.

The first passenger could choose from any of the 7 floors.

However, the second passenger would not be able to choose the same floor as the first passenger. Thus, the second passenger would have to choose from only (7 - 1) = 6 floors.

Likewise, the third passenger would have to choose from only (7 - 2) = 5 floors.

Thus, under the requirement that no two passenger could exit at the same floor, there would be only (7 \times 6 \times 5 \times 4 \times 3) unique ways for these two passengers to exit the elevator.

By the assumption that the choices of the passengers are independent and uniform across the 7 floors. Each of these 7^{5} combinations would be equally likely.

Thus, the probability that the chosen combination satisfies the requirements (no two passengers exit at the same floor) would be:

\begin{aligned}\frac{(7 \times 6 \times 5 \times 4 \times 3)}{7^{5}} \approx 0.15\end{aligned}.

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2 years ago
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Answer:

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Step-by-step explanation:

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