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tigry1 [53]
3 years ago
12

PLEASE HELP!!! Find the equation , in the standard form of the line passing through the points (3,-4) and (5,1)

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
5 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ 3 &,& -4~) 
%  (c,d)
&&(~ 5 &,& 1~)
\end{array}
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-3}\implies \cfrac{1+4}{5-3}\implies \cfrac{5}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{5}{2}(x-3)\implies y+4=\cfrac{5}{2}x-\cfrac{15}{2}

\bf y=\cfrac{5}{2}x-\cfrac{15}{2}-4\implies y=\cfrac{5}{2}x-\cfrac{23}{2}\impliedby 
\begin{array}{llll}
\textit{now let's multiply both}\\
\textit{sides by }\stackrel{LCD}{2}
\end{array}
\\\\\\
2(y)=2\left( \cfrac{5}{2}x-\cfrac{23}{2} \right)\implies 2y=5x-23\implies \stackrel{standard~form}{-5x+2y=-23}
\\\\\\
\textit{and if we multiply both sides by -1}\qquad 5x-2y=23

side note:  multiplying by the LCD of both sides is just to get rid of the denominators
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A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed down
shepuryov [24]

A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is  9.6 miles

<u />

The speed of an object refers to the change of the object's distance within a specified time.

Mathematically, we can have;

\mathbf{Speed =\dfrac{distance}{time}}

Distance = speed × time

From the information given;

  • The fisherman row upstream for 4 miles/ hour.
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  • The fisherman row downstream at 6 miles/ hour
  • The distance covered by the fisherman = 6 × t₂  ------ (2)

  • SInce it took the entire trip 2 hours, we can infer that:

  • t₁ + t₂ = 2
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From equation (2), replace the above value of t₂ into equation (2)

  • d = 6 t₂
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From equation (1)

  • d = 4 t₁  

Equation both distance together, we have:

  • 12 - 6t₁ = 4t₁
  • 12 = 4t₁ + 6t₁
  • 12 = 10t₁
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  • t₁ = 1.2  hours

From t₂ = 2 - t₁

  • t₂ = 2 - 1.2
  • t₂ = 0.8 hours

From d = 4t₁

Replace t₁ with 1.2 hours

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Also, from d = 6t₂

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Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles

Learn more about distance here:

brainly.com/question/12319416?referrer=searchResults

3 0
2 years ago
Four cookies and three cupcakes code $13.25. Five cookies and two cupcakes cost $11.75. Give the system of equations that could
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Answer:

  • cookie: $1.25
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Step-by-step explanation:

Let x and y represent the cost of a cookie and a cupcake, respectively.

  4x +3y = 13.25

  5x +2y = 11.75 . . . . . . the system of equations

___

By Cramer's rule:

  x = (3(11.75) -2(13.25))/(3(5) -2(4)) = 8.75/7 = 1.25

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The cost of one cookie is $1.25; the cost of one cupcake is $2.75.

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ruslelena [56]

Answer:

y=4x+47

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6 0
3 years ago
Read 2 more answers
Pls send answer and show work pls
I am Lyosha [343]
For question 7, if we add all votes for tiger and eagle, we get

tiger = 14 + 13 + 8 + 5 = 40
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so choices A and B are wrong.
C is also wrong because fifth and sixth grade votes for eagle are 6 + 7 = 13 and the 5th and 6th grade votes for tiger are 14 + 13 = 27. clearly 5th + 6th like tiger more.

D is the answer for question 7

question 8

rolling a cube does not affect the other cube so it is all independent probability.
cube: 1 2 3 4 5 6
3 even numbers and 3 odd numbers

so probability of rolling an even number is

1/6 + 1/6 + 1/6 = 3/6 = 1/2

multiplying by total number of rolls, she will get even numberss

300 * 1/2 = 150

about 150 time.
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choice C is answer for question 8
4 0
3 years ago
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