1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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
You might be interested in
At time t = 0 a car moves into the passing lane to pass a slow-moving truck. The average velocity of the car from t =1tot =1+his
nirvana33 [79]

The correct given equation is:

v = [3 (h + 1)^2.5 + 580 h – 3] / 10 h

So to solve for the instantaneous velocity at t = 1, we must set h = 0. However we cannot do that since h is in denominator and a number divided by a denominator is infinite. Therefore we must set h to something almost zero. In this case, h = 0.0000001, so that:

 

at t = 1

v = [3 (0.0000001 + 1)^2.5 + 580 (0.0000001) – 3] / 10 * 0.0000001

<span>v = 58.75 ft/s</span>

4 0
3 years ago
The lengths of the sides of a triangle are in the ratio
Anton [14]
HOW TO SOLVE:

1) use x as a variable
2) the starting equation is:
          4x + 3x + 5x = 18

3) add all the like terms on the left side of the equation:
          12x = 18

4) Divide by 12 on both sides:
          x=1.5

5) Find the lengths of the sides:

        - 4x = 4(1.5) = 6

        - 3x = 3(1.5) =  4.5

       - 5x = 5(1.5) = 7.5

SO, the lengths of the sides of this triangle are: 6, 4.5, and 7.5
5 0
3 years ago
2 × 30 = 2 × (3 × 10)
vampirchik [111]

Answer:They are equivalent, if that's what your trying to find out.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Help me with C number please. Show me how did you do that. It’s due in 30 minutes.
Paha777 [63]
I’m not 100% sure but isn’t it x2 +xy +y2?
6 0
3 years ago
Read 2 more answers
Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.
galben [10]

Answer:

∠EFD ≅ ∠EGD ⇒ A

Arc ED ≅ arc FD ⇒ C

m arc FD = 120° ⇒ E

Step-by-step explanation:

Let us revise some facts

  1. Equal chords subtended equal arcs
  2. The measure of an inscribed angle is one-half the measure of the central angle which subtended by the same arc
  3. The measure of a central angle is equal to the measure of its subtended arc
  4. If one angle of an isosceles triangle measure 60° then the triangle is equilateral
  5. The sum of the measures of the interior angles of any quadrilateral is 360°

In the quadrilateral  CDGE

∵ m∠G = 60°

∵ m∠GDC = m∠GEC = 90°

- By using the 5th rule above

∴ m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

∴ 60 + 90 + m∠DCE + 90 = 360

∴ 240 + m∠DCE = 360

- Subtract 240 from both sides

∵ m∠DCE = 120°

In circle C

∵ ∠DCE is a central angle subtended by arc DE

∵ ∠DFE is an inscribed angle subtended by arc DE

- By using the 2nd rule above

∴ m∠DFE = \frac{1}{2} m∠∠DCE

∵ m∠DCE = 120°

∴ m∠DFE = \frac{1}{2} (120)

∴ m∠DFE = 60°

- That means ∠EFD ≅ ∠EGD because their measure is 60°

∴ ∠EFD ≅ ∠EGD

In Δ EFD

∵ EF = FD

∵ m∠DFE = 60°

- By using the 4th rule above

∴ Δ EFD is an equilateral triangle

∴ ED = FD = FE

In circle C

∵ Side ED subtended by arc ED

∵ Side FD subtended by FD

∵ Side ED ≅ side FD ⇒ proved

- By using the 1st rule above

∴ Arc ED ≅ arc FD

∵ m∠ECD = 120°

∵ ∠ECD is a central angle subtended by arc ED

- By using the 3rd rule above

∴ m∠ECD = m arc ED

∴ m of arc ED = 120°

∵ Arc ED ≅ arc FD

∴ m arc ED = m arc FD

∴ m arc FD = 120°

5 0
2 years ago
Read 2 more answers
Other questions:
  • Arrange the following units in order from smallest to greatest: centimeter, kilometer, meter, millimeter
    12·2 answers
  • Tom says that he needs 6 rolls to obtain each possible outcome on a 6-sided die. On the fourth roll, he rolls his second "3". To
    13·2 answers
  • Evaluate the geometric series . 254 255 508 510
    13·2 answers
  • Which assignment for the events in the sample space will work?
    5·1 answer
  • Please help!!!!!!!!!!
    5·2 answers
  • What is the length of AB?
    9·2 answers
  • Directions - solve the liner system. enter your answer as an ordered pair. 2x + 3y = 31 y = x + 7
    15·1 answer
  • Find the height of a prism whose volume is 108 cm3<br> and the area of the base is 15 cm2.
    11·1 answer
  • Given that f(x) = x2 – 5x – 14 and g(x) = x – 7, find (f +g)(x) and
    14·1 answer
  • In God of Highschool: Who was the one opponent that Taek Jegal didn't view as trash?​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!