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3 years ago

Find, to four significant digits, the distance between the graphs of 2x-3y+4=0 and 2x-3y+15=0.

1 answer:

4 0

In analytical geometry, we can find the linear distance between two parallel lines by determining the coefficients of the variables and the constants. The general equation for a linear equation is: Ax + By = C.

Line 1: 2x - 3y = -4
Line 2: 2x - 3y = -15

In this case, A=2 and B=-3. The constants are C₁ = -4 and C₂ = -15. The distance follows this formula:

d = |C₁ - C₂|/(√(A²+B²)
d = |⁻4 - ⁻15|/(√(2²+⁻3²)
d = 3.051 units

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Helpppppppp plzzz!! People.

DIA [1.3K]

the answer to the equation is fifteen

8 0

3 years ago

Which graph matches the equation y+3=2(x+3)? Mark this and return

harkovskaia [24]

Answer:

x= y+3/2 -3

Step-by-step explanation:

y+3/2=x+3

y+3/2-3=x

5 0

2 years ago

Read 2 more answers

What is x and y? 2x-2y=-4 2x+y=11 Is there infinitely many solutions, 1 solution, or no solution? solve by elimination.

Kaylis [27]

Let's solve your system by substitution.

2x−2y=−4;2x+y=11

Rewrite equations:

2x+y=11;2x−2y=−4

Step: Solve2x+y=11for y:

2x+y=11

2x+y+−2x=11+−2x(Add -2x to both sides)

y=−2x+11

Step: Substitute−2x+11foryin2x−2y=−4:

2x−2y=−4

2x−2(−2x+11)=−4

6x−22=−4(Simplify both sides of the equation)

6x−22+22=−4+22(Add 22 to both sides)

6x=18

6x/6 = 18/6

(Divide both sides by 6)

x=3

Step: Substitute3forxiny=−2x+11:

y=−2x+11

y=(−2)(3)+11

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

5 0

2 years ago

find the equation of the perpendicular bisector of the line segment joining the points (3,8) and (-5,6).

IgorLugansk [536]

Answer:

y = - 4x + 3

Step-by-step explanation:

The perpendicular bisector is positioned at the midpoint of AB at right angles.

We require to find the midpoint and slope m of AB

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)

m = $\frac{6-8}{-5-3}$ = $\frac{-2}{-8}$ = $\frac{1}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{1}{4} }$ = - 4

mid point = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the coordinates of A and B, then

midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )

Equation of perpendicular in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

with m = - 4

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 7) into the partial equation

Using (- 1, 7), then

7 = 4 + c ⇒ c = 7 - 4 = 3

y = - 4x + 3 ← equation of perpendicular bisector

3 0

3 years ago

Read 2 more answers

Solve using any method. −2x+y=3 −3x+y=1 (-1, -2) (2, 7) (-2, -1) (-2, -5)

damaskus [11]

Answer:

Therefore the Final Solution is x = 2 and y = 7

i.e (2 ,7)

Step-by-step explanation:

Given:

$-2x+y=3$ ...............Equation ( 1 )

$-3x+y=1$ ...............Equation ( 2 )

$y=3x+1$ ..............Equation ( 3 )

To Find:

x = ?

y = ?

Solution:

Substituting Equation ( 3 ) in Equation ( 1) we get

$-2x+3x+1=3\\\\x=3-1\\\\\therefore x =2$

Now Substituting x = 2 in Equation ( 3 ) we get

$y=3\times 2+1=6+1\\\\\therefore y=7$

Therefore the Final Solution is x = 2 and y = 7

i.e (2 ,7)

3 0

3 years ago