Which of the followin, ordered pairs is represented by a point located on the y-axis?

What is the distance between the lines y = 2x and y = 2x+5? Round your answer to the nearest tenth.

The distance between both lines is 2.24 units

Step-by-step explanation:

There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.

Given

$y=2x\\Putting\ x=1\\y=2(1)\\y=2\\So, the\ point\ on\ y=2x\ is\ (1,2)$

We have to find the distance of this point from y=2x+5

$y=2x+5\\Subtracting\ y\ from\ both\ sides\\y-y=2x+5-y\\2x-y+5=0$

The formula for finding distance of a point (x,y) from a line is:

$d=\frac{|Ax+By+C|}{\sqrt{A^2+B^2}}$

A=2

B=-1

C=5

Putting the values in the formula

$d=\frac{|(2)(1)+(-1)(2)+5|}{\sqrt{(2)^2+(-1)^2}}\\d=\frac{|2-2+5|}{\sqrt{4+1}}\\d=\frac{|5|}{\sqrt{5}}\\d=\frac{5}{\sqrt{5}}\\d=2.236\ units$

Rounding off will give: 2.24 units

The distance between both lines is 2.24 units

Keywords: Equations of lines

Learn more about distance in lines at:

#LearnwithBrainly

7 0

3 years ago

Clare subscribes to an online music streaming service

xeze [42]

Answer:

She should go with service 2 because it is, cheaper. Service 1 cost $107.52, but service 2 cost only $105.

Step-by-step explanation:

Cost now+increase$=new cost

(Part=percent*whole)

Increase=percent increase*cost now

i=12%*$96

i=0.12*96=$11.52

$96+11.52=107.52

Service two⬇️

8.72*12=$105

5 0

3 years ago

Which symbol correctly compares these fractions? 3 7 ___ 5 14 < > = ×

GarryVolchara [31]

$\frac{3}{7}$ is more than $\frac{5}{14}$ , because:
$\frac{3}{7}$ = $\frac{6}{14}$
6>5

So, the correct sign for this is >.
Have a great day! ♪

7 0

3 years ago

Please help solve for PQ.

DerKrebs [107]

This problem cannot be solved unless we are given figure NPQR is a rhombus.
In that case, then all sides are equal, meaning
5x+16=9x-32
Solve for x
9x-5x=16+32
4x=48
x=12

Each side (including PQ) then equals 5x+16=5*12+16=76

8 0

3 years ago

A projectile is fired with muzzle speed 250 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe

qaws [65]

The projectile's horizontal and vertical positions at time $t$ are given by

$x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ\,t$

$y=30\,\mathrm m+\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ\,t-\dfrac g2t^2$

where $g=9.8\dfrac{\rm m}{\mathrm s^2}$ . Solve $y=0$ for the time $t$ it takes for the projectile to reach the ground:

$30+\dfrac{250}{\sqrt2}t-4.9t^2=0\implies t\approx36.2458\,\mathrm s$

In this time, the projectile will have traveled horizontally a distance of

$x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m$

The projectile's horizontal and vertical velocities are given by

$v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ$

$v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt$

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about $\sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}$ .

7 0

3 years ago