Solve for n p=-5m+7n-3

Please Help Quicly The equation 8x - 4y = 5 is dilated by a scale factor of 8 centered at the origin. What is the new slope and

Rzqust [24]

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

Note : Figure given is for reference to understand better.

Where redline is for given line and blueline for new line

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

$8x-4y=5$

$8(0)-4y=5$

$y=\frac{-5}{4}$

When y=0, x=?

$8x-4y=5$

$8x-4(0)=5$

$x=\frac{5}{8}$

We get points $A(0,\frac{-5}{4}), B(\frac{5}{8},0)$

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point $A(0,\frac{-5}{4})$ from origin is $( \frac{-5}{4})$ unit in x-direction and zero $\frac{-5}{4})$ unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $A'(0,-10)$

For point B:

Distance of point $B(\frac{5}{8},0)$ from origin is $(\frac{5}{8})$ unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $B'(5,0)$

Step 3: Find Equation of new line.

Points $A'(0,-10)$ and $B'(5,0)$ make a new line

The equation of given as

$\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}$

$\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}$

$\frac{y+(10)}{x} = 2$

$y+10= 2x$

$y= 2x-10$

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

8 0

3 years ago

In a topographical map of a city, the vertices of the city limits are A(10,9),B(18,9),C(18,2),D(14,4.5),E(10,4.5). The coordinat

Viefleur [7K]

I think it’s D??????

3 0

3 years ago

How many pairs of whole numbers have the sum of 99

valentina_108 [34]

50 pairs of whole numbers

7 0

3 years ago

A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft hi

zheka24 [161]

Weight of man and paint = 160 + 5 = 165 total pounds.

Gravitational force is independent of the path taken so we can ignore the radius of the silo.

Work done = total weight x height

The problem says he climbs to the top so overall height is 90 feet

Work = 165 lbs x 90 ft = 14,850 ft-lbs

5 0

3 years ago

Describe the differences between a parabola that has a horizontal directrix and a parabola that has a vertical directrix.

Readme [11.4K]

A parabola that has a horizontal directrix is a parabola that opens up or down.

Here are some of its components:
1) Standard equation of a parabola with a horizontal directrix: (x-h)^2 = 4a(y-k),
a = distance from vertex to focus
2) Vertex at (h,k)
3) Focus(h,k+a)
4) Directrix: y = k-a
5) Axis of symmetry: x = h

A parabola that has a vertical directrix opens to the right or left and is on its side.

Here are some components
1) Standard equation of a parabola with a vertical directrix: (y-k)^2 = 4a(x-h)
2) vertex (h,k)
3) focus (h+a,k)
4) directrix: x = h-a
5) Axis of symmetry: y = k

Hopes this helps :)

4 0

3 years ago