An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by 48 %, and increase the height by 18 %. By what factor has the volume of the room increased

Step-by-step explanation:

Initial volume of the rectangular room = Length * Width * Height

V = LWH 1

If the width is doubled then new width W2 = 2W

If the length is increased by 48%, the new Length L2 = L + 0.48L = 1.48L

If the height is increased by 18%, the new height H2 = H + 0.18H = 1.18H

The new volume after increasing all the dimensions will be;

V2 = L2W2H2

V2 = (1.48L)(2W)(1.18H)

V2 = 3.4928LWH 2

Now we will divide equation 2 by 1 to have;

V2/V = 3.4928LWH/LWH

V2/V = 3.4928

V2 = 3.4928V

This means that the volume of the room has increased by the factor of 3.4928.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4