Triangle XYZ is similar to Triangle PQR, in triangle XYZ, XY = 4cm, YZ=6cm, XZ=5cm, in triangle PQR PQ=8cm find remaining sides of triangle PQR

QR = 12 (cm), RP = 10 (cm)

Step-by-step explanation:

Corresponding sides of the triangles:

XY : PQ, YZ : QR, ZX : RP.

For similar triangles ratios of corresponding sides are the same

XY : PQ = 4 : 8 = 1 : 2

YZ : QR = 1 : 2

ZX : RP = 1 : 2

YZ : QR = 1 : 2

6 : QR = 1 :2, QR = 12 (cm)

ZX : RP = 1 : 2

5 : RP = 1 : 2, RP = 10 (cm)

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!