Rina draws a plan of her school on a coordinate grid. she plots the school gate at point p(-8,-1) and the library at point q(2,5). she notices that the science lab is also located on pq and is two thirds the distance from the library to the school gate. what are the coordinates of the science lab ?

The coordinates of the science lab is:

x = -14/3  ,  y = 1

Step-by-step explanation:

∵ P is (-8 , -1) and Q is (2 , 5)

∵ The point of the science lab is (x , y)

∵ The science lab point divided PQ at ratio 2 : 1 from Q (two thirds PQ)

∴

∴

∴

∴

∴ The point of science lab = (-14/3 , 1)

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!