2
7
) Write down a rational number which lies between
and
3
11​

43/66

Step-by-step explanation:

Let's write both fractions with the same denominator.  The LCD of 3 and 11 is 33.

2/3 = (2 * 11)/(3 * 11) = 22/33

7/11 = (7 * 3)/(11 * 3) = 21/33

The fractions 2/3 and 7/11 are equal to the fractions 22/33 and 21/33, respectively.

We need a fraction whose value is between 22/33 and 21/33.

We need a numerator between 21 and 22. Let's use 21.5 as the numerator.

The fraction 21.5/33 is between 2/3 and 7/11. In order not to have a decimal number as the numerator, we multiply the numerator and denominator of 21.5/33 by 2.

21.5/33 = 43/66

43/66

d) the triangle is a right triangle 60 squared +144 squared= 156 squared

step-by-step explanation:

156 squared is the hypothenuse

so 156= c

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!