Explanation

the square root of 8 is an irrational number.

A rational number is any number that can be written in the form of p/q,

where p and q are both integers and q≠0.

So √8 is not a rational Number

ND5-07-2023

Explanation

20 x w x 5 = W

10 x w x X = W 

Equating both equations, we get,

10 x W x X = 20 x w x 5

X = 100/ 10 

X = 10 

ND5-07-2023

Explanation

It is given a,b,c, and d are in proportion.

The product of means(a:b) is equal to the product of extremes(c:d).

Therefore, ad = bc is the correct option

ND5-07-2023

Explanation

a < b 

then 1/ a < 1/b

multiply by -1, we get 

-  1/ a < -1/ b 

ND5-07-2023

Explanation

The additive inverse of " b" is " a "

To find :

(A) ab = 1

(B) a = b

(C) a + b = 0

(D) a - b = 0

Solution :

Step 1

Define the additive inverse of a number

We know that 0 is the additive identity

Let N be any number and M be the additive inverse of N

So by the property of additive inverse

N + M = 0 = M + N

Step 2

Choose the correct option

Here it is given that the additive inverse of " b" is " a "

So by the given condition

a + b = 0 = b + a

Hence a + b = 0

ND5-07-2023

Explanation

Yes, every rational number does have an additive inverse.

By definition, the additive inverse of a number, x, is the number y that adds to x to give the additive identity of 0.

Notice that if we add any number, x, to its negative, -x, we will get 0.

ND5-07-2023

Explanation

3x+3y=7

3(x+y)=7

x+y=7/3

x+y=3.4(approx)

x=3.4-y......1)

8x+7y=12

8(3.4-y)+7y=12

27.2-8y+7y=12

-y=12-27.2

-y= -15.2

y=15.2

1)x=3.4-y

x=3.4-15.2

x= - 11.8

To find the average of x and y, we first need to find the values of x and y that satisfy the given equations. Let's solve the system of equations: 1. Multiply the first equation by 7 and the second equation by 3 to eliminate the y term: - 21x - 21y = 49 - 24x + 21y = 36 2. Add the two equations together: - 21x - 21y + 24x + 21y = 49 + 36 - 3x = 85 - x = 85/3 3. Substitute the value of x back into either of the original equations. Let's use the first equation: 3(85/3) + 3y = 7 85 + 3y = 7 3y = -78 y = -78/3 y = -26 So the solution to the system of equations is x = 85/3 and y = -26. To find the average of x and y, we add them together and divide by 2: Average = (x + y) / 2 = (85/3 - 26) / 2 = (85/3 - 78/3) / 2 = 7/3 / 2 = 7/6 Therefore, the average of x and y is 7/6 or 1.16

ND5-07-2023

Explanation

Rational numbers have a multiplicative inverse for every number except 0.

This is because the inverse of 0 is not defined in the number system.

This 0 does not have a multiplicative inverse.

ND5-07-2023

Explanation

 The sum of two irrational numbers is not always irrational, but it is always a real number.

- Example:  

  √2 + (−√2) = 0 → which is rational.  

  So, irrational + irrational = rational (sometimes), irrational (sometimes)  

  But always a real number.

ND5-07-2023

Explanation

The number 0 is the only number with its additive inverse being itself.

That is, the additive inverse of 0 is 0.

ND5-07-2023