Polynomial of Class 9

Simplify the following expressions

(√(5) + √(2)) ²

Solution:

Explanation:

Which of the following rational numbers lies between 0 and - 1

A: 0

B: - 1

C: -1/4

D: 1/4

Solution:

Explanation:

0 and 1 cannot be found between 0 and 1.

In addition,0= o/4  and -1= -4/4

We can see that -1/4 is halfway between 0 and -1.

Final Answer:

Hence, the correct option is (c) -1/4

Prove that the diagonals of a parallelogram bisect each other

Solution:

Explanation:

We must show that the diagonals of the parallelogram ABCD cross each other.

OA = OC & OB = OD, in other words.

Now AD = BC [opposite sides are equal] in ΔAOD and ΔBOC.

[alternative interior angle] ∠ADO = ∠CBO in ΔAOD and ΔBOC.

Similarly, ∠AOD = ∠BOC by ΔDAO = ΔBCO (ASA rule)

As a result, OA = OC and OB = OB [according to CPCT].

Final Answer:

Hence, it is prove that the diagonals of a parallelogram bisect each other.

What is total surface area of sphere

Solution:

Explanation:

• The radius of the sphere affects the formula for calculating the sphere's surface area.
• If the sphere's radius is r and the sphere's surface area is S.
• The sphere's surface area is therefore stated as Surface Area of Sphere 4πr ² , where ‘r’ is the sphere's radius.
• The surface area of a sphere is expressed in terms of diameter as S=4π(d/2) ² , where d is the sphere's diameter.

Final Answer:

Thus, total surface area of sphere is =4πr ² .

Fill in the blanks If two adjacent angles are supplementary

they form a __________.

Solution:

Explanation:

• If the non-common sides of two angles form a straight line, they are called linear pair angles.
• The sum of the angles of two linear pairs is  degrees.
• If the total of two angles is  degrees, they are called supplementary angles.

Final Answer:

A linear pair is formed.