There is 2 ways to solve this type of question.
Method 1
--------------------------------------------------
Formula
--------------------------------------------------
a² + b² = c²
--------------------------------------------------
Apply the formula
---------------------------------------------------
(7√2)² + (7√2)² = c²
c² = 98 + 98
c² = 196
c = √196
c = 14
--------------------------------------------------
Ans: The diagonal length is 14cm
--------------------------------------------------
_____________________________________________________________
Method 2
--------------------------------------------------
Identify the triangle
--------------------------------------------------
This is a special triangle
45° - 45° - 90°
--------------------------------------------------
Property of the Angles
--------------------------------------------------
x - x - x√2
--------------------------------------------------
Find hypotenuse
--------------------------------------------------
Given that the non-hypotenuse is 7√2
Hypotenuse = (7√2)(√2)
Hypotenuse = 7 x 2
Hypotenuse = = 14cm
--------------------------------------------------
Ans: The diagonal length is 14cm
--------------------------------------------------
Yeah what is the question
Answer:
i). x³ + 9x² + yz - 15
ii). -21m³np - 8p⁵q + mnp + 4mn + 100
Step-by-step explanation:
Question (38)
i). Two expressions are -5x² - 4yz + 15 and x³+ 4x²- 3yz
By subtracting expression (1) from expression (2) we can the expression by addition which we can get expression (1).
(x³+ 4x²- 3yz) - (-5x² - 4yz + 15) = x³ + 4x² - 3yz + 5x² + 4yz - 15
= x³ + 9x² + yz - 15
ii). -15m³np + 2p⁵q - 6m³pn + mnp + 4mn - 10qp⁵+ 100
= (-15m³np - 6m³np) + (2p⁵q - 10qp⁵) + mnp + 4mn + 100
= -21m³np - 8p⁵q + mnp + 4mn + 100