Answer/Step-by-step explanation (ac > b² or b² < ac.
)
A/c to question, we have to show:-
b² >ac in A.P ........ (1)
b² = ac in G.P .....(2)
b² < ac in H.P. ..... (3)
b = a+c/2 (A.P)
b = √ac ( G.P)
b = 2ac/a+c (H.P)
In A.P :
b² > ac = b² - ac
= (a+c/2)² - ac
= (a²+2ac+c²/4) - ac = a² + 2ac + c² - 4ac / 4
= a² - 2ac + c² / 4 = ( a - c ) ² / 4 > 0 Hence, b²>ac
In G.P:-
b = √ac
Hence, b² = ac
In H.P :- b² < ac = ac > b² = ac - b² = ac - ( 2ac / a+c)
= ac(a+c) - 2ac / a+c
= a²c + ac² - 2ac / a+c
= ac(2ac - 2) / a+c > 0
Hence, ac > b² or b² < ac.
Answer:
The no. of possible handshakes takes place are 45.
Step-by-step explanation:
Given : There are 10 people in the party .
To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?
Solution:
We are given that there are 10 people in the party
No. of people involved in one handshake = 2
To find the no. of possible handshakes between 10 people we will use combination over here
Formula : 
n = 10
r= 2
Substitute the values in the formula
No. of possible handshakes are 45
Hence The no. of possible handshakes takes place are 45.
The independent quantity is the average class size and the dependent quantity is the cost ⇒ c
Step-by-step explanation:
Lets revise the meaning of dependent and independent variables
- The dependent variable is the one that depends on the value of some other number
- The dependent variable is the output value and the independent variable is the input value
- Ex: if y = 2x + 3, x is the input and y is the out put, then is independent variable and y is dependent variable
∵ The cost of the textbook increases with the average class size
- The cost of the textbooks depends on the average of the
class size
∴ The input is the average class size
∴ The output is the cost of the textbooks
∵ The input variable is independent variable
∵ The output variable is dependent variable
∴ The average of the class size is independent
∴ The cost of the textbooks is dependent
The independent quantity is the average class size and the dependent quantity is the cost
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Answer:
$30 is the price of the original pair of sneakers.
Step-by-step explanation:
You wanna cross multiply so you put :
18. 60
_ = _
x. 100
You multiply 18 the cost of the sneakers by 100 and then divide the product (1800) by 60 and you get $30.
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