Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• 1 + cot²x = csc²x
Consider the left side
x - 
x
Factorise as a difference of squares
= (csc²x - cot²x)(csc²x + cot²x)
= (1 + cot²x - cot²x)(csc²x + cot²x)
= csc²x + cot²x
= csc²x + csc²x - 1
= 2csc²x - 1 = right side ⇒ verified
The difference between the 6th term and the 9th term of the sequence is 135
<h3>How to determine the difference</h3>
Given that the nth term is;
3n² + 11
For the 6th term, the value of n is 6
Let's solve for the 6th term
= 3( 6)^2 + 11
= 3 × 36 + 11
= 108 + 11
= 119
For the 9th term, n = 9
= 3 (9)^2 + 11
= 3( 81) + 11
= 243 + 11
= 254
The difference between the 6th and 9th term
= 254 - 119
= 135
Thus, the difference between the 6th term and the 9th term of the sequence is 135
Learn more about algebraic expressions here:
brainly.com/question/4344214
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1 basket is between 9 and 10 minutes .
<u>Step-by-step explanation:</u>
Here we have , John kept track of how many baskets were made in a basketball game. After 4 minutes, 5 baskets were made. We need to find How many baskets were made between 9 and 10 minutes . Let's find out:
In order to calculate baskets between 9 min and 10 min we will find baskets at 10 min and at at 9 min , will subtract than !
Baskets at 10 min :
At 4 min we have 5 baskets so , in 10 min
⇒ 
⇒ 
⇒ 
Baskets at 9 min :
At 4 min we have 5 baskets so , in 9 min
⇒ 
⇒ 
⇒ 
So , Baskets between 10 & 9 min is 
, which on rounding off gives 1 . Therefore , 1 basket is between 9 and 10 minutes .
1. When there are two events that need to happen, we must multiply the probability of each event happening.
Shawn losing to Mike: 5/8 chance
Shawn losing to Tim: 2/7 chance
5/8 × 2/7 = 10/56 = 5/28
There's a 5/28 chance of Shawn losing to Mike and Tim.
I don't know #2, sorry :/
Hope this helps!
Intersect at where x=x and y=y
see where they have the same x and y values
that is at x=-1 and y=-5
intersect at (-1,-5)
