Where’s the triangle, isn’t there supposed to be a picture with the question
Answer:
Step-by-step:
51⁷-51⁶ = 51⁶(51-1) = 51⁶(50)
50 is divisible by 25, so 51⁷-51⁶ is divisible by 25.
Answer:
Step-by-step explanation:
We can use the pascal triangle to find the coefficients of the expasion of the cube. It holds that
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Answer:
The given linear equation are
⇒9x+3y+12=0....eq1
⇒a1
=9,b1
=3,c1
=12
⇒18x+6y+24...eq2
⇒a2
=18,b2
=6,c2
=24
⇒a1/a2
=9/18 =1/2
⇒ b1/b2= 3/6 = 1/2
⇒ c1/c2= 12/24= 1/2
comparing
⇒ a1/a2,b1/b2,c1/c2
⇒ a1/a2=b1/b2=c1/c2
Hence, the line represented by eq1 and eq2 are coincidents
Step-by-step explanation:
