Answer:
a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) where a = 4p and b = 3q.
( 4p + 3q ) ( 4p - 3q )
Answer:
Line means going on upto point but line segment means limited line
Answer:
about 50
Step-by-step explanation:
that's all I can think of
Answer:
x = -2
Step-by-step explanation:
For this problem, we must simply solve for x. To do this, we will need equation operations, and the use of the distributive property.
Let's work this line by line until we have the value for x:
3{-x + (2x + 1)} = x - 1
3*-x + 3*(2x + 1) = x - 1
-3x + 6x + 3 = x - 1
3x + 3 = x - 1
2x = -4
x = -2
Now we can check our answer for x by plugging back into the original equation and see if the left hand side is equal to the right hand side:
3{-x + (2x + 1)} = x - 1
3{-(-2) + (2(-2) + 1)} ?= (-2) - 1
3{2 + (-4 + 1)} ?= -3
3{2 + (-3)} ?= -3
3{-1} ?= -3
-3 == -3
Thus, we have found the solution for x to be equivalent to negative 2.
Cheers.
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
