To complete the square, you can add (and subtract) the square of half the x coefficient.
... y = x² -10x + 30
... y = (x² -10x +25) + (30 -25)
... y = (x -5)² +5
Given the system of the equation below;
We can use the elimination method to solve the systems of equations
Step 1: Subtract equation 2 from equation 1 and solve for x
Step 2: Sustitute x = 1 in equation 1
Therefore, the solution to the system of equation is
Answer:
g(x) = e^(x + 2) + 2
Step-by-step explanation:
First, let's describe the shifts.
Vertical shift.
For a function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
If N is positive, then the shift is upwards.
If N is negative, then the shift is downwards.
Horizontal shift.
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x - N)
If N is positive, the translation is to the right
If N is negative, the translation is to the left.
Now let's solve the question.
f(x) = e^x
First, we have a vertical shift up of 2 units, then:
g(x) = f(x) + 2
Now we have a shift to the left of 2 units:
g(x) = f(x - (-2)) + 2
g(x) = f(x + 2) + 2
Then:
g(x) = e^(x + 2) + 2
Answer:
So the Commutative Property is the one that refers to moving stuff around, right.? So I guess for addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2.
$25a + $15s =$305
a + s = 17
a = 17 - s
$25a +$15s =$305
$25(17-s) + $15s=$305
425-25s +15s = $305
425-10s=305
-10s=305-425
-10s= -120
-10s/-10 = -120/-10
s = 12
a+ 12 = 17
a = 5
Check
$25a + $15s =$305
$25(5) + $15(12) =$305
125 + 180 = 305
305 = 305
