Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Answer:
Michael and Carlos will have the same amount after 7 weeks
Step-by-step explanation:
Assume the total number of baseball cards that Carlos and Michael need to have to be equal is y, and the amount of time in terms of weeks that it will take for this to be achieved is x.
The following expressions can be derived
For Carlos to achieve y, he will need 85 and an addition of 10 per week (x):
y=85+(10x)..........equation 1
For Michael to achieve y, he will need 120 and an addition of 5 per week (x):
y=120+(5x)..........equation 2
Equating equation 1 and 2 to solve for x
85+10x=120+5x
10x-5x=120-85
5x/5=35/5
x=7
Number of weeks it will take Michael and Carlos to have the same amount=x=7 weeks
Answer:
-3
2
5
Step-by-step explanation:
Solving for the missing term and the missing coefficient (6a − )5a = ( ) a^2 − 35a
Let the missing term be X
Let the missing coefficient be Y
Therefore, (6a – X)5a = Y(a^2) – 35a
6a x 5a – X.5a = Y.a^2 – 35a
30a^2 – X.5a = Y.a^2 – 35a
Equating co-efficients,
30a^2 = Y.a^2; X.5a = 35a
30 = Y; 5X = 35
Y = 30; X = 7
Therefore, (6a-7)5a = 30 a^2 – 35a
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