Let the function f be defined by f(x)= 5x-2a , where a is a constant.If f(10) + f(5)=55 , what is the value of a ?
f(10)=5*10+2a
f(5)=5*5+2a
f(10)+f(5)=75+4a=55
solve for a.
To find the value of a, we'll substitute the given values in the equation f(10) + f(5) = 55.
First, let's find the values of f(10) and f(5) using the function f(x) = 5x - 2a.
f(10) = 5 * 10 - 2a
= 50 - 2a
f(5) = 5 * 5 - 2a
= 25 - 2a
Now, we substitute these values back into the equation:
(50 - 2a) + (25 - 2a) = 55
Combining like terms, we get:
75 - 4a = 55
Next, we isolate the term with 'a' by subtracting 75 from both sides:
-4a = 55 - 75
-4a = -20
Finally, we solve for 'a' by dividing both sides by -4:
a = (-20) / (-4)
a = 5
So, the value of a is 5.