Answer:
The equation is P - 42 = 12
P = 54
Step-by-step explanation:
9514 1404 393
Answer:
85°
Step-by-step explanation:
The sum of arcs in a circle is 360°.
FG +140° +80° +55° = 360°
FG = 360° -275°
FG = 85°
Answer:
P(5) - P(3) = 4
Step-by-step explanation:
<em>Lets explain how to solve the problem</em>
Assume that P(x) is a linear function, that because the sum of P(2x),
P(4x), and P(6x) is linear ⇒ (24x - 6 is linear)
∵ The form of the linear function is y = ax + b
∴ P(x) = ax + b
Substitute x by 2x
∵ P(2x) = a(2x) + b
∴ P(2x) = 2ax + b
Substitute x by 4x
∵ P(4x) = a(4x) + b
∴ P(4x) = 4ax + b
Substitute x by 6x
∵ P(6x) = a(6x) + b
∴ P(6x) = 6ax + b
Add the three functions
∴ P(2x) + P(4x) + P(6x) = 2ax + b + 4ax + b + 6ax + b
Add like terms
∴ P(2x) + P(4x) + P(6x) = 12ax + 3b ⇒ (1)
∵ P(2x) + P(4x) + P(6x) = 24x - 6 ⇒ (2)
Equate (1) and (2)
∴ 12ax + 3b = 24x - 6
By comparing the two sides
∴ 12a = 24 and 3b = -6
∵ 12a = 24
Divide both sides by 12
∴ a = 2
∵ 3b = -6
Divide both sides by 3
∴ b = -2
Substitute these values in P(x)
∵ P(x) = ax + b
∴ P(x) = 2x + (-2)
∴ P(x) = 2x - 2
Now we can find P(5) - P(3)
∵ P(5) = 2(5) - 2 = 10 - 2 = 8
∵ P(3) = 2(3) - 2 = 6 - 2 = 4
∴ P(5) - P(3) = 8 - 4 = 4
* P(5) - P(3) = 4
Answer:
The practical domain of the function is the set of all integers from 1 to 5, inclusive.
Step-by-step explanation:
It is given the initial number of sheets of paper is 45.
A store has 5 reams of paper, and each ream contains 500 sheets of paper.
Let f(x) represent the number of sheets after purchasing x reams.
Domain is the set of input. In other words domain is the set of x-values.
Since number of reams can not be a negative or fraction value, therefore, the domain of the function is {1,2,3,4,5}.
Andre needs to buy more sheets, so number of reams of paper can not be 0.
Thus, the practical domain of the function is the set of all integers from 1 to 5, inclusive.
