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:
yes
Step-by-step explanation:
You can find the inverse of an equation by swapping the x and y, then solving for y.
f(x) = 4x - 12 f(x) is the equivalent of y in this case, so change it to a y
y = 4x - 12 Swap the x and y variables
x = 4y - 12
Solve for y
x = 4y - 12 Add 12 to both sides
x + 12 = 4y Divide both sides by 4
+ 3 = y Switch the sides to make it easier to read
y = + 3 Change y back into f(x) to match what you were given
f(x) = + 3
We have 3 sides
x,3x,3x+2
P=632
x+3x+3x+2=632
7x=632-2
7x=630
x=90
3x=270
3x+2=272
Answer:
a) 2.5 pounds of candy
b) 2.5 pounds of candy
y × 1 = 0.5 × 5
y = 2.5
Step-by-step explanation:
1 = 5
1/2 = y or 0.5 = y
y × 1 = 0.5 × 5
y = 2.5
