The rate of change is 15. We know this because 30 - 15 = 15, 45 - 30 = 15, and 60 - 45 = 15.
The next item in the sequence would be 75, since 60 + 15 = 75.
To solve this, you need to isolate/get the variable "m" by itself in the equation:
1. 2m - 1 = 3m Subtract 2m on both sides to get "m" on one side of the equation
2m - 2m - 1 = 3m - 2m
-1 = m
2. 2m = 1 + m Subtract m on both sides to get "m" on one side of the equation
2m - m = 1 + m - m
m = 1
3. m - 1 = 2 Add 1 on both sides to get "m" by itself
m - 1 + 1 = 2 + 1
m = 3
4. 2 + m = 3 Subtract 2 on both sides to get "m" by itself
m = 1
5. -2 + m = 1 Add 2 on both sides to get "m" by itself
m = 3
6. 3 = 1 + m Subtract 1 on both sides to get "m" by itself
2 = m
we can do this by 2 ways
1- by plotting the points on graph and then tracing the points to get shape,
for linear, we will get straight line
for quadratic, we will get parabola
in this case, it is linear as we get a straight line
2- by solving for values of x and y
consider standard linear equation y = mx +c where m is slope and c is constant
by putting given values of x and y we get
y + 2x = 4(answer)
if we consider standard parabola equation
y^2 = 4ax
this equation is not true for given points
Multiply by the reciprocal by 3 and divide the common denominator by 14
Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
= 2 , 
= 4
Now,
Budget constraint -
x + y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get
⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y = 
= 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
