Answer:
\[y < = 300\]
Step-by-step explanation:
Let x = number of out-of-state students at the college
Let y = number of in-state students at the college
As per the given problem, the constraints are as follows:
\[x < = 100\] --------- (1)
\[y = 3 * x\] --------- (2)
From the given equations (2), \[ x = y/3 \]
Substituting in (1):
\[y/3 < = 100\]
Or, \[y < = 300\] which is the constraint representing the incoming students.
Let width of the floor be x feet, them area is
x(x+2) = 168
x^2 + 2x - 168 = 0
(x - 12)(x + 14) - 0
so x = 12
the floor is 12 ft by 10 ft
the width of the rug should be 10 - 2(2) = 6 feet
2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 is the equation in slope intercept form.
slope = -2/3
y intercept = 490
Answer:
(-7,4)
Step-by-step explanation:
goal: (y-k)^2=4p(x-h)
y^2-8y=4x+12 Rearranged and added 4x and 12 on both sides
y^2-8y+(-8/2)^2=4x+12+(-8/2)^2 complete square time (add same thing on both sides)
y^2-8y+(-4)^2=4x+12+(-4)^2 (simplify inside the squares)
(y-4)^2=4x+12+16 (now write the left hand side as a square)
(y-4)^2=4x+28
(y-4)^2=4(x+7) factored...
vertex is (-7,4)
Answer:

Step-by-step explanation:


We use binomial expansion for 
This can be rewritten as
![[x(1+\dfrac{h}{x})]^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Bx%281%2B%5Cdfrac%7Bh%7D%7Bx%7D%29%5D%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)

From the expansion

Setting
and
,


Multiplying by
,



The limit of this as
is
(since all the other terms involve
and vanish to 0.)