Two stores opened on the same day. The profit for Store #1 is modeled by the equation f(x) =
3
2
x - 3. The profit for Store #2 is modeled by the equation g(x) = -
1
4
x + 4. On what day (x) was the profit from both stores the same?
A) 3
B) 4
C) 5
D) 6

Option B: On the day 4 the profit from both stores will be the same.

Explanation:

Given that two stores were opened on the same day.

The profit from store 1 is given by

The profit from store 2 is given by

We need to determine the day on which the profit from both the stores will be same.

Let us equate the two equations.

Thus, we have,

Adding both sides of the equation by 3, we get,

Adding both sides of the equation by , we get,

Multiplying both sides of the equation by , we get,

Thus, the value of x is 4.

Hence, On the day 4 the profit from both stores will be the same.

Therefore, Option B is the correct answer.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: