Answer:
f(x)= 2x fox x belonging to [1,30]
f(x)=x for x belonging to (30,150]
Step-by-step explanation:
We are given that, when the store gets open up , there are 100 muffins ready for sale. In Morning every customer is buying 2 muffins. However, this rate changes when the number of muffins comes down to 40 only.
Hence first 60 Muffins were sold to 30 customers.
There for if we take customers as x , and muffins as y
Y=2x ; [1<=x<=30]
When the number of muffins are 40 , 80 muffins are additionally baked and added to the store. Hence the total number of muffins now is 120. And now every customer buys one muffin. Hence these 120 muffins will be bought by 120 customers.
Thus over all we had 60+120 = 180 Muffins and 30+120 = 150 Customers.
So , if we take customers as x , and muffins as y
Y=x ; [30<x<=120]
Hence the function will be the piecewise function. As given under
f(x)= 2x fox x belonging to [1,30]
f(x)=x for x belonging to (30,150]
Let us now plot the graph by taking few random values of x ( number of customers ) and evaluating y ( Muffins bought by them ) in tabular form
x y
0 0
10 20
30 60
40 70
80 110
150 180
Please find the graph attached with this answer.
Answer:
(0,-9)
Step-by-step explanation:
The image of a point over a line
is given by the co-ordinate rule:
→
So, when we reflect a point over the line , the x co-ordinate and y co-ordinate change their places.
Here, is
. So, from the above rule, after reflection over the line
, the image has the following co-ordinates:
Answer:
<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop</em>
<em>Point of intersection: (x,y) = (4,360)</em>
Explanation:
Part 1 )
Let x = number of hours worked
Let y = total cost to you
Determining where to take the car:
<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295</em>
Mike's repair shop:
Service fee: $100
Per hour rate: $65
Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.
Therefore, total cost for Amy's repair shop can be written as:
y = 100 + 65x ------(1)
For 3 hours work: y = 100 + 65(3)
<em>Cost at Mike's, y = $100 + $195 = $295</em>
<em>Amy's repair shop: </em>
Service fee: $40
Per hour rate: $80
Charges per an hour are $40, so for x hours the charges will be 80x.
Therefore, total cost for Amy's repair shop can be written as:
y = 40 + 80x ------(2)
For 3 hours work: x = 3
y = 40 + 80(3)
<em>Cost at Amy's, y = $40 + $240 = $280</em>
<em>Part 2)</em>
<em>Find the point of intersection</em>
<em>Using elimination method:</em>
<em>y = 100 + 65 x ------1</em>
<em>y = 40 + 80x ------2</em>
<em>As the y coefficients are equal we will subtract eq1 from eq2</em>
<em>y - y = 40 + 80x - 100 - 65x</em>
<em>0 = -60 + 15x</em>
60 = 15x
x =
x = 4
put x = 4 in eq 1
we get y = 100 + 65 (4) = 100 + 260 = 360
x = 4, y = 360
Point of intersection: (x,y) = (4,360)