Think of the equation of a linear function:
Recall y = mx + b for vertical shifts, we just add or subtract from 'b' and that will move the line up or down accordingly.. However, for horizontal shifts, we will need to add or subtract from 'x'. Note that the slope or 'm' stays the same for each type of shift.
Now that we know how the shifts occur, we might consider a different form of the equation for a linear function: y = a(x - h) + k here the 'a' is just our slope, 'k' is our original y intercept, and 'h' will represent the amount of horizontal shift.
So to get the desired transformations of a horizontal shift to the left of 8 and a vertical shift of down 3 from our original function y = x, we can make the following changes: y = (x + 8) - 3 Now you might be confused with how we got the 'x + 8'.. Let's consider values of 'h'. For positive values of h, the result will be a shift to the right and for negative values of h the result will be a shift to the left. So since we want a shift to the left we need to use a '-8' and when we substitute that into our new form, y = (x - h) + k you can see the sign change.
Now we can simplify of course and get the final equation: y = x + 5 or in function form f(x) = x + 5
Answer:
Total number of notes is 11.
Step-by-step explanation:
Value is 100 rupees…
5x + 20y = 100 and x + y = 11 are the two equations.
We can simplify…
5x + 20 y - 5x - 5y = 100 - 55 = 45
15y = 45 so y = 3
x = 11 - y = 8
So, we have 8 notes of 5 rupees denomination and 3 notes of 20 rupees denomination.
I hope it helps you.
First you add 3+6, then take 9 and multiply by 2 which is 18, the do 26-18 which is 8×3=24.
12×3=36-12=24.
So 24=24
Your answer is A.
Answers:
1. The n-intercept is 12. That means after 12 visits the amount of money on the gift car is $0.
2. The A(n)-intercept is 150. Before the visits, the amount of money on the gift car is $150.
Solution:
Amount of money on the gift card after n number of visits: A(n)=$150-$12.50 n
A(n)=150-12.50 n
1. n-intercept
A(n)=0→150-12.50 n =0
Solving for n: Subtracting 150 both sides of the equation:
150-12.50 n-150 = 0-150
-12.50 n = -150
Dividing both sides of the equation by -12.50:
(-12.50 n) / (-12.50) = (-150) / (-12.50)
n=12
The n-intercept is n=12; for n=12→A(12)=0. Point (n, A(n))=(12,0)
2. A(n) intercept
n=0→A(0)=150-12.50 (0)
A(0)=150-0
A(0)=150
The A(n) intercept is 150; for n=0→A(0)=150. Point (n, A(n))=(0,150)
2/3
=0.6666666... is your final answer. Hope it help!
