F(x)=3x+1 (preimage)
g(x)=x+1 (image)
it is undergoing a reduction/compression with translation.
In general, a linear transformation is
g(x) = a*f(bx-h)+k
h=horizontal translation (right if h>0, left if h<0, note formula has minus sign)
k=vertical translation (up if k>0, down if k<0)
a=vertical stretching, (stretching if |a|>1, compression if |a|<1, also, if a<0, a reflection across the x-axis is performed)
b=horizontal stretching (|b|>0 compression, |b|<0 stretching, also, if b<0, a reflection across the y-axis is performed)
In this case,
g(x)=f(x/3), so it is a horizontal stretching.
Note that the y-intercept remains unchanged.
Answer:
C = 75 + 0.17x and R = 2x
2x - (75 + 0.17x) > 0
x ≥ 41
Step-by-step explanation:
The cost to make the cupcakes is a fixed $75 plus $0.17 per cupcakes made and the selling price of each cupcake is $2.00.
Part A: Now, the equation for the cost, C, for making x cupcakes is
C = 75 + 0.17x ......... (1)
Again the equation for the revenue, R, from selling x cupcakes is
R = 2x ............ (2)
Part B: So, the inequality that could be solved to find the number of cupcakes, x, that must be made and sold to make a profit is
R - C > 0
2x - (75 + 0.17x) > 0 ......... (3)
Part C: Solving inequality (3) we get
(2 - 0.17)x > 75
⇒ x > 40.98
⇒ x ≥ 41 {Since, x can not be a fraction}
(Answer)
8x51. 8x50=? 8x5=40. 40 x 10 = 400 8x50=400. 8x1=8 400+8=408.
