Question 1: The y-intercept is where the line crosses the y-axis. The increments of the y-axis is by 20, and the y-intercept is at (0, 20).
The slope is the change in y over the change in x. Find two points:
(0, 20) and (2, 80)
Now:
(80 - 20)/(2 - 0) = 60/2 = 30
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
So:
y = 30x + 20
Question 2: Again, look for the y-intercept, which is pretty clear. It's (0, 60).
Now find two points:
(0, 60) and (2, 40)
Find the slope:
(40 - 60)/(2 - 0) = -20/2 = -10
So, the equation is:
y = -10x + 60
And, there you go!
The given equation with t -1 is:
(t – 1)^3 + 6 (t – 1)^2 + 12 (t – 1) + 8
Expand each term before combining for easier visualization:
(t – 1)^3 = t^3 – 3 t^2 + 3t – 1
6 (t – 1)^2 = 6 t^2 – 12 t + 6
12 (t – 1) = 12 t - 12
Then substitute and combine:
-> t^3 – 3 t^2 + 3t – 1 + 6 t^2 – 12 t + 6 + 12 t – 12 + 8
t^3 + 3 t^2 + 3 t + 1 (ANSWER)
<span>A piecewise function uses different rules for different intervals of the DOMAIN</span>
Answer:
Shirt: $7.5
Sweater: $17.5
Step-by-step explanation:
25/2=12.5
Shirt is 5 less than Sweater
12.5-5=7.5
Add 5 to sweater cost
12.5+5=17.5
Shirt=7.5 Sweater=17.5
17.5+7.5=25
Answer:
x ≥ 12
Hope that helps!
Step-by-step explanation:
