Answer:
The minimum value = -38
Step-by-step explanation:
∵ f(x) = x² - 12x - 2
∵ -12x ÷ 2 = -6x ⇒ -6 × x
∴ (x - 6)² = x² - 12x + 36
∴ Add and subtract 36 in f(x)
∴ f(x) = (x² - 12x + 36) - 36 - 2
∴ f(x) = (x - 6)² - 38 ⇒ completing square
∴ The vertex of the parabola is (6 , -38)
∵ Its minimum point because the coefficient of x² is positive
∴ The minimum value = -38
Answer:
The resulting function after the sequence of transformations is 
Step-by-step explanation:
Given a function f(x)
- the function a*f(x) will be a vertical stretch of factor a, given a > 1
- the function f(x) + b will be the translated function vertically up b units
- the function f(x+c) will be horizontally translated function of the original by c units left
Remembering these points, we can apply the rules to
.
- Strech vertically by 3 would be

- translate up 1 unit would be

- translate left 2 units would make it

Hence the new function would be 
Expected value E(x) = 0.6(200,000) + 0.2(100,000) - 0.2(200,000) = 120,000 + 20,000 - 40,000 = 100,000
Therefore, the expected value is $100,000, so the company should build the mousetrap.
Three grams for one penny. three times eight (pennies)=24 grams
Answer:
y = -2x - 2
Plug the x- and y-values into the appropriate spaces in the slope-intercept form and see which value for b would make the equation true:
4 = -2(-3) +/- ?
4 = 6 - 2
4 = 4
I don't know if this makes sense, I'm sorry if it doesn't but the answer is correct because it goes through the point (-3,4)