Answer:
<h2>
Hence a = -1, b = 10</h2>
Step-by-step explanation:
Given h(x) = (x - 1)³ + 10, f(x) = x + a and g(x) = x³ + b so that h(x) = (gof)(x)
To get the value of a and b that will make the composite function true, we will first need to get the composite function (gof)(x).
(gof)(x) = g[f(x)]
g[f(x)] = g[ x + a]
To get g(x+a), we will replace the variable x in the function g(x) = x+b with x+a as shown;
g[x + a] = (x+a)³+b
Hence (gof)(x) = (x+a)+b
Equating h(x) = (gof)(x)
(x - 1)³ + 10 = (x+a)³+b
On comparing both sides of the equation;
(x - 1)³ = (x+a)³ and 10 = b
For (x - 1)³ = (x+a)³
Take cube root of both sides
∛ (x - 1)³ = ∛(x+a)³
x-1 = x+a
collect like terms
a = x-x-1
a = -1
Hence a = -1, b = 10
Answer:
The actual discount is a 68% discount.
Step-by-step explanation:
Remember that if something has a price P, and you have a discount of the X%, the new price will be:
P' = P - P*(X%/100%) = P*(1 - X%/100%)
Here we first have a 60% discount, then if the initial price is P, the new price is:
P' = P*(1 - 60%/100%) = P*(1 - 0.6)
Now we have an additional 20% discount (this applies to the new price)
then the final price is:
P'' = P'*(1 - 20%/100%) = P'*(1 - 0.2) = P*(1 - 0.6)*(1 - 0.2)
We want to rewrite this as something like:
P'' = P*(1 - k)
Let's do this:
P'' = P*(1 - 0.6)*(1 - 0.2) = P*(1 - 0.2 - 0.6 + 0.2*0.6)
= P*(1 - 0.8 + 0.12) = P*(1 - 0.68)
And this can be as:
P'' = P*(1 - 68%/100%)
Then the actual discount is a 68% discount.
So you multiply the two, use mathaway app
Answer:
Inscribed Angles Theorem
Step-by-step explanation:
Got it on edge 2021