Answer:
C and G
Step-by-step explanation:
(x^2+4)^2+32=12x^2+48 is written as .
We can simplify the expression using the term a by replacing x^2 + 4 with a.
This factors into (a-4)(a-8). Solve by setting each factor equal to 0 and solve for a.
a-4 = 0 a=4
a-8=0 a=8
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
To shift vertically n units, we can simply add n to our function. Hence:
So, a vertical shift of 5 units up implies that n=5. So:
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
Or:
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
Answer:
and
Step-by-step explanation:
Let x be the altitude of a commercial aircraft
=>The expression " A minimum altitude of 29,000 feet" is equal to
All real numbers greater than or equal to 29,000 ft
=>The expression " A maximum altitude of 41,000 feet" is equal to
All real numbers less than or equal to 41,000 ft
therefore, The compound inequality is equal to
and
All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft
The solution is the interval [29,000,41,000]