Answer:
1) x ≤ 2 or x ≥ 5
2) -6 < x < 2
Step-by-step explanation:
1) We have x^2 - 7x + 10, so let's factor this as if this were a regular equation:
x^2 - 7x + 10 = (x - 2)(x - 5)
So, we now have (x - 2)(x - 5) ≥ 0
Let's imagine this as a graph (see attachment). Notice that the only place that is above the number line is considered greater than 0, and that's when x ≤ 2 or x ≥ 5 (the shaded region).
2) Again, we have x^2 + 4x - 12, so factor this as if this were a regular equation:
x^2 + 4x - 12 = (x + 6)(x - 2)
So now we have (x + 6)(x - 2) < 0
Now imagine this as a graph again (see second attachment). Notice that the only place that is below 0 (< 0) is when -6 < x < 2 (the shaded region).
Hope this helps!
Answer:
a= -1
B
Step-by-step explanation:
My opinion:
the slope m = (y2 - y1) / (x2 - x1)
slope m is -5
y2 is 7
y1 is 2
x2 is -2
x1 is a
so the equation will be
-5 = (7 - 2) / (-2 -a )
10 + 5a = 5
5a = -5
a = -1
Then you can plug the value a = -1 into the equation of the slope m to double check it.
Hey there!
To start, when you perform (f+g)(x), you are adding the functions together. This would mean, you would add 4x+9 to 4x^2. This should look like this:
(4x+9)+(4x^2)
Because there are no like terms, your final answer would be 4x+9+4x^2 or the last answer choice.
Hope this helps and have a marvelous day! :)
Yes, 61 is a prime number. The prime numbers<span> between 2 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, </span>61<span>, 67, 71, 73, 79, 83, 89 and 97.</span>
The inverse of this function would be f(x) = 
.
You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.
f(x) = 
- 6 ----> Switch f(x) and x
x = 
- 6 ----> Add 6 to both sides
x + 6 = -----> Take the logarithm of both sides in order to get the f(x) out of the exponent
Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2
= f(x) ----> And switch the order for formatting purposes.
f(x) =
And that would be your new inverse function.
