Answer:
Step-by-step explanation:
Given
Set: -10 to 10
Required
Write as interval notation
We start by writing the given parameter as an inequality
The direct representation of and
in interval representation of sets is
and
, which shows that the beginning and end of the interval are inclusive;
So, the above inequality in interval notation is:
Answer:
C, E, and F
Explanation:
There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.
A better way is to simply solve each equation for x.
You could rewrite
2x + 7 < -3
as
2x + 7 = -3
and solve:
Subtract 7 from both sides
Now divide both sides by 2
Now we can simply replace the equals sign with the inequality
x < -5
Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.
Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:
Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.
These answers are:
C. -10
E. -8.24
and
F. -15/2 which is -7.5
NOTE: -5 is equal to but not less than -5 so G is not included.
Answer:
The value of r is 0.451
The percentage decrease is about 45.1%
Step-by-step explanation:
The given exponential function is
Using the exponent rule,
Now the value of
Thus, we can rewrite the function as
Therefore, the function in form
The value of r is 0.451
The percentage decrease is about 0.451 ×100 = 45.1%