We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:
Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:
Now, we have our final range: -5 < x < 9
ANSWER
a. d+4
b. 4d+16
EXPLANATION
The area of the square coaster is represented by:
We split the middle term to obtain,
We factor by grouping to get,
Since area of a square is l² , it means the side length of the square is
b) The perimeter of a square is given by
We substitute the length in terms of d, to obtain;
Or
Answer:
When the range is wide
Step-by-step explanation:
First one = 9x3=27
Second one 12x9=108
3rd one = 3x4=12
Idk what that last one is
Answer:
The simplified expression for the given expression will be:
c. 
Step-by-step explanation:
Given expression:
To simplify the expression.
Solution:
In order to simplify the expression, we will first remove the parenthesis by reversing the signs of the terms inside the parenthesis which lies after a negative sign out side the parenthesis.
<em>This is because negative multiplies to a negative to give a positive and negative multiplies to a positive to give a negative.</em>
So, we have:
⇒ 
Combining like terms
⇒ 
<em>The like terms can be evaluated as</em>
Thus, the simplified expression will be:
⇒
