Answer:
9). x = 36.9°
10). x = 18.3°
Step-by-step explanation:
9). By applying tangent rule in the given triangle,
tan(x) = 
tan(x) = 
x = 
x = 36.87°
x = 36.9°
10). By applying sine rule in the given triangle,
sin(x) = 
sin(x) = 
x = 
x = 18.32
x ≈ 18.3°
Okay, so, to solve these inequalities, your goal is to get the variable equal to one number, so let's take a look at the first problem:
-3 / 4x < 12,
to get rid of the numbers attached to the variable 'x', you would divide the numbers, since, the original is multiplying with x, you would do the opposite, and the opposite of multiplication, is division.
So, now our equation is, - 3 / 4x divided by - 3 / 4, which would leave X by itself, then we have to do that same thing to the 12, which would be, 12 divided by - 3 / 4, which would equal, 16.
-3 / 4 < 12
÷ - 3 / 4 ÷ - 3 / 4
_____________
X > 16
Now, our equation is X > 16, which is the answer, to problem number one.
(Also a quick note, when you divide by a negative, the inequality symbol flips, for example, when we divided by -3 / 4, our inequality symbol changed from the less than symbol, to the more than symbol.)
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Let's take a look at problem number two:
13c < -169,
Okay, so, again, you're trying to get C by itself. The number 13 is multiplying with C, so, you need to do the opposite, and divide, so you can get C by itself.
13c divided by 13 equals C
13c/13 = C
and
- 169 divided by 13, equals, -13,
So, the answer is, C < -13
Or,
13c < - 169
÷ 13 ÷ 13
__________
C < - 13
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Let's take a look at problem number 3:
5B - 28 > 27,
Okay, so now, we have another number on the same side as B, so, we get rid of that first, it's subtracting, so now we do the opposite, and add it to the other side.
5B - 28 > 27
+28 +28
__________
5B > 55
Now, we divide both sides by 5:
5B > 55
÷5 ÷5
_______
B > 5
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Now, Let's take a look at problem number 4:
3x - 7 > 4x + 2,
okay, so, we have multiple steps to take with this equation.
First, we want to get X by itself, so, we have to get rid of the -7, so, we do the opposite, and the opposite of subtracting, is adding.
3x - 7 > 4x + 2
+ 7 + 7
___________
3x > 4x + 9
Now, you only want to have one number with X, per equation, so, you need to move 4x to the other side, the way we do that, is by subtracting 4x.
3x > 4x + 9
-4x -4x
__________
-1x > 9
We can't have a negative number attached to the x, because that's like having a negative X, so, we have to divide one more time.
-1x > 9
÷-1 ÷-1
_______
Since, we are dividing by a negative, the inequality sign is going to flip, which would make the answer:
X < -9
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I hope this helps!
