I believe the answer is 3240^9/2 g^33/8
N= numerator
D= denominator
N:D ==> 2:3
2:3, 4:6, 6:9... And so on...
The pattern here is that the numerator increases by 2 and the denominator by 3. Easy right?
Now 5 is added to the "n".
Now it is N:D ==> 3:2
3:2, 6:4, 9:6... And so on...
The pattern here is inverted then the 2:3 one.
If I'm right then which one (you might have to continue the process/pattern) then one of them will increase by 5.
3 => 2 = +1 (2+1=3)
6 => 4 = +2 (4+2=6)
9 => 6 = +3 (6+3=9)
12 => 8 = +4 (8+4=12)
15 => 10 = +5 (10+5=15)
18 => 12= +6 (12+6=18)
Q. Which one is +5?
A. 15:10
That is what "I" think it is.
Now, the question is,
Does it work? Does it fit the above description?
Q. Does it even work? Does it fit the above description?
Our system of equations is:
y = x - 4
y = -x + 6
We can solve this system of equations by substitution. We already have one equation solved for the variable y in terms of x, so we can substitute in this equivalent value for y into the second equation as follows:
y = -x + 6
x - 4 = -x + 6
To simplify this equation, we first are going to add x to both sides of the equation.
2x - 4 = 6
Next, we are going to add 4 to both sides of the equation to separate the variable and constant terms.
2x = 10
Finally, we must divide both sides by 2, to get the variable x completely alone.
x = 5
To solve for the variable y, we can plug in our solved value for x into one of the original equations and simplify.
y = x - 4
y = 5 - 4
y = 1
Therefore, your final answer is x = 5 and y = 1, or as an ordered pair (5,1).
Hope this helps!
Answer:
- There are two solutions:
- B = 58.7°, C = 82.3°, c = 6.6 cm
- B = 121.3°, C = 19.7°, c = 2.2 cm
Step-by-step explanation:
You are given a side and its opposite angle (a, A), so the Law of Sines can be used to solve the triangle. The side given is the shorter of the two given sides, so it is likely there are two solutions. (If the given side is the longer of the two, there will always be only one solution.)
The Law of Sines tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
Of course, the sum of angles in a triangle is 180°, so once you find angle B, you can use that fact to find angle C, thus side c.
The solution process finds angle B first:
B = arcsin(b/a·sin(A)) . . . . . . or the supplement of this value
then angle C:
C = 180° -A -B = 141° -B
finally, side c:
c = a·sin(C)/sin(A)
___
A triangle solver application for phone or tablet (or the one on your graphing calculator) can solve the triangle for you, or you can implement the above formulas in a spreadsheet (or even do them by hand). Of course, you need to pay attention to whether the functions involved give or take <em>radians</em> instead of <em>degrees</em>.
