Answer:
x = 36 , y = 64 , z = 80
Step-by-step explanation:
Exterior angle equals the sum of opposite interior angle.
3x + 8 = x + z
3x - x - z = -8
2x - z = -8 ------------ (I)
z + 3x - 8 = 180 {linear pair}
3x + z = 180 + 8
3x + z = 188 --------------(II)
Add (I) and (II) and z will be eliminated and we can find the value of 'x'
(I) 2x - z = -8
(II) <u> 3x + z = 188</u> {Now add}
5x = 180
x = 180/5
x = 36
Plugin x = 36 in equation (II)
3*36 +z = 188
108 + z = 188
z = 188- 108
z = 80
x + y + z = 180 ----------------(III) {angle sum property of triangle}
36 + 80 +y = 180
116 + y = 180
y = 180 - 116
y = 64
Answer:
A polynomial can have fewer x-intercepts than its number of roots when a pair of complex conjugate roots exist.
Example:
Consider the 4-th degree polynomial
f(x) = x⁴ - x³ - x² - x - 2
According to the Remainder theorem
f(-1) = 1 + 1 - 1 + 1 - 2 = 0
Therefore (x + 1) is a factor.
f(2) = 16 - 8 - 4 - 2 - 2 = 0
Therefore (x - 2) is a factor.
(x+1)*(x-2) = x² - 2x + x - 2 = x² - x - 2
To find the remaining factor, perform long division.
x² + 1
-------------------------------
x²-x-2 | x⁴ - x³ - x² - x - 2
x⁴ - x³ - 2x²
-----------------------------
x² - x - 2
x² - x - 2
Therefore
f(x) = (x+1)(x-2)(x²+1)
Notice that (x² + 1) has no real factors.
However,
x² + 1 = (x + i)(x - i),
so it has a pair of conjugate zeros +i and -i.
A graph of the function confirms that there are only two real zeros (shown in red color).
9x/18 = 14 I’m not sure if I’m right but I think it’s that
Answer: The graph is shown below
The solution to the system is (x,y) = (2,3)
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Explanation:
To graph , we need two points. Generating any (x,y) point involves picking a random x value to find its paired y value. For instance, if you plugged in x = 0, you should get to y = -2 which is the y intercept. Then trying something like x = 2 will lead to y = 3. This line goes through (0,-2) and (2,3). This line is shown in red below.
The blue line is horizontal and goes through 3 on the y axis. Every point on this horizontal line has the same y coordinate of 3. The x value doesn't matter, so it's not part of the equation y = 3.
The intersection of the red and blue line is the solution to the system. That intersection occurs at (x,y) = (2,3). This means x = 2 and y = 3 pair up together to make both original equations true.
Since this system has at least one solution, we consider it a consistent system.
Answer:
$x=2$
Step-by-step explanation:
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