if BD is perpendicular to AC M angle DBE equals 2x - 1 + m angle CBE equals 5x - 42 find the value of x
1 answer:
<h2>Answer:</h2><h2>Step-by-step explanation:</h2>
I've drawn a graph in order to a better understanding of this problem. We know that:
BC is perpendicular to AC
∠DBE = 2x - 1
∠CBE = 5x - 42
Let's call the intersection of line BC and AC the point P, so:
∠P=90°
And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:
∠PCB = ∠CBE = 5x - 42
Moreover:
∠PBC = 2x - 1 - (5x - 42)
∠PBC = 2x - 1 - 5x + 42
∠PBC = -3x + 41
The internal angles of any triangle add up to 180°. Hence for ΔBPC:
90° + ∠PBC + ∠PCB = 180°
90° - 3x + 41 + 5x - 42 = 180°
2x + 89 = 180
2x = 91
x = 45.5°
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Answer : Remaining two observation becomes 97 and 107.
Explanation :
Since we have given that
Mean = 100
Modal value = 98
Range = 10
As we know that ,
Range = Highest-Lowest
Let highest observation be x
Let lowest observation be y
So equation becomes x-y=10 ----equation 1
So, observation becomes
x,98,98,y
Now, we use the formula of mean i.e.
Mean =
So, mean =
So our 2nd equation becomes
x+y=204
On using elimination method of system of linear equation on these two equation we get,
x=97
and
Hence , remaining two observation becomes 97 and 107.