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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Use the law of cosines:
We have:
substitute:
Answer:
Hello your question is incomplete attached below is the complete question
Ix = 0 Ux =
Iz = 0 Uz =
Iy = 5 Uy = 10
Step-by-step explanation:
Ix = 0 Ux =
Iz = 0 Uz =
Iy = 5 Uy = 10
attached below is the detailed solution
Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula
Explanation:
The given recursive formula is for
and
We need to determine the sequence.
The sequence can be determined by substituting n = 1, 2, 3, 4,....
<u>2nd term of the sequence:</u>
Substituting n = 1 in the formula , we get,
Simplifying, we have,
Thus, the 2nd term of the sequence is -7.5
<u>3rd term of the sequence:</u>
Substituting n = 2 in the formula , we get,
Simplifying, we have,
Thus, the 3rd term of the sequence is -5
<u>4th term of the sequence:</u>
Substituting n = 3 in the formula , we get,
Simplifying, we have,
Thus, the 4th term of the sequence is -2.5
Therefore, the sequence is –10, –7.5, –5, –2.5, …
Hence, Option C is the correct answer.