Answer:
Please check the explanation.
Step-by-step explanation:
Part a)
Given that the two parallel lines are crossed by a transversal line.
Given that
m∠2 = 2x + 54 and m∠6 = 6x - 11
Angle ∠2 and ∠6 are corresponding angles.
Corresponding angles are congruent.
Thus,
m∠2 = m∠6
2x + 54 = 6x - 11
flipe the equation
6x - 11 = 2x + 54
subtract 2x from both sides
6x - 2x - 11 = 2x - 2x + 54
4x - 11 = 54
adding 11 to both sides
4x - 11 + 11 = 54 + 11
4x = 65
dvide both sides by 4
4x/4 = 65/4
x = 16.2500 (round to 4 decimal places)
Part b)
We have already determined
x = 16.2500
Given
m∠2 = 2x + 54
substitute x = 16.2500 in the euation
= 2(16.2500) + 54
= 86.5°
As angle ∠2 and angle ∠1 lie on a straight line. Hence, the sum of their angles must be 180°.
i.e.
m∠1 + m∠2 = 180°
substituting m∠2 = 86.5° in the equation
m∠1 + 86.5° = 180°
subtracting 86.5° from both sides
m∠1 + 86.5° - 86.5° = 180° - 86.5°
m∠1 = 93.5°
Therefore, the measure of angle m∠1 is:
Invisible braces would cost 5300. I think that’s it. Hope that helped
2x+x-7+3x-20=87cm
6x-27=87
6x=114
x=19
Therefore the sides are:12cm, 38cm, and 37cm
Answer:
2 pieces
Step-by-step explanation:
Given


Required
Calculate the number of pieces
To do this, we have to divide the length of the wood by the length of each piece.
Represent this with x


Convert mixed numbers to improper fraction

Change division to multiplication



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Answer:

Step-by-step explanation:
Use the FOIL method of multiplying binomials.
First term in each binomial: 
Outside terms: 
Inside terms: 
Last term in each binomial: 
Now, rearrange the terms correctly. 
This is our final answer, since it can not be simplified any more.