Based on the given parameters, the value of x in the rectangle is 6
<h3>How to determine the value of x in the rectangle?</h3>
The given parameters are
Perimeter = 62
From the figure, we have
Length = 2x
Width = x + 13
The perimeter is calculated as:
P =2 * (L + W)
This gives
2 * (2x + x + 13) = 62
So, we have
2 * (3x + 13) = 62
Divide both sides in the above equation by 2
3x + 13 = 31
Subtract both sides in the above equation by 13
3x = 18
Divide both sides in the above equation by 3
x = 6
Hence, the value of x in the rectangle is 6
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Answer:
a = 144
b = 67
Step-by-step explanation:
Where a transversal meets parallel lines, consecutive interior angles are supplementary.
<h3>Angles</h3>
a° +36° = 180° . . . . . . consecutive angles are supplementary
a = 144 . . . . . . . . . . divide by ° and subtract 36
b° +113° = 180° . . . . . . consecutive angles are supplementary
b = 67 . . . . . . . . . . divide by ° and subtract 113
2 = coefficient
e = variable
- = operation
f = variable
2e = 2 × e
f subtracted from the product of two and e
The normal form of a line is given by the equation x * cos theta + y * sin theta = p where theta is the angle of the normal line from the positive x-axis and p is the length of the normal line. Converting to normal line form, the equation must first be converted into standard form: 2x + 7y = 4. Then dividing the whole equation by sqrt(a^2 + b^2): sqrt(2^2 + 7^2) = sqrt(53). Hence, the equation becomes 2 / sqrt(53) * x + 7 / sqrt(53) * y = 4 / sqrt(53). Therefore, the length of the normal line is 4 / sqrt(53), and the angle is arctan(7/2) = 74.05 degrees.
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