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The value of x in the equation is 2.
<h3>What is indices?</h3>Indices singular index is a branch of algebra that deals with the power or exponent of variables.
Laws of indices help us to evaluate indicial expressions and equations.
Analysis:
= 256
Here 4 is the base number while 8-2x is the exponent or index.
So for us to evaluate this, we need to write 256 in its index form having its base as 4 also.
so 256 in base 4 index form is
=
since both sides have the same base number, we equate only their exponent
8-2x = 4
-2x = 4 - 8
-2x = -4
x = -4/-2 = 2
Learn more about indices: brainly.com/question/10339517
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The height of the triangle that forms the train track is 145,38 ft
<h3>How to calculate the height of the triangle?</h3>To calculate the height of the triangle we must take into account the information provided by
- Base of the triangle = 1 mile = 5280 feet
- Railroad track expansion = 8 feet
According to the above, we must perform the following operations:
- 5280 ÷ 2 = 2640
- 8 ÷ 2 = 4
- 2640 + 4 = 2644
Subsequently, we must apply the Pythagorean theorem to find the height of the triangle having 2 data:
- Base: 2640ft
- Hypotenuse: 2644 ft
- 2644² = x² + 2640²
- x² = 2644² - 2640²
- x =
.
- x =
- x = 145,38 ft
That makes x approximately 145,38 ft.
Learn more about triangles in: brainly.com/question/2269348