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Answer:
Let's solve your equation step-by-step.
4 ( 8x − 1 ) = 19 + 32x
Step 1: Simplify both sides of the equation.
4 ( 8x − 1 ) = 19 + 32x
( 4 ) ( 8x ) + ( 4 ) ( −1 ) = 19 + 32x ( Distribute )
32x + −4 = 19 + 32x
32x − 4 = 32x + 19
Step 2: Subtract 32x from both sides.
32x − 4 − 32x = 32x + 19 − 32x
−4 = 19
Step 3: Add 4 to both sides.
−4 + 4 = 19 + 4
0 = 23
Answer:
There are no solutions.
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Not sure why such an old question is showing up on my feed...
Anyway, let
and
. Then we want to find the exact value of
.
Use the angle difference identity:
and right away we find
. By the Pythagorean theorem, we also find
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
, then (by Pythagorean theorem)
, so
. And from this,
.
So,
9514 1404 393
Answer:
(d) 36 feet
Step-by-step explanation:
Use your sense of geometry.
The hypotenuse of a right triangle will never be less than the longest side, and will never be greater than 1.5 times the longest side*.
That means the only reasonable answer choices will be between 30 and 45 feet. There is only one such choice.
The measure is about 36 feet.
__
If you like, you can find a more exact value using the Pythagorean theorem. The distance d of interest is ...
d^2 = 20^2 +30^2 = 1300
d = √1300 = 10√13 ≈ 36.0555 ≈ 36 . . . feet
_____
* The longest hypotenuse will be √2 ≈ 1.4142 times the longest right triangle leg when the two legs are equal length.
