The linear equation y=1/2x+3 is written in form
1 answer:
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Answer:
This is equivalent to
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Explanation:
To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.
This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.
The expression is the same as
after we multiply top and bottom by sqrt(3) to rationalize the denominator.
Side notes:
- This entire process only applies to 30-60-90 triangles.
- The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is
units long.
- You could use the tangent ratio to help isolate x. You would either say tan(30) = x/10 or tan(60) = 10/x as the first equation to set up.
We want to solve
√(2x+4) - √(x) = 2
Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0
Either
√x = 0 => x = 0
or
√x = 4 => x = 16
Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)
A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.
Answer: B. x = 0 and x = 16.
√(2x+4) - √(x) = 2
Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0
Either
√x = 0 => x = 0
or
√x = 4 => x = 16
Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)
A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.
Answer: B. x = 0 and x = 16.