Solve 1/2+1/2x=x^2-7x+10/4x by re-writing the equation as a proportion. Which proportion is equivalent to the original equation?

Mathematics

2 answers:

denis-greek [22]3 years ago

7 0

Answer:

The answer is C. x+1/2x=x^2-7x+10/4x

The next two answers are x=1 and x=8 (true solutions);

AND x=o (extraneous solution)

Step-by-step explanation:

Nitella [24]3 years ago

6 0

Rewriting the equation as a proportion, we have
(1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10)/4x
(2x/4x) + (2/4x) = (x^2 - 7x + 10)/4x

Multiplying both sides of the equation by 4x to clear the denominators:
2x + 2 = x^2 - 7x + 10
We now have a new equation that is equivalent to the original equation:
x^2 - 9x + 8 = 0

We can also write the equation into its factored form:
(x - 8)(x - 1) = 0
Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero.
x - 8 = 0 => x = 8
x - 1 = 0 => x = 1
Therefore, our solutions are x = 8 and x = 1.

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Anna [14]

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3 years ago

Read 2 more answers

Which function has the domain x>-11

Marat540 [252]

<h2>Answer</h2>

$y=\sqrt{x+11} +5$

<h2>Explanation</h2>

Remember that the square root function is not defined, in the set of real numbers, for negatives values, so its radicand (the thing inside the square root) must be zero or bigger than zero. In other words, to find the domain of a square root function, you should set the thing inside the radical bigger or equal to zero and solve for x. Let's find the domain of each one of our functions:

For $y=\sqrt{x+11} +5$

The thing inside the square root is $x+11$ , so we are setting that bigger or equal than zero and solve for x to find the domain of the function: