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Mathematics

2 answers:

Bogdan [553]3 years ago

8 0

Answer:

Step-by-step explanation:

Luda [366]3 years ago

5 0

If there’s 18 pink butterflies then if you look at the ration for every 3 pink butterflies there are 5 yellow butterflies, so divide 3/18 to get 6 the multiply 6*5 to get 30 yellow butterflies

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What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following

skelet666 [1.2K]

For this case we have the following expression:

$x ^ 2-4x + 10 = 4x + 10$

We follow the steps below:

We subtract 4x on both sides of the equation:

$x ^ 2-4x + 10-4x = 4x + 10-4x\\x ^ 2-8x + 10 = 10$

We subtract 10 from both sides of the equation:

$x ^ 2-8x + 10-10 = 10-10\\x ^ 2-8x = 0$

Now, we must complete squares.

When we have an equation of the form:

$ax ^ 2 + bx + c = 0$ , if we want to complete squares we must subtract c on both sides of the equation obtaining:

$ax ^ 2 + bx + c-c = -c\\ax ^ 2 + bx = -c$

The square is completed by adding to both sides of the equation: $(\frac{b}{2})^{2}$

So, we have left:

$ax^2+bx + (\frac {b} {2})^{2} = - c + (\frac {b} {2}) ^ {2}$

In the given expression we have:

$a = 1\\b = -8\\c = 0$

And to complete the square we have:

$(\frac {b} {2}) ^ {2} = (\frac {-8} {2}) ^ {2} = 16$

Rewriting we have:

$x ^ 2-8x + 16 = 16$

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

$-4-4 = -8\\-4 * -4 = 16$