Mathematics, 05.12.2020 15:40 carma43

Write the following expression in the form (x+a)^2+b

a)x^2+6x+4

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Answer from: itasykamila

The given expression $x^2 + 6\, x + 4$ is equivalent to (x + 3)^2 - 5 . In this expression, a = 3 whereas b = -5 .

Step-by-step explanation:

Expand (x + a)^2 + b using binomial expansion.

$\begin{aligned} & (x + a)^2 + b \\ &= (x + a) \cdot (x + a) + b \\ &= \left(x^2 + a\, x\right) + \left(a\, x + a^2\right) + b \\ &= x^2 + 2\, a\, x + (a^2 + b)\end{aligned}$ .

Compare this expression to $x^2 + 6\, x + 4$ to find information about and .

In particular, these two expressions are supposed to be equal to one another. Therefore:

The coefficient of the x^2

term in these two expressions should be the same. The coefficient of $x^2\!$ in both expression is

. That does not provide any information about

or about

. The coefficient of the

term in these two expressions should be the same. In the first equation, the coefficient of $x\!$ is $2\, a$ . In the second equation, that coefficient is

. Therefore, $2\, a = 6$ . The constant term of these two expressions should be the same. That gives the equation: a^2 + b = 4

The first equation $2\, a = 6$ implies that a = 3 . Substitute that value into the second equation and solve for . The conclusion is that a= 3 and b = -5 .

Therefore, the original equation is equivalent to (x + 3)^2 - 5 .

Answer from: Quest

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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Write the following expression in the form (x+a)^2+b

a)x^2+6x+4...

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