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2 years ago

A student factors a6 - 64 to (a2 - 4)(a4 + 4a2 + 16).Which statement about (a2 − 4)(a4 + 4a2 + 16) is correct?

Mathematics

1 answer:

IrinaK [193]2 years ago

4 0

Answer:

Option (b) is correct.

The expression is equivalent, but the term is not completely factored.

Step-by-step explanation:

Given : a student factors to

We have to choose the correct statement about from the given options.

Given is factored to

Consider

Using algebraic identity,

comparing and b = 4, we have,

Thus, the factorization is equivalent but we can simplify it further also, as

Using algebraic identity,

Thus,

Can be written as

Thus, the expression is equivalent, but the term is not completely factored.

Option (b) is correct.

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the combined age of april and laura is 23 years. laura's age is two years more than half of april's age. what is laura's age

Kipish [7]

Laura's age is 9 years.

Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

<u>Convert statement into algebraic expression:</u>

Half of April's age = $\frac{x}{2}$

2 years more than half of April's age = $\frac{x}{2}+2$

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

$$\Rightarrow \ \ x+(\frac{x}{2}+2) =23$

$$\Rightarrow \ \ x+\frac{x}{2}+2 =23$

$$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23$

To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

$$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23$

$$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23$

Denominators are same, now add the fractions.

$$\Rightarrow \ \ \frac{2x+x+4}{2} =23$

Do cross multiplication.

$$\Rightarrow \ \ 2x+x+4=23\times2$

$$\Rightarrow \ \ 3x=46-4$

$$\Rightarrow \ \ 3x=42$

$$\Rightarrow \ \ x=14$

Aprils's age = 14 years

Laura's age = $\frac{14}{2}+2$

= 7 + 2

Laura's age = 9

Hence Laura's age is 9 years.

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