What is the sum of (w^(6)+(2)/(3)w^(2)) and ((1)/(2)w^(6)+(1)/(3)w^(2)+(1)/(4)) ? Choose 1 answer: (A) (1)/(2)w^(6)+(1)/(3)w^(2)-(1)/(4) (B) (1)/(2)w^(6)+w^(2)+(1)/(4) (C) (3)/(2)w^(6)+(1)/(3)w^(2)-(1)/(4) (D) (3)/(2)w^(6)+w^(2)+(1)/(4)

Write expressions to be added: Write down the expressions to be added. We have two expressions: w^(6) + (2/3)w^(2) and (1/2)w^(6) + (1/3)w^(2) + (1/4) We need to add these two expressions together.Combine like terms: Combine like terms. To add the expressions, we combine the coefficients of the like terms, which are the terms with the same power of w. For w^(6) terms: 1 * w^(6) + (1/2) * w^(6) = (3/2) * w^(6) For w^(2) terms: (2/3) * w^(2) + (1/3) * w^(2) = (3/3) * w^(2) = w^(2) The constant term (1/4) has no like term in the first expression, so it remains as it is.Write final expression: Write the final expression. The sum of the two expressions is: (3/2)w^(6) + w^(2) + (1/4)Match final expression with choices: Match the final expression with the given choices. The final expression (3/2)w^(6) + w^(2) + (1/4) matches with choice (D).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the sum of
(w^(6)+(2)/(3)w^(2)) and
((1)/(2)w^(6)+(1)/(3)w^(2)+(1)/(4)) ?
Choose 1 answer:
(A)
(1)/(2)w^(6)+(1)/(3)w^(2)-(1)/(4)
(B)
(1)/(2)w^(6)+w^(2)+(1)/(4)
(C)
(3)/(2)w^(6)+(1)/(3)w^(2)-(1)/(4)
(D)
(3)/(2)w^(6)+w^(2)+(1)/(4)

What is the sum of $\left(w^{6}+\frac{2}{3} w^{2}\right)$ and $\left(\frac{1}{2} w^{6}+\frac{1}{3} w^{2}+\frac{1}{4}\right)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2} w^{6}+\frac{1}{3} w^{2}-\frac{1}{4}$ $\newline$ (B) $\frac{1}{2} w^{6}+w^{2}+\frac{1}{4}$ $\newline$ (C) $\frac{3}{2} w^{6}+\frac{1}{3} w^{2}-\frac{1}{4}$ $\newline$ (D) $\frac{3}{2} w^{6}+w^{2}+\frac{1}{4}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

Q. What is the sum of

\left(w^{6}+\frac{2}{3} w^{2}\right)

and

\left(\frac{1}{2} w^{6}+\frac{1}{3} w^{2}+\frac{1}{4}\right)

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2} w^{6}+\frac{1}{3} w^{2}-\frac{1}{4}

\newline

(B)

\frac{1}{2} w^{6}+w^{2}+\frac{1}{4}

\newline

(C)

\frac{3}{2} w^{6}+\frac{1}{3} w^{2}-\frac{1}{4}

\newline

(D)

\frac{3}{2} w^{6}+w^{2}+\frac{1}{4}

Write expressions to be added: Write down the expressions to be added. $\newline$ We have two expressions: $\newline$ $w^{6} + \frac{2}{3}w^{2}$ $\newline$ and $\newline$ $\frac{1}{2}w^{6} + \frac{1}{3}w^{2} + \frac{1}{4}$ $\newline$ We need to add these two expressions together.
Combine like terms: Combine like terms. $\newline$ To add the expressions, we combine the coefficients of the like terms, which are the terms with the same power of $w$ . $\newline$ For $w^{6}$ terms: $1 \cdot w^{6} + \frac{1}{2} \cdot w^{6} = \frac{3}{2} \cdot w^{6}$ $\newline$ For $w^{2}$ terms: $\frac{2}{3} \cdot w^{2} + \frac{1}{3} \cdot w^{2} = \frac{3}{3} \cdot w^{2} = w^{2}$ $\newline$ The constant term $\frac{1}{4}$ has no like term in the first expression, so it remains as it is.
Write final expression: Write the final expression. $\newline$ The sum of the two expressions is: $\newline$ $(\frac{3}{2})w^{6} + w^{2} + (\frac{1}{4})$
Match final expression with choices: Match the final expression with the given choices. $\newline$ The final expression $(\frac{3}{2})w^{6} + w^{2} + (\frac{1}{4})$ matches with choice (D).