Which equation has both 1/4 and -1/4 as possible values of x? Select all that apply. Multi-select Choices: (A)x^2 = 1/2 (B)x^3 = 1/2 (C)x^2 = 1/16 (D)x^3 = 1/16 (E)x^2 = 1/64 (F)x^3 = 1/64

Check x = 1/4: Step 1: Check if x = 1/4 and x = -1/4 satisfy equation (A) x^2 = 1/2. Calculation: (1/4)^2 = 1/16 and (-1/4)^2 = 1/16. Does not match 1/2. Check x = -1/4: Step 2: Check if x = 1/4 and x = -1/4 satisfy equation (B) x^3 = 1/2. Calculation: (1/4)^3 = 1/64 and (-1/4)^3 = -1/64. Does not match 1/2. Check x^2 = 1/16: Step 3: Check if x = 1/4 and x = -1/4 satisfy equation (C) x^2 = 1/16. Calculation: (1/4)^2 = 1/16 and (-1/4)^2 = 1/16. Matches 1/16. Check x^3 = 1/16: Step 4: Check if x = 1/4 and x = -1/4 satisfy equation (D) x^3 = 1/16. Calculation: (1/4)^3 = 1/64 and (-1/4)^3 = -1/64. Does not match 1/16. Check x^2 = 1/64: Step 5: Check if x = 1/4 and x = -1/4 satisfy equation (E) x^2 = 1/64. Calculation: (1/4)^2 = 1/16 and (-1/4)^2 = 1/16. Does not match 1/64. Check x^3 = 1/64: Step 6: Check if x = 1/4 and x = -1/4 satisfy equation (F) x^3 = 1/64. Calculation: (1/4)^3 = 1/64 and (-1/4)^3 = -1/64. Matches 1/64.

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Math Problems

Algebra 2

Sin, cos, and tan of special angles

Full solution

Q. Which equation has both

\frac{1}{4}

and

-\frac{1}{4}

as possible values of

x

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

x^2 = \frac{1}{2}

\newline

(B)

x^3 = \frac{1}{2}

\newline

(C)

x^2 = \frac{1}{16}

\newline

(D)

x^3 = \frac{1}{16}

\newline

(E)

x^2 = \frac{1}{64}

\newline

(F)

x^3 = \frac{1}{64}

Check $x = \frac{1}{4}$ : Step $1$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (A) $x^2 = \frac{1}{2}$ . $\newline$ Calculation: $\left(\frac{1}{4}\right)^2 = \frac{1}{16}$ and $\left(-\frac{1}{4}\right)^2 = \frac{1}{16}$ . $\newline$ Does not match $\frac{1}{2}$ .
Check $x = -\frac{1}{4}$ : Step $2$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (B) $x^3 = \frac{1}{2}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Does not match $\frac{1}{2}$ .
Check $x^2 = \frac{1}{16}$ : Step $3$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (C) $x^2 = \frac{1}{16}$ . $\newline$ Calculation: $\left(\frac{1}{4}\right)^2 = \frac{1}{16}$ and $\left(-\frac{1}{4}\right)^2 = \frac{1}{16}$ . $\newline$ Matches $\frac{1}{16}$ .
Check $x^3 = \frac{1}{16}$ : Step $4$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation $(D) x^3 = \frac{1}{16}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Does not match $\frac{1}{16}$ .
Check $x^2 = \frac{1}{64}$ : Step $5$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation (E) $x^2 = \frac{1}{64}$ . $\newline$ Calculation: $(\frac{1}{4})^2 = \frac{1}{16}$ and $(-\frac{1}{4})^2 = \frac{1}{16}$ . $\newline$ Does not match $\frac{1}{64}$ .
Check $x^3 = \frac{1}{64}$ : Step $6$ : Check if $x = \frac{1}{4}$ and $x = -\frac{1}{4}$ satisfy equation $(F) x^3 = \frac{1}{64}$ . $\newline$ Calculation: $(\frac{1}{4})^3 = \frac{1}{64}$ and $(-\frac{1}{4})^3 = -\frac{1}{64}$ . $\newline$ Matches $\frac{1}{64}$ .