Respuesta :
The true statement is [tex]\boxed{{\text{if }}9z = 3,{\text{ then }}z = 0.3333 \ldots }[/tex]. Option D is correct.
Further explanation:
Given:
The options are as follows,
A. [tex]{\text{if }}9z = - 3,{\text{ then }}z = 0.3333 \ldots[/tex]
B. [tex]{\text{if }}9z = 3,{\text{ then }}z = - 12[/tex]
C. [tex]{\text{if }}9z = 3,{\text{ then }}z = 3[/tex]
D. [tex]{\text{if }}9z = 3,{\text{ then }}z = 0.3333 \ldots[/tex]
Explanation:
In option A the statement is [tex]{\text{if }}9z = - 3,{\text{ then }}z = 0.3333 \ldots[/tex].
The equation is [tex]9z=-3[/tex] and the value of [tex]z[/tex] can be obtained as follows,
[tex]\begin{aligned}9z&= - 3\\z&= \frac{{ - 3}}{9}\\z&= - \frac{1}{3}\\z&= - 0.3333 \ldots \\\end{aligned}[/tex]
Since, the value of [tex]z[/tex] is [tex]0.3333 \ldots.[/tex]Therefore,option A is not correct.
In option B the statement is [tex]{\text{if }}9z = 3,{\text{ then }}z = - 12.[/tex]
The equation is [tex]9z=3[/tex] and the value of z can be obtained as follows,
[tex]\begin{aligned}9z&=3\\z&=\frac{{ 3}}{9}\\z&= \frac{1}{3}\\z&= 0.3333 \ldots\\\end{aligned}[/tex]
Since, the value of [tex]z[/tex] is [tex]0.3333 \ldots.[/tex] Therefore,option B is not correct.
In option C the statement is [tex]{\text{if }}9z = 3,{\text{ then }}z = 3.[/tex]
The equation is 9z=3 and the value of z can be obtained as follows,
[tex]\begin{aligned}9z &= 3\\z&= \frac{{ 3}}{9}\\ z&=\frac{1}{3}\\z&= 0.3333 \ldots\\\end{aligned}[/tex]
Since, the value of [tex]z[/tex] is [tex]0.3333 \ldots.[/tex] Therefore,option C is not correct.
In option D the statement is [tex]{\text{if }}9z = 3,{\text{ then }}z = 3.[/tex]
The equation is [tex]9z=3[/tex] and the value of [tex]z[/tex] can be obtained as follows,
[tex]\begin{aligned}9z &= 3\\z&= \frac{{ 3}}{9}\\z &= \frac{1}{3}\\z &= 0.3333 \ldots\\\end{aligned}[/tex]
Since, the value of [tex]z[/tex] is [tex]0.3333 \ldots[/tex]. Therefore,option D is correct.
The true statement is [tex]\boxed{{\text{if }}9z = 3,{\text{ then }}z = 0.3333 \ldots }[/tex]. Option D is correct.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Fractions
Keywords: statement, true, nearest tenth, round, true statement, fraction, rational, numbers, [tex]9z=-3, 9z=3, z=0.3333, z=-12.[/tex]
