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------------------------------------------------ Select each equation that the decimal 35.9 makes true.

1. [tex]0.01 \times \square = 3,590[/tex]

2. [tex]0.01 \times \square = 0.359[/tex]

3. [tex]0.1 \times \square = 0.359[/tex]

4. [tex]0.01 \times \square = 3.59[/tex]

5. [tex]0.1 \times \square = 3.59[/tex]

Answer :

Let's go through the solution step-by-step to determine which equations the decimal 35.9 makes true:

1. Equation 1: [tex]\(0.01 \times \boxtimes = 3,590\)[/tex]

To find what [tex]\(\boxtimes\)[/tex] should be, we divide 3,590 by 0.01:

[tex]\[
\boxtimes = \frac{3,590}{0.01} = 359,000
\][/tex]

Since 359,000 is not equal to 35.9, this equation is not true for 35.9.

2. Equation 2: [tex]\(0.01 \times \boxtimes = 0.359\)[/tex]

To find what [tex]\(\boxtimes\)[/tex] should be, divide 0.359 by 0.01:

[tex]\[
\boxtimes = \frac{0.359}{0.01} = 35.9
\][/tex]

Since 35.9 is equal to our decimal 35.9, this equation is true.

3. Equation 3: [tex]\(0.1 \times \boxtimes = 0.359\)[/tex]

To find what [tex]\(\boxtimes\)[/tex] should be, divide 0.359 by 0.1:

[tex]\[
\boxtimes = \frac{0.359}{0.1} = 3.59
\][/tex]

Since 3.59 is not equal to 35.9, this equation is not true for 35.9.

4. Equation 4: [tex]\(0.01 \times \boxtimes = 3.59\)[/tex]

To find what [tex]\(\boxtimes\)[/tex] should be, divide 3.59 by 0.01:

[tex]\[
\boxtimes = \frac{3.59}{0.01} = 359
\][/tex]

Since 359 is not equal to 35.9, this equation is not true for 35.9.

5. Equation 5: [tex]\(0.1 \times \boxtimes = 3.59\)[/tex]

To find what [tex]\(\boxtimes\)[/tex] should be, divide 3.59 by 0.1:

[tex]\[
\boxtimes = \frac{3.59}{0.1} = 35.9
\][/tex]

Since 35.9 is equal to our decimal 35.9, this equation is true.

In summary, the equations that the decimal 35.9 makes true are Equation 2 ([tex]\(0.01 \times \boxtimes = 0.359\)[/tex]) and Equation 5 ([tex]\(0.1 \times \boxtimes = 3.59\)[/tex]).