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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]).
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]).
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