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a number multiplied by 54 the result is positive number less than 54 which of these was multiplied by 54

11 answers

To find a number that, when multiplied by 54, results in a positive number less than 54, we can set up the following mathematical expression:

Let \( x \) be the number we are looking for. The condition can be expressed as:

\[ 0 < 54x < 54 \]

To determine the possible values for \( x \), we can divide the entire inequality by 54 (noting that since 54 is positive, we do not need to flip the inequality signs):

\[ 0 < x < 1 \]

This means \( x \) must be a positive number that is less than 1.

Thus, any number satisfying \( 0 < x < 1 \) can be multiplied by 54 to yield a positive result less than 54. For example, \( x = 0.5 \) or \( x = 0.1 \) would work, since:

  • \( 54 \times 0.5 = 27 \) (which is less than 54)
  • \( 54 \times 0.1 = 5.4 \) (which is also less than 54)

In conclusion, any positive number less than 1 when multiplied by 54 will fulfill the condition.

A: A number less then zero

B: a number between zero and one

C: a number greater than one

D: zero

To determine which option results in a product that is positive and less than 54 when multiplied by 54, let's analyze each option:

A: A number less than zero

  • If a number is less than zero (negative), then multiplying it by 54 will yield a negative product (e.g., \( 54 \times (-1) = -54 \)). This does not satisfy the condition of being a positive number.

B: A number between zero and one

  • If a number is between zero and one (e.g., \( 0.5 \)), then multiplying it by 54 will yield a positive product that is less than 54 (e.g., \( 54 \times 0.5 = 27 \)). This satisfies the condition.

C: A number greater than one

  • If a number is greater than one (e.g., \( 2 \)), then multiplying it by 54 will yield a product greater than 54 (e.g., \( 54 \times 2 = 108 \)). This does not satisfy the condition of being less than 54.

D: Zero

  • Multiplying zero by any number results in zero (e.g., \( 54 \times 0 = 0 \)). While this is not negative, it does not satisfy the requirement of being a positive number.

Conclusion:

The only option that results in a product that is a positive number less than 54 is B: a number between zero and one.

use properties of rational numbers to multiply the following -2.2 x (-60.4)

To multiply the rational numbers \(-2.2\) and \(-60.4\), we can follow these steps:

  1. Identify the signs: Both numbers are negative.

  2. Multiply the absolute values: Ignore the signs and multiply the positive versions of the numbers. \[ 2.2 \times 60.4 \]

  3. Calculating \(2.2 \times 60.4\):

    • You can perform the multiplication directly: \[ 2.2 \times 60.4 = 2.2 \times (60 + 0.4) = (2.2 \times 60) + (2.2 \times 0.4) \]
    • Calculate \(2.2 \times 60\): \[ 2.2 \times 60 = 132 \]
    • Next, calculate \(2.2 \times 0.4\): \[ 2.2 \times 0.4 = 0.88 \]
    • Now sum these results: \[ 132 + 0.88 = 132.88 \]

  4. Determine the sign: Since both numbers are negative, we multiply two negatives, which results in a positive. \[ -2.2 \times -60.4 = 132.88 \]

Final Answer:

\[ -2.2 \times -60.4 = 132.88 \]

The altitude of an airplane is decreasing at a rate of 42 feet per second what is the change in altitude of the airplane over a period of 27 seconds

To find the change in altitude of the airplane over a period of 27 seconds, given that it is decreasing at a rate of 42 feet per second, you can use the formula for change in altitude:

\[ \text{Change in altitude} = \text{Rate} \times \text{Time} \]

In this case:

  • Rate = -42 feet per second (the negative sign indicates a decrease)
  • Time = 27 seconds

Now, plug in the values:

\[ \text{Change in altitude} = -42 , \text{feet/second} \times 27 , \text{seconds} \]

Now, calculate:

\[ \text{Change in altitude} = -1134 , \text{feet} \]

Conclusion:

The change in altitude of the airplane over a period of 27 seconds is a decrease of 1134 feet.

-26 x (-58/221)

To multiply \(-26\) by \(-\frac{58}{221}\), you can follow these steps:

  1. Multiply the absolute values: Ignore the signs for the moment and multiply the numbers. \[ 26 \times 58 = 1508 \]

  2. Determine the sign: Since both numbers are negative, the product will be positive. Thus, the final result will be: \[ -26 \times -\frac{58}{221} = \frac{1508}{221} \]

  3. Simplify if possible: Now we check if \(\frac{1508}{221}\) can be simplified.

  • 1508 divided by 221 is approximately equal to \(6.818\). However, for the exact value, we can calculate \(1508 \div 221\), which does not yield a whole number, hence the fraction is in its simplest form.

So, the final answer is: \[ \frac{1508}{221} \]

If you prefer a decimal approximation, you can calculate: \[ \frac{1508}{221} \approx 6.818 \]

Final Answer:

\[ -26 \times -\frac{58}{221} = \frac{1508}{221} \quad \text{or} \quad \approx 6.818 \]

A: 116/17

B: -84\221

C: 2873/29

D: 58\17

Let's find which of these options is equivalent to the result we calculated, \(\frac{1508}{221}\).

Check each option:

  1. Option A: \(\frac{116}{17}\)

    • Dividing numerator by denominator: \[ \frac{116}{17} \approx 6.8235 \]

  2. Option B: \(-\frac{84}{221}\)

    • This is a negative fraction and cannot be equal to \(\frac{1508}{221}\), which is positive.

  3. Option C: \(\frac{2873}{29}\)

    • Dividing numerator by denominator: \[ \frac{2873}{29} = 99.069 \quad (\text{not equivalent to } \frac{1508}{221}) \]

  4. Option D: \(\frac{58}{17}\)

    • Dividing numerator by denominator: \[ \frac{58}{17} \approx 3.41176 \quad (\text{not equivalent to } \frac{1508}{221}) \]

Summary:

From this analysis, none of the options A, B, C, or D are equivalent to \(\frac{1508}{221}\).

To clarify the calculations, we can check the approximate decimal value of \(\frac{1508}{221}\):

  • It can be calculated as: \[ 1508 \div 221 \approx 6.818 \quad \text{(which is the result we obtained)} \]

Since none of the options are equal to this value, it seems there is no correct choice among the options provided. If you need further assistance or a different context, feel free to ask!