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Ed spoke to his cousin in Australia, who told him it was 30°C30°C that day. Ed wasn’t sure if that was hot or cold, so he converted the temperature to degrees Fahrenheit. Use the formula F=95C+32F=95C+32 where F is degrees Fahrenheit and C is degrees Celsius. What is the temperature in degrees Fahrenheit? NOTE: Enter the number of degrees Fahrenheit in the box in order for this problem to be scored correctly. (1 point)

The power 9^2 is equivalent to 81 . What is the value of 9^−2 ?(1 point) Responses −81 −9 1/9 1/81
Which statement describes what these four powers have in common? 4^0 (−2)^0 (1/3)^0 9^0 (1 point) Responses All the powers have a value of –1 because the exponent is zero. All the powers have a value of –1 because the exponent is zero. All the powers have a value of 1 because the exponent is zero. All the powers have a value of 1 because the exponent is zero. All the powers have a value of 0 because the exponent is zero. All the powers have a value of 0 because the exponent is zero. All the powers have a fractional value because the exponent is zero.

1 answer

Let's solve each part of the problem step by step.

  1. Convert 30°C to Fahrenheit: We use the formula \( F = \frac{9}{5}C + 32 \).

    Substituting \( C = 30 \): \[ F = \frac{9}{5}(30) + 32 \ F = 54 + 32 \ F = 86 \] So, the temperature in degrees Fahrenheit is 86.

  2. Calculate \( 9^{-2} \): The negative exponent indicates that we take the reciprocal of the base raised to the positive exponent. \[ 9^{-2} = \frac{1}{9^2} = \frac{1}{81} \] Therefore, the value of \( 9^{-2} \) is \( \frac{1}{81} \).

  3. Commonality of the powers: The expressions \( 4^0 \), \( (-2)^0 \), \( (1/3)^0 \), and \( 9^0 \) all have an exponent of zero. Any non-zero number raised to the power of zero is equal to 1.

    Therefore, the correct statement is: All the powers have a value of 1 because the exponent is zero.

Final Answers:

  1. 86
  2. \( \frac{1}{81} \)
  3. All the powers have a value of 1 because the exponent is zero.