Answer :
To determine which functions are equivalent to the expression [tex]\( f \times 0 = \sqrt[4]{162} \times \)[/tex], we need to analyze each option and compare it to this expression. However, given the result, None, it's indicated that none of the provided options is equivalent to the given expression.
Here's a breakdown of the given expressions:
1. [tex]\( F x = 152^{\frac{x}{4}} \)[/tex]
- This expression cannot be equivalent to zero since it's dependent on [tex]\( x \)[/tex] and raises 152 to a power, which means it won't consistently result in zero.
2. [tex]\( 5 \times 0 = [3 \times \sqrt{2}]^ \)[/tex]
- Anything multiplied by zero equals zero, but there's some confusion here with the placeholder that does not equate to zero when applied in any usual sense with these operations.
3. [tex]\( 150 = 94 \sqrt{2} \)[/tex]
- This is a non-zero expression since [tex]\( 94 \times \sqrt{2} \)[/tex] does not equal 150.
4. [tex]\( 700 = 152^{\frac{\pi}{x}} \)[/tex]
- Again, raising 152 to a power will not yield zero unless specifically formatted to do so, which is not the case here.
5. [tex]\( F x 0 = \left[B Q^{\frac{2}{4}} 2\right]^x \)[/tex]
- This expression depends on variables and powers and does not simplify to zero in any straightforward way unless specific values cause such, which can't be determined with the given information.
Since none of these options straightforwardly satisfy the condition of equivalence to zero as described in [tex]\( f \times 0 = \sqrt[4]{162} \times \)[/tex], the conclusion is that none are equivalent.
Here's a breakdown of the given expressions:
1. [tex]\( F x = 152^{\frac{x}{4}} \)[/tex]
- This expression cannot be equivalent to zero since it's dependent on [tex]\( x \)[/tex] and raises 152 to a power, which means it won't consistently result in zero.
2. [tex]\( 5 \times 0 = [3 \times \sqrt{2}]^ \)[/tex]
- Anything multiplied by zero equals zero, but there's some confusion here with the placeholder that does not equate to zero when applied in any usual sense with these operations.
3. [tex]\( 150 = 94 \sqrt{2} \)[/tex]
- This is a non-zero expression since [tex]\( 94 \times \sqrt{2} \)[/tex] does not equal 150.
4. [tex]\( 700 = 152^{\frac{\pi}{x}} \)[/tex]
- Again, raising 152 to a power will not yield zero unless specifically formatted to do so, which is not the case here.
5. [tex]\( F x 0 = \left[B Q^{\frac{2}{4}} 2\right]^x \)[/tex]
- This expression depends on variables and powers and does not simplify to zero in any straightforward way unless specific values cause such, which can't be determined with the given information.
Since none of these options straightforwardly satisfy the condition of equivalence to zero as described in [tex]\( f \times 0 = \sqrt[4]{162} \times \)[/tex], the conclusion is that none are equivalent.
