The diagonal of a suitcase measures 30 inches and the height is 18 inches. What is the width of the suitcase to the
2 answers:
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Megan:
x to the one third power =
<span>x to the one twelfth power = </span>
<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span>
<span>
Since </span>
then
Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4
Julie:
x times x to the second times x to the fifth = x * x² * x⁵
<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span>![\sqrt[32]{x* x^{2} * x^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%20)
<span>
Since </span>
Then![\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%3D%20%5Csqrt%5B32%5D%7B%20x%5E%7B1%2B2%2B5%7D%20%7D%20%3D%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D)
Since![\sqrt[n]{x^{m}} = x^{m/n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7Bm%2Fn%7D%20%7D%20)
Then![\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D%3D%20x%5E%7B8%2F32%7D%20%3D%20x%5E%7B1%2F4%7D%20)
Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.
x to the one third power =
<span>x to the one twelfth power = </span>
<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span>
<span>
Since </span>
then
Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4
Julie:
x times x to the second times x to the fifth = x * x² * x⁵
<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span>
<span>
Since </span>
Then
Since
Then
Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.
Answer:
The correct options are:
Option B) is never zero.
Option F) When x=0, y≠0
Step-by-step explanation:
Consider the provided function.
When we substitute x=0 in above function we get:
When we substitute x=-1 in above function we get:
When we substitute x=1 in above function we get:
The above function is exponential function which does not pass through the origin and the range of the function is a positive number.
The graph of the function is shown in figure 1.
Now consider the provided options.
Option A) is always greater than or equal to 1.
The option is incorrect as the value of the function is less than 1 for negative value of x.
Option B) is never zero
The option is correct.
Option C) When y=0, x=0
The option is incorrect.
Option D) When x=0, y=4
When x=0 the value of y is 1.
Thus, the option is incorrect.
Option E) is zero when x=0
When x=0 the value of is 1.
Thus, the option is incorrect.
Option F) When x=0, y≠0
The option is correct as 0≠1.
