We will use the following law of indices (or 'index law') to check each pair of expression
![x^{ \frac{m}{n}} = ( \sqrt[n]{x} )^{m}](https://tex.z-dn.net/?f=%20x%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D%20%3D%20%28%20%5Csqrt%5Bn%5D%7Bx%7D%20%29%5E%7Bm%7D%20)
With fractional power, the denominator is the root and the numerator is the power of the term. When the denominator is 2, we usually only write the normal square symbol (√). Denominator other than 2, we usually write the value of the root, for example, the cubic root ∛
Option A - Incorrect
should equal to
![( \sqrt[7]{7} )^{5}](https://tex.z-dn.net/?f=%20%28%20%5Csqrt%5B7%5D%7B7%7D%20%29%5E%7B5%7D%20)
Option B - Correct
does equal to
Option C - Incorrect
should equal to
Option D - Incorrect
should equal to
![( \sqrt[3]{5} )^{2}](https://tex.z-dn.net/?f=%20%28%20%5Csqrt%5B3%5D%7B5%7D%20%29%5E%7B2%7D%20)
Answer:
m = -1/2
Step-by-step explanation:
Hope this helps.
Answer:
Option B
Step-by-step explanation:
Let the point O is the origin.
Then the coordinates of the vertices A,B and C will be,
A → (-12, -8)
B → (-8, 0)
C → (-6, -4)
Rule for the dilation of a point (x, y) by scale factor 'k' about the origin is,
(x, y) → (kx, ky)
By this rule, coordinates of the vertices of the image triangle will be,
If k = 
,
A(-12, -8) → A'(-6, -4)
B(-8, 0) → B'(-4, 0)
C(-6, -4) → C'(-3, -2)
From the given options,
Option B is the answer.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.
First, all the heights have to be converted to similar units, say feet.
Therefore,
Building= 20 feet
Tree = 252*0.083333 = 21 feet
Flagpole = 6*3 = 18 feet
The tallest of the three is the tree and thus should cast the longest shadow. However, it should be noted that at exactly noon when the sun is overhead, all the three will have equal length of shadow (that is, 0 feet long).
