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DaniilM [7]
2 years ago
11

A rabbit started at point 0 and made 3 jumps: a jump of 4 units, then a jump of 2 units, and then a jump of 1 unit. We do not kn

ow the direction of either jump. Where on the number line can this rabbit be now?
Mathematics
1 answer:
allochka39001 [22]2 years ago
7 0

Answer:

<u>The rabbit could be at eight different numbers of the number line:</u>

<u>-7, - 5, - 3, - 1, 1, 3, 5, and 7.</u>

Step-by-step explanation:

Let's simulate each of the jumps of the rabbit in all the possible directions, as follows:

Option 1: - 4 - 2 - 1 = -7

Option 2: - 4 - 2 + 1 = -5

Option 3: - 4 + 2 - 1 = - 3

Option 4: - 4 + 2 + 1 = - 1

Option 5:  4 - 2 - 1 = 1

Option 6: 4 - 2 + 1 = 3

Option 7: 4 + 2 - 1 = 5

Option 8: 4 + 2 + 1 = 7

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Which option lists an expression that is not equivalent to 4 2/3?
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Answer:

Option A and Option B are not equivalent to the given expression.

Step-by-step explanation:

We are given the following expression:

4^{\frac{2}{3}}

Applying properties of exponents and base:

(a^x)^y = a^{xy}\\a^{-x}= (\frac{1}{a})^x\\

A. Using the exponential property a^{-x}= (\frac{1}{a})^x\\, we can write:

0.25^{\frac{3}{2}} = (\frac{1}{0.25})^{\frac{-3}{2}} = (4)^{\frac{-3}{2}}

which is not equal to the given expression.

B. Using the exponential property a^{-x}= (\frac{1}{a})^x\\, we can write:

(0.25)^{\frac{-3}{2}} = (\frac{1}{0.25})^{\frac{3}{2}} = (4)^{\frac{3}{2}}

which is not equal to the given expression.

C. First we convert the radical form into exponent form. Then by using the property (a^x)^y = a^{xy} of exponent, we can write the following:

^3\sqrt{16} = (16)^{\frac{1}{3}} = (4^2)^{\frac{1}{3}} = 4^{\frac{2}{3}}

which is equal to the given expression.

D. First we convert the radical form into exponent form. Then by using the property (a^x)^y = a^{xy} of exponent, we can write the following:

(^3\sqrt{4})^2 = (4^{\frac{1}{3}})^2 = 4^{\frac{2}{3}}

which is equal to the given expression.

Option D and Option C are equivalent to the given expression.

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