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bixtya [17]
4 years ago
10

Explain why 81 3/4 equals 27

Mathematics
2 answers:
professor190 [17]4 years ago
8 0
81 to the 4th root is 3 and 3 cubed is 27.
Volgvan4 years ago
7 0

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

<u>Exponent rules:</u>

Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n}

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}  \\ \\  Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27

Conclusion:

The above explanation explains why 81^{\frac{3}{4}} =27

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The vertices of ΔABC are A(−3,4)​, B(−2,4)​, and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image Δ​A'B'C
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The coordinates of vertex B' is P'(x,y) = (-2, -8).

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P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)] (1)

Where:

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If we know that P(x,y) = (-2,4) and x_{P} = -2, then the coordinates of the vertex is:

P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)]

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P'(x,y) = (-2, -8)

The coordinates of vertex B' is P'(x,y) = (-2, -8). \blacksquare

To learn more on reflections, we kindly invite to check this verified question: brainly.com/question/1878272

3 0
3 years ago
I'll give brainliest to who can answer this!
Kitty [74]

Answer:

the answer is 3

Step-by-step explanation:

6 0
3 years ago
20 POINTS
dmitriy555 [2]

Answer:


Step-by-step explanation:

Its correct corrdenates are -8, 1  and 5, -3

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uhh the slope formula is

To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). The equation used to calculate the slope from two points is: On a graph, this can be represented as: There are three steps in calculating the slope of a straight line when you are not given its equation

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