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3 years ago

Which exponential expression is equivalent to the one below? (6x3)^5

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

Answer:

Hi! The answer to your question is D. $6^5 * 3^5$

Step-by-step explanation:

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Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

4 0

3 years ago

If the diagonal of a square is approximately 12.73, what is the length of its sides?

Alja [10]

Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

$D^{2} = L^{2} + L^{2}$

Solving further, we have

$D^{2} = 2L^{2}$

Divide both sides by 2

$\frac{D^{2}}{2} = \frac{2L^{2}}{2}$

$\frac{D^{2}}{2} = L^2$

Take Square root of both sides

$\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}$

$\sqrt{\frac{D^{2}}{2}} = L$

Reorder

$L = \sqrt{\frac{D^{2}}{2}}$

Now, the value of L can be calculated by substituting 12.73 for D

$L = \sqrt{\frac{12.73^{2}}{2}}$

$L = \sqrt{\frac{162.0529}{2}}$

$L = \sqrt{{81.02645}$

$L = 9.001469325$

$L = 9.0015$ (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

7 0

3 years ago

Does anyone know what the vertex is?

sveticcg [70]

Answer:

A vertex (or node) of a graph is one of the objects that are connected together. The connections between the vertices are called edges or links. A graph with 10 vertices (or nodes) and 11 edges (links). For more information about graph vertices, see the network introduction.

7 0

3 years ago

Giving brainliest but has to be a actual answer

vaieri [72.5K]

Answer:

2,800 Books to be the same.

3 0

3 years ago

2-1= plz help me i need help

Alinara [238K]

Answer:

1 :)

Step-by-step explanation:

5 0

4 years ago

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