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Bas_tet [7]
3 years ago
8

Which equation represents the data shown in the table provided in the image?

Mathematics
1 answer:
VladimirAG [237]3 years ago
4 0

The correct answer is A. y = 2x +1

Explanation:

An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.

First  column

5 = 2 · 2 + 1

5 = 4 + 1

5 = 5

Second Column

9 = 2 · 4 + 1

9 = 8 + 1

9 = 9

Third column

13 = 6 · 2 + 1

13 = 12 + 1

13 =  13

Fourth column

17 = 8 · 2 + 1

17 = 16 + 1

17 = 17

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4
gtnhenbr [62]

Answer:

Simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

Step-by-step explanation:

We need to simplify the expression (6^{-2})(3^{-3})(3*6)^4

Solving:

(6^{-2})(3^{-3})(3*6)^4

Applying exponent rule: a^{-m}=\frac{1}{a^m}

=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\

Factors of 18=2\times 3\times 3=2\times3^2

Factors of 6=2\times 3

Replacing terms with factors

=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\

Using exponent rule: (a^m)^n=a^{m\times n}

=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}

Using exponent rule: a^m.a^n=a^{m+n}

=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}

Now using exponent rule: \frac{a^m}{a^n}=a^{m-n}

=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108

So, simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

7 0
3 years ago
In the adjoining figure O is the centre of the circle the tangent to the circle of radius 6 cm from the exterior point P of the
slamgirl [31]

Answer:

Let P be the external point. O be the origin. join O and P get OP and nearest point on the circle from P be A.

Let Q be the point onthe circle  in which, tangent make 90° with radius at Q.

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we get a right angled triangle  PQO right angled at Q.

so, OP^2 = OQ^2 + PQ^2= 8^2 + 6^2 = 64 + 36 =1==

therefore OP =10cm

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3 years ago
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Answer:

It is a solution

Step-by-step explanation:

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3 years ago
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