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4 years ago

Algebraic expression that best describes the sequence 2,4,8,16,32,...?

Mathematics

2 answers:

dexar [7]4 years ago

5 0

Answer:

Algebraic expression that best describes the sequence is:

$2^{n}$

Step-by-step explanation:

We have the sequence 2, 4, 8, 16, 32,...?

With the Algebraic expression:

$2^{n}$ (1)

n is the number into the sequence that you want to find, we can prove it if we replace in the equation (1)

For example in the first term, n=1

$2^{1}=2$

in the second term, n=2, and so on

$2^{2}=4\\2^{3}=8\\2^{4}=16\\2^{5}=32\\2^{6}=64\\$

IRINA_888 [86]4 years ago

4 0

The algebraic expression that beat describes the sequence is X times 2

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The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,

klasskru [66]

Given:

The scale factor is $s=\dfrac{1}{3}$ and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

$(x,y)\to (k(x-a)+a,k(y-b)+b)$

According to the given information, the scale factor is $\dfrac{1}{3}$ and the center of dilation is at (4,2).

$(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)$ ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

$C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)$

$C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)$

$C(-2,11)\to C'(-2+4,3+2)$

$C(-2,11)\to C'(2,5)$

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

$A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)$

From the given figure it is clear that the image of point A is (8,4).

$A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)$

On comparing both sides, we get

$\dfrac{1}{3}(m-4)+4=8$

$\dfrac{1}{3}(m-4)=8-4$

$(m-4)=3(4)$

$m=12+4$

$m=16$

And,

$\dfrac{1}{3}(n-2)+2=4$

$\dfrac{1}{3}(n-2)=4-2$

$(n-2)=3(2)$

$n=6+2$

$n=8$

Therefore, the coordinates of point A are (16,8).

5 0

3 years ago

Find out the answers to this

meriva

Answer:

$\tan \theta = - \frac{1}{5} = - 0.2$

$\cos \theta = 0.98$

$\sin \theta = - 0.196$

Step-by-step explanation:

It is given that $\cot \theta = - 5$ and $\theta$ is in the fourth quadrant.

So, only $\cos \theta$ will have positive value and $\sin \theta$ , $\tan \theta$ will have negative value.

Now, $\cot \theta = - 5$

⇒ $\tan \theta = \frac{1}{\cot \theta} = -\frac{1}{5}$ (Answer)

We know, that $\sec^{2} \theta - \tan^{2} \theta = 1$

⇒ $\sec \theta = \sqrt{1 + \tan^{2} \theta } = \sqrt{1 + (- \frac{1}{5} )^{2} } = 1.019$

{Since, $\cos \theta$ is positive then $\sec \theta$ will also be positive}

⇒ $\cos \theta = \frac{1}{\sec \theta} = \frac{1}{1.0198} = 0.98$ (Answer)

We know, that $\csc^{2} \theta - \cot^{2} \theta = 1$

⇒ $\csc \theta = - \sqrt{1 + \cot^{2} \theta } = - \sqrt{1 + (- 5 )^{2} } = - 5.099$

{Since, $\sin \theta$ is negative then $\csc \theta$ will also be negative}

⇒ $\sin \theta = \frac{1}{\csc \theta} = \frac{1}{- 5.099} = - 0.196$ (Answer)

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3 years ago

Write this number in standard form.<br> two hundred million.

Sergio039 [100]

Standard Form has many faces including polynomial, decimal, equation and etc. According to your question transforming that in polynomial for Two hundred million would be 200,000,000 or 2 x 10^8 in scientific notation

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3 years ago

If the rate of inflation is 3.7% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following

larisa86 [58]

Answer:

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Step-by-step explanation:

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3 years ago

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Ipatiy [6.2K]

Answer:

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Step-by-step explanation:

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3 years ago