What is the line of symmetry

Mathematics

1 answer:

Lerok [7]3 years ago

6 0

Answer:

is the imaginary line where you could fold the image and have both halves match exactly.

You might be interested in

What is the rule for the following sequence: 2, 9, 21, 65

Helga [31]

There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get

... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9

The next term using this rule is 174 34/39, not an integer.

The coefficients p and q for a[n-2] and a[n-1] can be found from

$2p+9q=21\\9p+21q=65$

_____

Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be

... a[n] = 4.5n³ -24.5n² +49n -27

Using this rule, the next two terms are 168 and 357.

5 0

3 years ago

Given the data points, (x, y) of a linear function: (2, 11), (4, 10), (6, 9), (12, 6), what is the function? What is the slope?

NeX [460]

Answer:

The function is $y~=~12 ~-~ 0.5 \cdot x$ .

The slope is $m=-0.5$ .

The y-intercept is $b=12$ .

Step-by-step explanation:

Our aim is to calculate the values m (slope) and b (y-intercept) in the equation of a line :

$y=mx+b$

We have the following data:

$\begin{array}{c|cccc}x&2&4&6&12\\y&11&10&9&6\end{array}$

To find the line of best fit for the points given, you must:

Step 1: Find $X\cdot Y$ and $X\cdot X$ as it was done in the table below.

Step 2: Find the sum of every column:

$\sum{X} = 24 ~,~ \sum{Y} = 36 ~,~ \sum{X \cdot Y} = 188 ~,~ \sum{X^2} = 200$

Step 3: Use the following equations to find b and m:

$\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 200 - 24 \cdot 188}{ 4 \cdot 200 - 24^2} \approx 12 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 4 \cdot 188 - 24 \cdot 36 }{ 4 \cdot 200 - \left( 24 \right)^2} \approx -0.5\end{aligned}$