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3 years ago

Which two transformations preserve their orientation?

Mathematics

2 answers:

Rashid [163]3 years ago

7 0

Answer:

Rotation and translation preserve orientation, as objects' pieces stay in the same order. Reflection does not preserve orientation.

Ghella [55]3 years ago

5 0

Answer:

hm................................. I'll I'll and answer in. a minute I gotta do sjm rq

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SCORPION-xisa [38]

Expression A decays at a rate of 5% every three months, while Expression B grows at a rate of 12% every four months and Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

<h3>What is an Expression ?</h3>

It is a mathematical statement tat consists of variables , constants and mathematical operators.

It is given that

The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.

The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.

$\rm Expression\; A = 624(0.95)^{4t}\\\\Expression \; B = 725(1.12)^{3t}$

From observing both the expression the initial value is when t = 0

when t = 0,

A = 624

B = 725

and so Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every four months and Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

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2 years ago

The Coast Starlight Amtrak train runs from Seattle to Los Angeles. The mean travel time from one stop to the next on the Coast S

Goshia [24]

Solution :

a).

Given :

R = 0.636, $S_x = 99$ , $S_y=113, M_x=108, M_y=129$

Here R = correlation between the two variables

$S_x , S_y$ = sample standard deviations of the distance and travel time between the two train stops, respectively.

$M_x, M_y$ = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, $b_1$ $=R \times \left(\frac{S_y}{S_x}\right)$

$=0.636 \times \left(\frac{113}{99}\right)$

= 0.726

Therefore, the slope of the regression line $b_1$ is 0.726

The equation of the regression line is given by :

$\overline {y} = b_0+b_1 \overline x$

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line $b_0$ is given by :

$b_0=M_y-(b_1 \times M_x)$

= 129 - (0.726 x 108)

= 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b). $\text{ The slope of the line predicts that it will require 0.726 minutes}$ for each additional mile travelled.

The intercept of the line, $b_0$ = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because it seems we have travelled zero distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). $R^2=0.404$