Find the 3 ×3 matrix that produces the described composite 2D transformation​ below, using homogeneous coordinates. Translate by ​( −6​, 3​), and then scale the​ x-coordinate by 0.3 and the​ y-coordinate by 1.3.

Answers

Answer 1

Answer:  

               「0.8   0   -2

                    0    1.2   3

                    0     0     1 」

Step-by-step explanation:

Answer 2

The [tex]3\times 3[/tex] matrix will be "[tex]\left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]".

According to the question,

The [tex]3\times 3[/tex] with homogenous coordinates is:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Translation from (0, 0) to (a, b) will be:

[tex]T = \left[\begin{array}{ccc}1&0&a\\0&1&b\\0&0&1\end{array}\right][/tex]

Here,

a = -6b = 4

Translation by (-5,4)

[tex]T = \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]

Now,

Let's find the scaling matrix 5.Scale the x-coordinated by "0.3" and y-coordinates by "1.3".

i.e.,

[tex]S = \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right][/tex]

then,

The [tex]3\times 3[/tex] matrix will be:

→ [tex]A = ST[/tex]

      [tex]= \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right] \ \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]

      [tex]= \left[\begin{array}{ccc}0.3&0&-0.3\times 6\\0&1.3&1.3\times 3\\0&0&1\times 1\end{array}\right][/tex]

      [tex]= \left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]

Thus the above answer is correct.

       

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Related Questions

8. A substance has a half life of 2.347 minutes.
a. If the initial amount of the substance was 110.4 grams, how many half-lives will have passed
before the substance decays to 6.9 grams.
b. What is the total time of the decay?

Answers

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

[tex]A=A_0b^{\frac{t}{c}}[/tex]

Where [tex]A[/tex] is the final population

[tex]A_0[/tex] is the initial population

[tex]b[/tex] is the growth factor

[tex]c[/tex] is the time taken for the growth 'b'

[tex]t[/tex] is the amount of time

Here, we are given that:

[tex]A[/tex] = 6. 9 grams

[tex]A_0[/tex] = 110.4 grams

[tex]b = \dfrac{1}{2}[/tex]

[tex]c = 2.347[/tex] min

To find:

a.) Number of half lives taken for the decay.

b.) Total time in the decay.

Solution:

a.) Number of half lives taken for the decay is nothing but equal to [tex]\frac{t}{c}[/tex].

Putting the values in the formula, we get:

[tex]6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4[/tex]

Therefore, the answer is:

4 half lives have passed.

b.) Total time of decay. We have to find the value of [tex]t[/tex] here.

From answer of part a.):

[tex]\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}[/tex]

Determine the y-intercept for 3x+2y=14​

Answers

Answer:

Using the slope-intercept form, the y-intercept is 7

Step-by-step explanation:

Answer: y=7-3x/2      3x/2 is seen as a fraction

Step-by-step explanation:

Move all the terms that don’t contain y to the right and then solve

hey guys what is this type of equation/ question called 1 < x < 30

Answers

Answer:

2,3,4,5,6,7,8,9,10,...29

Step-by-step explanation:

Which equation represents a line which is parallel to the line 2y-5x=-162y−5x=−16?

Answers

Answer:

Step-by-step explanation:

For two lines to be parallel to each other, they must have the same slope.

The standard form of expressing equation of a line is y = mx+c

m is the slope.

First let us get the slope of the given line

Given the line 2y-5x = -16

Rerwrite in standard form;

2y-5x = -16

2y = 5x-16

Divide through by 2;

2y/2 = 5x/2 -16/2

y = 5x/2 - 8

The slope of the line is 5/2

Since we are not given options, we can as well say that the equation of the line parallel to this line must have a slope of 5/2 no matter the intercept. Example of such line are;

y = 5/2 x + 2

In the figure above, how would you set up your equation?

Answers

Step-by-step explanation:

2×+6 + 5 = X+10

2x -x =10 -11

x= - I

BC = 2(-1) + 6=4

AC = -1+10 = 9

Biologists tagged 134 fish in a lake on January 1. On February 1, they returned and collected a random sample of 56 fish, 14 of
which had been previously tagged. On the basis of this experiment, approximately how many fish does the lake have?

Answers

Answer:

There should be 120 fishes approximately in the lake

Isidro wants to purchase a used scooter that costs $89.75. The sales tax is found by multiplying the price of the scooter by 0.08. Find the ​total amount​ of money Isidro will pay. Round to the nearest cent.

Answers

Answer:

96.93

Step-by-step explanation:

89,75+

Please help, this chapter was on derivatives...

Answers

(3) Differentiating both sides of

[tex]2x^{3/2} + y^{3/2} = 29[/tex]

with respect to x gives

[tex]3x^{1/2} + \dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]

Solve for dy/dx :

[tex]\dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = -3x^{1/2} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{-3x^{1/2}}{\frac32y^{1/2}} = \dfrac{-2x^{1/2}}{y^{1/2}} = -2\sqrt{\dfrac xy}[/tex]

Then the slope of the tangent line to the curve at (1, 9) is

[tex]\dfrac{\mathrm dy}{\mathrm dx} = -2\sqrt{\dfrac19} = -\dfrac23[/tex]

The equation of the tangent line would then be

y - 9 = -2/3 (x - 1)   ==>   y = -2/3 x + 29/3

(4) The slope of the tangent line to

[tex]y=\dfrac{ax+1}{x-2}[/tex]

at a point (x, y) on the curve is

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{a(x-2)-(ax+1)}{(x-2)^2} = -\dfrac{2a+1}{(x-2)^2}[/tex]

When x = -1, we have a slope of 2/3, so

-(2a + 1)/(-1 - 2)² = 2/3

Solve for a :

-(2a + 1)/9 = 2/3

2a + 1 = -18/3 = -6

2a = -7

a = -7/2

help big points, need quickly pls pls pls

Answers

Answer:

use photomath and if that dont work use m a t h w a y

Step-by-step explanation:

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

113

Step-by-step explanation:

Answer:

diameter =6 cm

radius =3cm

shaded area =area of square- area of circle

= a^2 - πr^2

=(6)^2-3.142(3)^2

=36-3.142×9

=36-28.278

=7.622

15% of 24% of $3500 is $___?

Answers

Answer:

126

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

24% of 3500=840

15% of 840=126

Maria needs to be at the airport terminal at 15:20. It will take 2 hours to
drive to the airport from her home, and a further 30 minutes to park and get
to the terminal.
What is the latest time she should leave home?
Give
your answer as a time in the 24-hour clock.

Answers

Answer:

12:50

Step-by-step explanation:

15:20 - 2h= 13:20

13:20-30 min= 12:50

Answer:

12:50

Step-by-step explanation:

If it takes 2 hours to get there, you subtract 2 hours from 15:20 which gives you 13:20. It also says that she needs 30 minutes to park so you subtract that from 13:20 giving you 12:50

Gina bought 4 bags of grapes that weighed 2.29 pounds each. The grapes were priced at $2.50 per pound. The expression below represents the total cost of the bags of grapes Gina bought, in dollars.
(2.29×2.50)×4

Which expression below is also equivalent to the total cost of the grapes?


( 2.29 + 4 ) × 2.50

4 × ( 2.50 + 2.29 )

( 2.29 × 4 ) + 2.50

2.29×(2.50×4)

Answers

Answer:

2.29 × (2.50 × 4) is equivalent.

Step-by-step explanation:

It doesn't matter what order multiplication happens in, it will result in the same answer!

Help anyone 5th grade math

Answers

Answer:

Equal???

Step-by-step explanation:

Answer this please thanks

Answers

Answer:

No.

Step-by-step explanation:

Because the line doesn't pass through the origin (0,0).

Please help me thank you.

Answers

Answer:

-4+2

Step-by-step explanation:

The equation of the line would be: y = 1

Describe your understanding of finding percents of a whole.

Answers

Step-by-step explanation: Write down the whole number amount, for example: 500. Calculate the equation. The result is the decimal equivalent of the percentage. Multiply the decimal equivalent of the percentage by 100; or move the number's decimal point over two places to the right.

Francesca obtains a loan of $18.965.00. The loan has a simple interest rate of 3%. How much interest will Francesca owe at the end of the first year?

Answers

Answer:

$568.95

Step-by-step explanation:

Given parameters:

Value of loan  = $18965

Interest rate  = 3%

Time  = 1year

Unknown:

Interest = ?

Solution:

The interest on a particular amount is given as:

        I  = [tex]\frac{PRT}{100}[/tex]  

I is the interest

P is the principal

R is the rate

T is the time

       I  = [tex]\frac{18965 x 3 x 1}{100}[/tex]   = $568.95

pattern 60 52 44 36​

Answers

Decreasing by 8 each time

The area of the rectangle flower bed shown is
20.4 square meters. How many meters of edging are needed to go around the flower bed?

Answers

Answer:

I think 5.4

Step-by-step explanation:

Take it and divide by the number of sides

The Perimeter of rectangle is 27.4 m

What is Area of rectangle?

The area of rectangle is product of its length to tis width.

So, Area of rectangle = length  x width

Given:

Area of the flower bed = 20.4 square meters.

length = 12 m

As a rectangle, its area be

A = l x w

20.4 = 12 w

w= 20.4/ 12

w= 1.7

Now, Perimeter of rectangle

= 2( l + w)

= 2( 12+ 1.7)

= 27.4 m

Hence, the Perimeter of rectangle is 27.4 m

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Set up a proportion for the problem.

11 is what percent of 33 ?

Answers

Answer:

its 3 percent

Step-by-step explanation:

12.009 write in word form

Answers

twelve and nine thousandths

Choose a system of equations with the same solution as the following system:

6x + 2y = −6
3x − 4y = −18

a) 8x + 4y = −4
17x + 2y = −28

b)12x + 4y = 12
21x + 2y = −36

c) 6x + 8y = −36
15x + 6y = −60

d)6x + y = 15
15x − y = −9

Answers

Answer: A. 8x + 4y = -4

                    17x + 2y = -28

Step-by-step explanation:

Suppose that 2 were subtracted from each of the values in a data set that
originally had a standard deviation of 7.5. What would be the standard
deviation of the resulting data?
A. 2
B. 7.5
C. 9.5
O D. 5.5

Answers

Answer:

Option B. 7.5 is the correct answer

Step-by-step explanation:

Let us define standard deviation first.

Standard deviation is the square root of variance. Standard Deviation tells us that how far are the values in a data set from the mean.

Now, if a constant is subtracted from all values of a dataset, the standard deviation remains the same. Only the origin or mean of the data changes by subtracting a constant from whole data set.

Given that the standard deviation of dataset is 7.5

Subtracting 2 from each value of dataset will not change the standard deviation as 2 is a constant.

Hence,

Option B. 7.5 is the correct answer

Answer:

7.5 it stays the same

Step-by-step explanation:

The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.
a. Find the probability that the truck driver goes more than 650 miles in a day.
b. Find the probability that the truck drivers goes between 400 and 650 miles in a day.
c. At least how many miles does the truck driver travel on the furthest 10% of days?

Answers

Answer:

(A) 0.125 probability

(B) 0.625 probability

(C) 660 miles

Step-by-step explanation:

The distance driven by a truck driver daily, falls between 300miles and 700miles and follows a uniform distribution.

(A) The probability that the truck driver goes more than 650 miles a day is:

[700 - 650] / [700 - 300]  = 50/400  = 0.125

(B) The probability that the truck driver goes between 400 and 650 miles a day is:

[650 - 400] / [700 - 300]  = 250/400  = 0.625

(C) The minimum number of miles the truck driver travels on the furthest 10% of days is given thus:

10% of 400  = 40

Subtract this from the farthest distance;

700miles - 40miles  = 660miles

mrs Moore worked 42 hours and 35 minutes last week. How many hours and minutes did she average in each of the five days?

Answers

Answer:

6.08333333 hours

Step-by-step explanation:

((42 hours) + (35 minutes)) / 7 = 6.08333333 hours

hope this helps LOL :)

Answer:

511 min or 8 hrs and 52 min

Step-by-step explanation:

first you need a common subject so convert 42 hours into min, which is 2,520 then add the 35 which gives you 2,555 total.

then divide by 5 which gives you the adverage of 511 min

convert answer into hours which is about 8 hours and 52 min rounding up

A chess game comes with two kings, two queens, four rooks, four Bishops, four knights, and sixteen pawns (a total of 32 pieces). A game piece is randomly selected, replaced, then another is chosen. Find the probability of selecting a king or queen, then a pawn.

Answers

Answer:

3/32

Step-by-step explanation:

Plz mark as brainliest!!!

Choose True or False for each statement.


Column A

1.

If the distance from 0 to x on a number line is equal to 2, then -2 + X = 0.:

If the distance from 0 to x on a number line is equal to 2, then -2 + X = 0.

2.

If the distance from 0 to x on a number line is less than 2, then -2 + X = is negative.:

If the distance from 0 to x on a number line is less than 2, then -2 + X = is negative.

3.

If the distance from 0 to x on a number line is greater than 2, the -2 + X is positive.:

If the distance from 0 to x on a number line is greater than 2, the -2 + X is positive.

4.

If the distance from 0 to x on a number line is greater than 0, then -2 + X is positive.:

If the distance from 0 to x on a number line is greater than 0, then -2 + X is positive.

Answers

17372!82!. 9hhhhhh nooo

Which is the net force acting on a 1.7-kg object that is accelerating at 5.0 m/s??

A. 8.5 N

B. 2.9 N

C. 0.34 N

D. 3.3 N

Answers

Answer:

A. 8.5 N

Step-by-step explanation: F = 8.5 N

Estimate 9146 x 174 by first rounding each number so that it has only 1 nonzero digit.

Answers

Answer:

1,800,000

Step-by-step explanation:

9146 * 174

Estimate: 9000 * 200 = 1,800,000

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