Answer:
「0.8 0 -2
0 1.2 3
0 0 1 」
Step-by-step explanation:
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 = 4Translation 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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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?
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
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
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?
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?
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?
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.
Answer:
96.93
Step-by-step explanation:
89,75+
Please help, this chapter was on derivatives...
(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
Answer:
use photomath and if that dont work use m a t h w a y
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
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 $___?
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.
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)
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
Answer:
Equal???
Step-by-step explanation:
Answer this please thanks
Answer:
No.
Step-by-step explanation:
Because the line doesn't pass through the origin (0,0).
Please help me thank you.
Answer:
-4+2
Step-by-step explanation:
Describe your understanding of finding percents of a whole.
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?
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
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?
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 ?
Answer:
its 3 percent
Step-by-step explanation:
12.009 write in word form
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
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
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?
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?
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.
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.
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
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.
Answer:
1,800,000
Step-by-step explanation:
9146 * 174
Estimate: 9000 * 200 = 1,800,000