Answer:
The answer is below
Step-by-step explanation:
Show that f(x) f(y) = f(x+y)
From trigonometric:
sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy - cosxsiny
cos(x + y) = cosxcosy - sinxsiny
cos(x - y) = cosxcosy + sinxsiny
[tex]f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\[/tex]
[tex]f(x+y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\Therefore\ f(x)f(y)=f(x+y)[/tex]
Cameron will spin a spinner that is divided into four sections. He will then flip two coins. How many outcomes are possible?
A. 2
B. 4
C. 8
D. 16
Answer:
16 outcomes
Step-by-step explanation:
4 outcomes for spinner
2 outcomes for 1st coin
2 outcomes for 2nd coin
4 x 2 x 2 = 16
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime's account after his deposit on Thursday?
Answer:C
Step-by-step explanation:
37 +17.42-12.60-9.62+62.29 = 94.49
28.3m by 21.5m, what is the area
Probably of Carl solving the 10 problems if there's 20 to study and he knows 15 and ten of the 20 are on the test.
Answer:
1/3
Step-by-step explanation:
Probability of solving ten problems by Carl
Given
Total number of problems = 20
Number of problems studied by Carl = 15
Number of problems out of the 20 set of problem coming in test is 10
Case I - All ten problems come from the set of known 15 question
10/15 * 10/20 = 1/3
PLS HELP QUICK !!!!!
what is the area of this figure?
Answer:
400 in²
Step-by-step explanation:
Consider the figure as a triangle on top of a parallelogram. The tic marks on the sides mean that the lengths with the same tic marks are equal.
The area of the parallelogram is 20×16=320
The area of the triangle is (20×8)/2= 80
Add the two areas: 320 + 80 = 400
Jon has to pay $9.00 admission for the skating rink and $2 per hour to
rent roller blades. How many hours can he skate for $19?*
3
5
06
Answer:
The answer is 5 hours
Step-by-step explanation:
A sales representative for a hardware company receives $8,000 per year plus a 6% commission on total sales. During one year the sales representative's sales totaled $320,000. Find the representatives total earnings for this year
Answer:p5
65=8poi
Step-by-step explanation:
The following are Noah's scores on his first ten exams: 89, 90, 79, 92, 80, 94, 86, 91, 82, 89. Calculate the sum of Noah's points
(Only enter the numeric answer - NO WORDS!)
I
Answer:
872
Step-by-step explanation:
89+90+79+92+80+94+86+91+82+89
Darwin's best time for running 5000 metres is 16 minutes. He wants to run it in 15 minutes and 30 seconds.
What percentage reduction in time is this?
Please include explanation!
Answer:
3 percent
Step-by-step explanation:
convert to seconds
960 seconds to 930 seconds
30 seconds ÷ 960=3 per cent
The percentage reduction in time is required.
The percentage reduction is [tex]3.125\%[/tex]
The initial value of time = 16 minutes
Final value of time = 15 minutes and 30 seconds = 15.5 minutes
Percentage reduction is given by
[tex]\dfrac{\text{Old value}-\text{New value}}{\text{Old value}}\times 100\\ =\dfrac{16-15.5}{16}\times100=3.125\%[/tex]
The percentage reduction is [tex]3.125\%[/tex]
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3800 people attended a basketball game. 1026 of the people attending supported the
home team, while 2774 supported the visiting team. What percentage of people
attending supported the home team?
Answer: 27%
Explantion:
1026/3800 =x/100
cross mulitply and get 102600 then divid both sides by 3800.
Answer:
27
Step-by-step explanation:
r
hi please help i will mark brain list giving all my points
Answer:
B
Step-by-step explanation:
It looks like addition to me.
Answer:
Its B. Addition Property of Equality
Step-by-step explanation:
An arc is 70.7 meters long and is intercepted by a central angle 5pi/4 radians. Find the diameter of the circle
Answer:
36.008 or 36
Step-by-step explanation:
Use the equation for the length of any circular arc
s = r(radians)
s - length of a circular arc
r - radius
radians - radian measure of the central angle
Then, set-up the equation:
s = r(radians)
70.7m = r(5pi/4)
Get variable "r" on one side by multiplying both sides by 4/5pi, which should result in the following:
r = 70.7m x 4/5pi
then solve for r
r = 282.8/5pi = 18.004
The radius is half the diameter therefore just multiply the radius by 2
d = 18.004 x 2
= 36.008 or 36
The diameter of the circle is 36 meters.
What is an arc?The arc is a portion of the circumference of a circle.
We have been given that an arc is 70.7 meters long and is intercepted by a central angle of 5π/4 radians.
We have to determine the diameter of the circle
For the length of the circular arc, use the equation.
⇒ 70.7 m = R(5π/4)
Multiply both sides by 4/5π to get the variable "R" on one side, which should get the following:
⇒ R = 70.7 m × 4/5π
⇒ R = 282.8/5π
∵ π = 3.14
⇒ R = 282.8/5(3.14)
⇒ R = 18.004
Since the radius is equivalent to half the diameter, simply double the radius by 2.
⇒ D = 18.004 × 2
⇒ D = 36.008 ≈ 36
Hence, the diameter of the circle is 36 meters.
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If the mean of 5 numbers is 10 and the mean of other 15 numbers is 20 , what is the combined mean of both 20 numbers
9514 1404 393
Answer:
17.5
Step-by-step explanation:
The sum of the 5 numbers is 5·10 = 50.
The sum of the 15 numbers is 15·20 = 300.
The sum of all 20 numbers is then 50+300 = 350, so their mean is ...
mean = sum/number = 350/20 = 17.5
The combined mean of the 20 numbers is 17.5.
HELP I forgot how to do this (show work please)
The answer is 23[tex]\sqrt{x} \pi[/tex].
Sorry that I didn't explain and made it short my annual examination is going on but I really wanted to help you.
What is an
equation of the line that passes through the points (4,-4) and
(-6,-4)? PLEASE I HAVE TO AWNSER IN 5 minutes
Step-by-step explanation:
[tex]y = - 4[/tex]
[tex]y = - 4[/tex]
Answer:
y=-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-(-4))/(-6-4)=(-4+4)/-10=0/-10=0
slope is 0
y-y1=m(x-x1) where m=slope
y-(-4)=0(x-4)
y+4=0
y=0-4=-4
y=-4
Pedro placed an order with an online nursery for
6 apple trees and 5 azaleas and the order came to
$147. The next order for 3 apple trees and 4 azaleas
came to $96. What was the unit cost for each
apple tree and for each azalea?
Hope this helps! I really need points to ask a question , so I'm just answering people who need help
Solve for the volume of the 3D shape.
27 m3
27
180 m3
180m
360 m3
360 m
Answer:
360 m3
Step-by-step explanation: just multiply 18m times 5m times 4 m then you get your answer :)
hope this helps :D
Answer:
360 m3
Step-by-step explanation:
Make the other guy brainlist cuz he helped me. :p
Help me please :( I’m going to get beat if I don’t do these topics it’s finding the angles measures given two parallel lines
Write log7(2 ⋅ 6) + log73 as a single log. Log Subscript 7 Baseline 11 Log Subscript 7 Baseline 15 Log Subscript 7 Baseline 36
Answer:
C. log7 36....................................
The given logarithmic expressions together can be written as log₇ 36
What is a logarithmic function ?The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.
Formulae for logarithmic function are,
LogAB = LogA + LogB
Logₐaᵇ = b
Given that,
= log₇(2 x 6) + log₇3
= log₇ 36
We have the result
log A + log B = log AB
Here the question is log₇(2 x 6) + log₇3.
Using the property of logarithm we will get,
= log₇(2 x 6) + log₇3
= log₇(2 x 6 x 3)
= log₇ 36
So, log₇(2 x 6) + log₇3 = log₇ 36
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help please with math
Answer:
(2 x a)+(3 x b)+c=total points
Step-by-step explanation:
Select all the numbers that round to 387.4 when rounded to the nearest tenth
The numbers that round to 387.4 when rounded to the nearest tenth are in the following interval.
387.35 <= x < 387.4
How to round the numbers?To round a number to the nearest tenth, we must observe the second decimal digit of the number:
If the second decimal digit is less than five, the first digit remains constant and the other decimal digits are removed, example, 387.34 = 387.3.If the second decimal digit is at least five, one is added to the first digit and the other decimal digits are removed, example, 387.35 = 387.4.More can be learned about rounding at https://brainly.com/question/28128444
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Someone plz help me I will give brainliest
Answer:
Step-by-step explanation:
5. 3/4 +3/4 + 3/4 + 3/4 + 3/4 + 3/4 = (6 x 3)/4 = 18/4 = 4 1/2
6. 16 x 3 x 1/8 = (48x 1)/8 = 48/8 = 6
7. 500 x 2/5 = 500 x 2 x 1/5 = (1000 x 1)/5 = 1000/5 = 200
A fish is swimming at a constant rate toward the ocean floor. The equation
y = -7x - 3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming.
Which statement best describes the depth of the fish, given this equation?
Answer: Y = 21
Step-by-step explanation:
WILL MARK BRAINLEST, 15 POINTS
HURRY FAST
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 80 miles per hour. The westbound train travels at 90 miles per hour. How long will it take for the two trains to be 204 miles apart?
Do not do any rounding.
Answer:
one hour and 12 minutes
Answer:
1 hour and 12 minutes
Step-by-step explanation:
Let's say x = time it takes for the trains to be 204 miles apart.
Speed = Distance/Time,
Time = Distance/Speed,
x = 204/ (80 + 90) = 204/170 = 1 and 1/5 hours or 1 hour and 12 minutes
The height of 5 boys is 5.4 ft, 6.12 ft., 7.02 ft. 4.9 ft, and 6.25 ft. What is the average
height of these 5 boys?
What are the operation to solve the problem?
pls answer
Wll not just this question, but whenever you need to find average, you have to:
Wait, for example let's take ur question:
1st step we will add up all the values aka heights:
5.4+6.12+7.02+4.9+6.25=29.69
And then how many values did you take???
Its, 5 values
1st value= 5.4
2nd value=6.12
aaand so on....
However, then we will have to divide the sum by no.of values
29.69÷5=5.938
Aaand this is your FINAL ANSWER
Done!!!!
Hope I helped you!!!
Step-by-step explanation:
For the average height of fhe boys:
[tex] \frac{5.4ft + 6.12ft + 7.02ft + 4.9ft + 6.25ft}{5} \\ = 5.938 \: ft[/tex]
In solving for the average height, we used addition and division operations.
What is the slope and y intercept?
Answer:
slope: 1/2 Y Intercept: 25 (I'm just guessing by the coordinates (60,25)Step-by-step explanation:
Lets all remember rise over run to figure out slop and at coordinates (60, 25) we see that we go up 1 (rise) and go on the positive side 2 (run)
For the Y intercept (I'm really not sure about this answer) I figured it out by looking at the first point I saw (60, 25)
so I inferred that the y intercept is 25
9*10^7 is how many times as large as 3*10^-2
A right triangle has legs 2m and 3m in length. What is the
length of its hypotenuse?
Answer:
First option) √13 m
Step-by-step explanation:
Using the Pythagorean theorem. 2^2+3^2=c^2
4+9=c^2
13=c^2
c=3.61
3.61 meters
Which terms can be combined in the expression below? Select three options.
PLEASE HELP 50 POINTS
StartFraction 5 over 6 EndFraction a minus 2 b minus 16.3 + StartFraction b over 12 EndFraction + c minus 0.9 b
StartFraction 5 over 6 EndFraction a
–2b
–16.3
StartFraction b over 12 EndFraction
–0.9b
Answer:
This doesnt make sense
Step-by-step explanation:
Juan cuts a piece of rope that is 16 meter long into 2 equal pieces.
What is the length of each shorter piece of rope?
Enter your answer as a fraction in simplest form by filling in the boxes
