Condense the right side a single sine expression:
sin(6x) - cos(6x) = R sin(6x - t)
Expanding the right side gives
sin(6x) - cos(6x) = R sin(6x) cos(t) - R cos(6x) sin(t)
Then we have
R cos(t) = 1
R sin(t) = 1
Solve for R and t:
(R cos(t))² + (R sin(t))² = 1² + 1²
R² = 2
R = √2
and
(R sin(t))/(R cos(t)) = 1/1
tan(t) = 1
t = arctan(1) = π/4
So we rewrite the equation as
√2 sin(6x - π/4) = √2
Solve for x :
sin(6x - π/4) = 1
6x - π/4 = arcsin(1) + 2nπ
(where n is any integer)
6x - π/4 = π/2 + 2nπ
6x = 3π/4 + 2nπ
x = π/8 + nπ/3
A smart watch was marked 150 and is sold at 120. Find discount percentage
Step-by-step explanation:
100 % = 150
1% = 100%/100 = 150/100 = 1.5
the discount was 150 - 120 = 30.
how many percent are in 30 ? that is our discount preventative.
30/1.5 = 20
so, the watch was sold with 20% discount.
x+y=3
2x-y=0
substituition method
Answer:
(1, 2 )
Step-by-step explanation:
x + y = 3 (subtract x from both sides )
y = 3 - x → (1)
2x - y = 0 → (2)
Substitute y = 3 - x into (2)
2x - (3 - x) = 0
2x - 3 + x = 0
3x - 3 = 0 ( add 3 to both sides )
3x = 3 ( divide both sides by 3 )
x = 1
Substitute x = 1 into (1)
y = 3 - 1 = 2
solution is (1, 2 )
Johnny ate seven apples, his bus comes around 3 in the morning, the neighbors dog took a dump on the ground weighing 2.67 kilograms. Whats the mass of the sun??
Answer:
mass if the sun is 123
Step-by-step explanation:
I saw the dog take a dump
(-1, 5) (3,y) m=5 whats the value of my and whats the slope <3
Answer:
slope: 5
y = 25
Step-by-step explanation:
slope is m, and m = 5, so slope is 5.
y-5=5(x+1)...........set up point slope form
y-5=5x+5............distribute 5
y=5x+10..............add 5 to both sides
y=5(3)+10............plug in 3
y=25.....................simplify
Step-by-step explanation:
I am not sure you posted the question correctly.
m is the slope already. this comes from the point slope form
y - y1 = m(x - x1)
where x1, y1 are the coordinates of a point on the line.
so, the slope is 5 (and cannot be <3).
so, using the first point we get
y - 5 = 5(x - -1) = 5(x + 1) = 5x + 5
therefore
y = 5x + 10
for (3, y) we put 3 in as x
y = 5×3 + 10 = 15 + 10 = 25
it is (3, 25) for m = 5.
Write the equation of a horizontal line going through the point (8, -1)
Answer:
y =-1
Step-by-step explanation:
An easy way to answer any type of these questions is looking at the part where it said "Write the equation of a horizontal line", if this is the case you have to look at the 2nd point given to you which is -1 and simply make y = to that. Having y = -1 covers every possible x value which is why it is valid.
15
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What value of p makes the equation true?
–3p +1/8 = -1/4
p=
Reset
Next
Answer:
[tex]p=\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]-3p+\frac{1}{8}=-\frac{1}{4}[/tex]
Subtract [tex]\frac{1}{8}[/tex] from both sides:
[tex]-3p=-\frac{1}{4}-\frac{1}{8}[/tex]
Multiply [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{2}[/tex] and simplify:
[tex]-3p=-\frac{3}{8}[/tex]
Divide both sides by -3:
[tex]p=\frac{3}{24}[/tex]
Simplify:
[tex]p=\frac{1}{8}[/tex]
Alex paid $9 to park her car for 2 hours. Write an equation that shows the relationship between p, the numbers of hours parked, and c, the cost in dollars.
Answer:
Step-by-step explanation:
Parking charge for 2 hours = $ 9
Parking charge for 1 hour = 9/2 = $ 4.50
c = 4.50*p
c = 4.5p
Trevor has a collection of 600 dinosaur trading cards. If he has 60 pages in an album, how many cards can Trevor put on each page?
1
4
10
4
Answer:
10
Step-by-step explanation:
600 divided by 60 is 10
What function represents the next graph?
[tex](x {}^{2} - 4) {}^{2} [/tex]
Brainliest me please please
What is an equation of the line that passes through the points (2, -7)(2,−7) and (2, -2)(2,−2)
Answer:
X = 2
Step-by-step explanation:
Slope: (- 7 - -2)/(2 - 2) = -5/0 = 0
The line is vertical (undefined
4. Jenny sells two types of lanyards, solid color or
striped. She charges more for striped lanyards than
for solid color lanyards. The amount of money, in
dollars, that she collects from selling x lanyards of
one type and y lanyards of the other type can be
modeled by the expression 3x + 5y.
What does the variable y represent in this
situation?
A. The number of solid color lanyards sold.
B. The number of striped lanyards sold.
C. The selling price of one solid color lanyard.
OD. The selling price of one striped lanyard.
Answer:
The selling price of one striped lanyard
The price of the trail mix at the health food store is $7.50 per pound at this rate what is total cost of 8 ounces bags of trail mix
Answer:
Below
Step-by-step explanation:
1 pound = 16 ounces
Therefore if you're looking for 8 ounces, divide $7.50 in half.
You get $3.75
Answer:
At this rate, the total cost of 8 ounce bag of trail mix would be $3.75.
Step-by-step explanation:
So first I found that for 1 LB (pound), there is 16 ounces so 8 oz is half of 16. If we know that, we have to divide 7.5 by 2 to get 3.75.
A boat is carrying containers that weigh 2000 pounds each.
Use this information to fill in the table. Then plot the ordered pairs given by the table.
2 Weight?
4. Weight?
9. Weight?
Answer:
Write seven and twelve hundredths in standard form.
Step-by-step explanat
plsss help me again:((((
#carry on learning
there are 50 students in a class and 30 of these students passed their social studies test. what percentage of these students passed their test.
Answer: 60 %
Step-by-step explanation:
Percentage of students passed the test = (number of students who passed the test / total number of students) x 100
= 30 / 50 x 100 % = 60 %
I need some help please
The length is 5 units.
PLEASE HELP!!
100 POINTS
5^a = 2^b = 10, what is a^-1 +b^-1
Answer:
1.
Step-by-step explanation:
5^a = 10
a log 5 = log 10
a log 5 = 1
a = 1 /log 5
a^-1 = log 5
In the same way:
b = 1 / log 2
b^-1 = log 2,
So a^1 + b^-1 = log5 + log 2 = log (2*5)
= log 10
= 1.
Which linear equation represents a line with a slope of -7 and a y-intercept of 12
Answer:
Answer → y = -7x + 12
Step-by-step explanation:
General equation of a line:
[tex] \hookrightarrow \: { \tt{y = mx + c}} \\ [/tex]
m is the slopec is the y interceptFrom the question;
m is -7
c is 12
[tex]{ \tt{y = - 7x + 12}}[/tex]
Someone plz help me :(
Answer:
should be 7 let me know if i'm wrong
ASP please
What is the slope of the line on the graph
Answer: 6
Step-by-step explanation:
Let's look at two points on this line (1, 5), and (0, -1)
Using the slope formula ([tex]\frac{y_2-y_1}{x_2-x_1}[/tex])
[tex]\frac{((5) - (-1))}{(1)-(0)}[/tex]
[tex]\frac{6}{1}[/tex]
Hope it helps :)
Answer:
Well you could count and use the Rise/Run method, or you could use the Slope formula (x2 - x1) / (y2 - y1)
From point (0, -1) to point (1, 6) would look like this
(1 - 0) / (6 + 1) = 1/7, so your slope is 1/7
Since you already have you y-intercept (where x is 0), your whole equation would be this:
y = 1/7x - 1
Find the ending balance if $500 was deposited at 5% annual interest compounded quarterly for 3 years.
Answer:
$575 ,
Step-by-step explanation:
5% of $500 is only $25
multiply that by 3YRS due to annual interest it would amount too
an addition $75 dollars so the answer is $575
The table below shows a proportional relationship. True or False?
Answer:
True
Step-by-step explanation:
translate figure:RIGHT 2 DOWN 1
note:only use four point when drawing the translation
Answer:
Your answer is in the image linked below.
Step-by-step explanation:
When the shape is moved right 2, down 1, you should have this translation, hope this helps.
The temperature of one furnace is 1,200°C and cools at a rate of 15°C per minute. The temperature of another furnace is 900°C and is heated at a rate of 5°C per minute. After how many minutes will the furnaces be the same temperature? Write the answer as a whole number or decimal. __ minute(s)
Step-by-step explanation:
how many cups of water do you need to fill fill one jar
a transversal shown below.
True
or
False
Answer:
true
Step-by-step explanation:
because i just finished doing this in geometry
guys pa help po thank you
Answer: Should be 90
Step-by-step explanation:
Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.
(correct the error below!)
first term =4
common difference =8
tenth term =4 +10(8) = 84
Answer: The tenth term is 76
=======================================================
Explanation:
We use this arithmetic sequence formula to get the nth term
[tex]a_n = a_1 + d(n-1)[/tex]
Plug in [tex]a_1 = 4, \ d = 8, \ n = 10[/tex] and you should get the following:
[tex]a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\[/tex]
The tenth term is 76
---------
We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.
[tex]\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}[/tex]
---------
In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in [tex]a_n = a_1 + d(n-1)[/tex] which shifts everything one spot to the left.
help me on this please
Answer:
1: AOB is 180 degrees 2: AOF + FOG = 180 degrees 3: 60 + 90 + 30 + 180 4: x = 15
Step-by-step explanation:
x = 15
Add up 5x - 15 + 90 + 2x = 180 degrees
FOG = 90 degrees (right angle)
Combine like terms to get 7x + 75 = 180
subtract 75 on both sides to get 7x = 105
Divide both sides by 7 to isolate x to get x = 15
Substitute 15 for every x you see so 5(15) - 15 and 2(15)
5(15) - 15 = 60
2(15) = 30
Hope this works!!! :)
helppp plz is fue today
Answer:
Step-by-step explanation:
A CHOOSE A
Answer:
A
Step-by-step explanation:
sorry:c
One of my grandmother's most vivid memories of Camp 3 was a riot between the Nisei and the Kibei. The Nisei and Kibei were Japanese Americans born in the United States, but they weren't all educated in America. The Nisei went to school in the United States, whereas the Kibei were mainly educated in Japan. Then they returned to the United States. In general, the Kibei opposed those Nisei who joined the U.S. Army to fight.
Answer:
Step-by-step explanation:
what is the question?