The reduced form of Sin⁴(6x) in terms of the first power of Cosine is; 1 - 1/4(Cos (24x)).
Reducing Trigonometric identitiesIt follows from the task content that;
Trigonometric identity, Sin⁴(6x) = 1 - Cos⁴(6x)Hence, from product identity;
Cos⁴(6x) = (1/2) (Cos²(12x)Upon further use of the product identity;
(1/2) (Cos²(12x) = 1/4(Cos (24x)).On this note, it follows that use of the power reducing formula on the function sin⁴(6x) is;
= 1 - 1/4(Cos (24x)).Read more on power reducing formula;
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Find the solution to each problem. Show all of your work.
1. Haley and her family went on a vacation. To get to the beach, they drove for 3 hours and 25 minutes. When they headed back home, it took them 230 minutes to get home. Did it take longer to get to the beach or to get home from the beach?
2. Yesterday, it rained for 335 minutes. The day before that it rained for 5 hours and 10 minutes. On which day did it rain for a longer period of time?
3. Wendy’s family lost the power at their house when there was a bad storm. The powerwas out for 3 days! Wendy’s neighbors lost power for 68 hours. Whose power was outfor a greater amount of time?
4. Paul finished his 800 meter race in 2 minutes and 2 seconds. Jeff finished in 121 seconds. Who finished first? (Remember, the person with the lowest time finishes first.)
5. Write your own question that involves time conversion and ask someone to solve it. Make sure you solve it too so you know if they get the correct answer!
1. 1 hour = 60 minutes
We convert 3 hours and 25 minutes to minute : 3 x 60 + 25 = 205 (minutes). Since 205 < 230, it took longer to get home than getting to the beach.
2. (Same convertion)
5 hours and 10 minutes = 5 x 60 + 10 = 310 (minutes)
So, the last day rained longer than the day before it.
3. 1 day = 24 hours.
We convert 3 days to hours : 3 x 24 = 72 (hours)
Since 72 > 68, Wendy's family lost their power longer than their neighbors.
4. 1 minute = 60 seconds
Convert 2 minutes and 2 seconds to seconds : 2 x 60 + 2 = 122 (seconds)
Since 122 > 121, it means Paul took longer to finish his race, which mean Jeff finished first (Rip Paul)
5.
Question : Bob bought 2 pizzas for him and his friend, Kevin. They both ate 1 pizza. Bob finished his pizza in 6 minutes and 45 seconds. Kevin finished his pizza in 400 seconds. Who finished first?
Solution : Convert 6 minutes and 45 seconds to seconds : 6 x 60 + 45 = 405 (seconds)
Since 405 > 400, Bob took longer to finish his pizza -> Kevin finished first.
The circumference of a circle is 19π m. What is the area, in square meters? Express your answer in terms of pi
Find the greatest common factor of 12x3y2 and 24xy3.
24xyz
O 12x3y3
O 12
O 12xyz
Answer:
b: 12
Step-by-step explanation:
24xy3 doesnt have x3 in it
So it cant be regarded as a factor
Brainliest please
PLEASE HELP ME WITH THIS!! IM STRUGGLING
Answer:
A: (0,-12)
Step-by-step explanation:
This chart is really helpful!
You just have to flip the coordinates and make the x value negative.
Have a great day!
Whats the answer please help!
Please help me thank you!
Answer:17.2414 percent!
Step-by-step explanation: I've done this before hope this helps
Two similar triangles are shown on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 2, negative 1, vertex B on ordered pair 0, 0, and vertex C on ordered pair 1, negative 3. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair negative 4, 2 , vertex B prime on ordered pair 0, 0 and vertex C prime on ordered pair 2, 6. Which set of transformations has been performed on triangle ABC to form triangle A'B'C'? Dilation by a scale factor of 4 followed by reflection about the x-axis Dilation by a scale factor of 2 followed by reflection about the x-axis Dilation by a scale factor of 4 followed by reflection about the y-axis Dilation by a scale factor of 2 followed by reflection about the y-axis\
The set of transformation that has been performed on triangle ABC
to form triangle A'B'C' is " Dilation by a scale factor of 2 followed by
reflection about the x-axis " ⇒ 2nd answer
Step-by-step explanation:
Lets revise some important rules
The corresponding sides of similar triangles have constant ratio
Dilation makes a triangle and its image similar
Reflection about x-axis change the sign of the y-coordinate of a point after reflected about the x-axis
Δ ABC and Δ A'B'C are similar after set of transformations has been
performed on Δ ABC to form Δ A'B'C'
∵ The vertices of triangle ABC are:
A = (-2 , -1) , B = (0 , 0) , C = (1 , -3)
∵ The vertices of triangle A'B'C' are:
A' = (-4 , 2) , B' = (0 , 0) , C' = (2 , 6)
∵ x-coordinate of point A = -2 and x-coordinate of point A' = -4
∵ y-coordinate of point A = -1 and y-coordinate of point A' = 2
∵ x-coordinate of point B = 0 and x-coordinate of point B' = 0
∵ y-coordinate of point B = 0 and y-coordinate of point B' = 0
∵ x-coordinate of point C = 1 and x-coordinate of point C' = 2
∵ y-coordinate of point C = -3 and y-coordinate of point C' = 6
∵ Each coordinate of the vertices A , B , C is multiplied by 2 to give
the coordinates of the of the vertices A' , B' , C'
∴ Δ ABC is dilated by scale factor of 2
∵ The signs of y-coordinates of the vertices A , B , C is opposite to
the signs of y-coordinates of the of the vertices A' , B' , C'
∴ Δ ABC is reflected about the x-axis
The set of transformation that has been performed on triangle ABC
to form triangle A'B'C' is " Dilation by a scale factor of 2 followed by
reflection about the x-axis "
A bakery sells 6 lemon poppy muffins for every 42 bran muffins sold. Which table represents the relationship between lemon poppy and bran muffins?
The answer is B.
Answer:
B
Step-by-step explanation:
The table shows the ratio 1:7 pretty well
Julia is going to invest $860 and leave it in an account for 8 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Julia to end up with $1,190?
Answer:
$860(860×12×8×1190÷100)
81872_860
=$81012
Which of the following best describes AB in the regular pyramid below? A B A. Altitude B. Slant height C. Face D. Edge
Answer:
the correct answer is
option b
slant height
Step-by-step explanation:
slant height of a pyramid is defined as a distance measure along a lateral face from a base of a triangle because hypotenuse of a right angle triangle is half on the base
distance from the center of the base to the point where the slant height segment
The line AB in the pyramid is the slant height of the pyramid.
What is a pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
Given is a pyramid with AB labelled at one of its face, we need to determine the name for AB,
So, here AB is the slant height.
Slant height of a pyramid is defined as a distance measure along a lateral face from a base of a triangle because hypotenuse of a right angle triangle is half on the base distance from the center of the base to the point where the slant height segment.
Hence, the line AB in the pyramid is the slant height of the pyramid.
Learn more about pyramids, click;
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Look at this rectangle. Find the value of t.
Answer:
t=8
Step-by-step explanation:
t=8 is your answer
If you need solution do let me know in the comments
Mrs. Girard bought a 2-ounce tube of eye cream. Each night, she carefully applies 0.1
ounces.
Write an equation that shows how the number of ounces of eye cream remaining, y, depend
on the number of nights Mrs. Girard uses it, X.
y =
If right angle ABC C is a right angle and sin a = sinB what is m a
Answer: As a result, the angle between m and n is 45 degrees.
Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c.
Which equation can be used to determine c, the unknown concentration?
30c + 10(0.2) = 40(0.32)
StartFraction 3 Over 4 EndFraction left-parenthesis c right parenthesis plus left-parenthesis StartFraction 1 Over 4 EndFraction left-parenthesis 0.2 right-parenthesis right-parenthesis equals 40 times 0.32.(c) + StartFraction 1 Over 4 EndFraction cup.(0.2) = 40(0.32)
(c)( (0.2)) = 40(0.32)
30(c)(10(0.2)) = 40(0.32)
Answer:
Solution 1 : 10mL with 20% acid
Solution 2 : 30mL with x% acid
Solution 3 : 40mL with 32% acid
Step-by-step explanation:
Since solution 1 + solution 2 = solution 3, let us substitute the given values we have:
10(0.2) + 30(x) = 40(0.32)
2 + 30x = 12.8
To solve for the unknown concentration x, we subtract 2 from both sides:
2 + 30x - 2 = 12.8 - 2
30x = 10.8
Dividing both sides by 30:
30x/30 = 10.8/30
x = 0.36
Therefore the unknown solution is 36% acid.
Answer:
The first option (30c + 10(0.2) = 40(0.32)
can somebody help me? anybody know the answer
Answer:
25 = c
Step-by-step explanation:
You had a good start on filling in the values in the Pythagorean Theorem. The work needed to be finished.
[tex]a^2 +b^2 = c^2\\\\20^2 +15^2=c^2\\\\400+225=c^2\\\\625=c^2\\\\\sqrt{625}=\sqrt{c^2}\\\\\boxed{25=c}[/tex]
At the Kansas City Airport, a group of pilots for Skyways and Yellow Jet airlines were asked whether their flights were flying east or west. The two-way table shows their answers.
Flight Directions
A 4-column table with 3 rows. The first column has no label with entries skyways, yellow jet, total. The second column is labeled East with entries 30, 65, 65. The third column is labeled West with entries 33, 34, 67. The fourth column is labeled total with entries 63, 69, 132.
Which joint frequency has the most flights?
The joint frequency with the most flights in the given two-way frequency table is: yellow jet, going east.
What is a Two-way Frequency Table?A two-way frequency table is a table that displays joint frequency of two categorical variables using rows and columns to represent each.
Looking at the two-way table given, yellow jet, going east is the cell with the most flight. So, the joint frequency with the most flights is: yellow jet, going east.
Learn more about two-way frequency table on:
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Answer:
c
Step-by-step explanation:
Calculate the distance between the points G= -2.2) and C = (5, -1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
Distance: 0
Answer:
Step-by-step explanation:
What do I do with my hands
Answer:
eat them
Step-by-step explanation:
expand and simplify (2x + 1) (x + 3)
A betta fish tank is in the shape of a cube. The volume of the fish tank is 216
cubic inches. What is the edge length, in inches, of the fish tank?
Answer:
6in³
Step-by-step explanation:
get the volume by the formula: L x W x H
L = Length
W = Width
H = Height
there are 3 units required to know for getting the volume, if that's true, then, do the inverse operation of finding the volume. That can be done by using the formula:
a= edge
Solving for a
a=V⅓=216⅓=6
So each of the Cube shaped Fish Tank is 6in³
to find out if the answer is right or wrong we have to do
6x6=36
36x6=216
So the answer is right!
Anyone know where I can find the answers to this packet
Answer:
Step-by-step explanation:
I'll give you a guide — use the formula
[tex]y = mx + b[/tex]
For Question 1, [tex]y = \frac{2}{3}x + 2[/tex]
[tex]y = mx + b[/tex]
So, m = [tex]\frac{2}{3}[/tex] and b = 2
For question 3,
[tex]y = mx + b[/tex]
if m = [tex]\frac{1}{3}[/tex] and b = 3
[tex]y = \frac{1}{3}x + 3[/tex]
For the graphs, You label the center as 0, and go up/down 1 right to left and up down
You use every number on the x-axis (horizontal left-right line) and put it in your equation (e.g. [tex]y = \frac{2}{3}x + 2[/tex]) to get the value for the y-axis.
Which problem solving strategy would be best to solve this problem?
Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn? Ples help me some one
Answer:
$62.50
Step-by-step explanation:
what is 37/16 as a decimal rounded to the nearest tenth
Answer:
the answer is 2
Step-by-step explanation:
Use the point–slope formula to write an equation of the line that passes through −4,15 and has a slope of m = − 4. Write the answer in slope–intercept form (if possible).
The equation of the line is_____
Let's split this problem into several steps:
Let's first put it into the point-slope form:
⇒ Point-slope form ⇒ [tex](y-y0)=m(x-x0)[/tex]
(x0,y0) --> any point on the linem --> slopeConsider the information given:
(x0,y0) --> (-4,15)m --> -4Let's plug the numbers in:
[tex]y - 15=-4(x+4)\\[/tex]
To put this format into slope-intercept form, we will solve for y:
⇒as in, move everything else to one side and y by itself on the other
[tex]y - 15=-4(x+4)\\y-15=-4x-16\\y = -4x-16+15\\y=-4x-1[/tex]
Thus the equation of the line is --> [tex]y = -4x - 1[/tex]
Hope that helps!
1. What is the domain and range for the following function and its inverse? f(x) = x² +3
Answer:
Step-by-step explanation:
x^2 + 3
The domain is All Real x and the range is f(x) ≥ 3.
Find its inverse:
y = x^2 + 3
x^2 = y - 3
x = √(y - 3)
So f-1(x) = √(x - 3)
The domain is x ≥ 3 and range is f(x) ≥ 0.
Which answer choice correctly represents an algebraic expression for the sum of 15 and a number?
Let the number be x
Sum of 15 and the numberSum of 15 and xWe use addiition sign
x+15The expression is x+15
A recipe calls for 1/2 cup of sugar for every 3/4 cup of flour. How much sugar is required for every cup of flour?
Answer:
2/3
Step-by-step explanation:
cup of sugar used for 3/4 cup of flour = 1/2
cup of sugar used for 1 cup of flour = 1/2*4/3 =2/3
After participating in a track meet, athletes were given the option to drink a sports drink or water. The results showed that 85 athletes chose a sports drink, 62 athletes chose water, and 14 athletes chose not to drink anything. Of those that chose water or a sports drink, 27 athletes choose to drink both.
How many athletes did not choose water?
1.) 99
2.) 85
3.) 72
4.) 58
Of the 103 people enrolled in mathematics class, 91% are present How many are present? 114 113 94 93
Answer:
Just find the 91% of 103
103 * 91% = 103 * 0.91 = 93.73
About 94 are present from the 103 people
Step-by-step explanation:
hope this helps
pls mark brainliest
(7x - 1) + (-x - 2) in simplest terms
Answer:
6x-3
Step-by-step explanation: