Answer:
the nth term of a sequence is usually denoted by the symbole an . a1 =2 the second term is a2=6 and so....
A term is multiplied by 3 to get the next term . if you know the formula for the nth term of a sequence of n , then you can find any term .
formula : an =a1 + ( n - 1 ) d
hope its helpful . Good luck ;)
Performance task trigonometric identities
x = 0
Simplify — x/ 2
x ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))-((ta•(n2))•—) = 0 2
xtan2 ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))
Equivalent Fraction:
Rewrite the whole as a fraction using 2 as the denominator :
-2c3sx2ot + c3sx + cxot2 (-2c3sx2ot + c3sx + cxot2) • 2 -2c3sx2ot + c3sx + cxot2 = 0
The equations are solved below using trigonometric identities.
What are trigonometric identities?Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]\frac{sin(x)}{1-cos(x)} -cot(x) = cosec(x) \\\\LHS= \\\\=\frac{sin(x)}{1-cos(x)} -cot(x) \\\\=\frac{sin(x)}{1-cos(x)} -\frac{cos(x)}{sin(x)}\\ \\\frac{sin^{2}(x) - (1-cos(x))cos(x) }{sin(x)(1-cos(x))}\\\\=\frac{sin^{2}(x)-cos(x) +cos^{2}(x) }{sin(x)(1-cos(x))}\\\\=\frac{1-cos(x)}{sin(x)(1-cos(x))}\\ \\=\frac{1}{sin(x)} \\\\=cosec(x)\\\\RHS=\\\\=cosec(x)[/tex]
[tex]cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} = tan^{2}(\frac{x}{2})\\\\LHS= \\\\= cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} \\\\=( cosec(x) - cot(x) )^{2} \\\\=(\frac{1-cos(x)}{sin(x)}) ^{2}\\\\=(\frac{(1-cos(x))(1+cos(x))}{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x)^{2} }{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x) }{1+cos(x)}) ^{2}\\\\=(\frac{2sin(x/2)cos(x/2) }{1+2cos^{2}(x/2)-1}) ^{2}\\\\= (\frac{sin(x/2)cos(x/2) }{cos^{2}(x/2)}) ^{2}\\\\= tan^{2}\frac{x}{2}\\\\RHS = \\\\=tan^{2}\frac{x}{2}[/tex]
Learn more about trigonometric identities here
https://brainly.com/question/14746686
#SPJ2
Write the slope-intercept form of the line with a slope of 2 and a
y
-intercept of -4. Include your work in your final answer. Type your answer in the box provided to submit your solution.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept. y=2x-4 is the slope-intercept form of the line with a slope of 2 and a y-intercept of -4.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope intercept form of a line is y=mx+b,
where m is slope and b is the y intercept.
slope-intercept form of the line with a slope of 2 and a y intercept of -4.
m=2 and b=-4
Substitute the m and b value in slope intercept form.
y=2x-4.
Hence y=2x-4 is the slope-intercept form of the line with a slope of 2 and a y-intercept of -4.
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ2
Yesterday the children at Deion’s preschool chose to pursue various play with stuffed animals 15, read books 2, paint 1, play math game 1, Based on past data, if 24 preschoolers are at school today, how many should you expect to read books?
Based on past data, we can expect that 2 preschoolers will be reading books today out of the total of 24 preschoolers present. we can apply this ratio to the total number of preschoolers present today.
To determine the expected number of preschoolers who should be reading books today, we can use the ratio of the number of preschoolers who chose to read books yesterday to the total number of preschoolers present yesterday.
Yesterday, there were 24 preschoolers present, and 2 of them chose to read books. Therefore, the ratio of preschoolers reading books to the total number of preschoolers yesterday is:
2 / 24
To find the expected number of preschoolers reading books today, we can multiply this ratio by the total number of preschoolers present today (which is 24):
(2 / 24) * 24
Simplifying this expression, we find:
2
For more such questions on past data
https://brainly.com/question/30915447
#SPJ8
The function y=5x+10 represents the total cost y of a group of x members to go paintballing.
What do the independent and dependent variables represent?
Answer:
The independent variable (x) represents the members to go paintballing.
The dependent variable (y) represents the total cost.
Step-by-step explanation:
The y is always dependent on the x. The number of people attending affects the total cost of the trip. The more people attend, the more it costs.
Please someone answer fast
The Maya______predicted the end of the world on December 21,2012
Answer: Calendar
Step-by-step explanation:
Basically, the Mayan Calendar was going through cycles, and December 21 2012 was the end of a cycle. It was close to the 13th Bak’tun, but instead of moving towards the next Bak’tun and so on, the Mayan calendar actually reset itself back to 0. But the Mayans did not predict the end of the world, we decided to interpret the calendar that way.
21 p?=u² + 2as
u= 12 a = -3
s= 18
(a) Work out a value of v.
Answer:
6 or -6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
[tex]v^2 = 12^2 + 2(-3)(18)[/tex] [tex]v^2 = 144 + (-6)(18)[/tex] [tex]v^2 = 144- 108[/tex] [tex]v^2 = 36[/tex]Step 2: Take square root of both sides.
[tex]\sqrt{v^2} =[/tex] ± [tex]\sqrt{36}[/tex] [tex]v =[/tex] ± [tex]\sqrt{36}[/tex] [tex]v = 6[/tex] or [tex]-6[/tex]Therefore, the answer is 6 or -6.
May I please receive help?
Hi there!
We know that:
m∠WXZ = 112°
Since m∠1 is 48° greater than m∠2, we can write an expression:
m∠2 = x°
m∠1 = (x + 48)°
Since both angles sum up to m∠WXZ, we can write this as:
112° = x° + (x + 48)°
Solve for x:
112 = 2x + 48
64 = 2x
x = 32°
answer these two pls
1. Ivy wants to earn at least $800 this week in commission. What is the minimum amount she needs to sell in order to earn $800 if she earns a 6.25% commission on everything she sells? Round your answer to the nearest dollar if necessary.
2.Tim’s savings account pays a simple annual interest rate of 3.5%. Suppose he deposits $5,500 in the account and makes no additional deposits or withdrawals for 5 years. What will the total value of the account be after 5 years?
Answer:
1.) $12,800: 800÷0.0625=12,800
2.)$6,311.37: 5500×(0.035(5))
Consider the following data set:
0, 10, 12, 3, 13, 7, 2, 5
Find the upper quartile.
Answer:
11
Step-by-step explanation:
The upper quartile Q3 is the median of the upper half of the data.
The ratio of the number of cups of yellow paint to the number of cups of blue paint that Greg mixed to make a shade of green paint is 2:1.
Part A: Write a sentence to describe the number of cups of yellow paint that Greg mixed with each cup of blue paint. (4 points)
Part B: How many cups of blue paint should Greg add to each cup of yellow paint to make the shade of green? Explain your reasoning. (4 points)
Part C: If Greg purchased 6 cups of yellow paint for $54, what is the unit price per cup of yellow paint? (2 points)
(GIVING 15 points)
Answer:
Part A: A ratio of 2:1 means that he uses 2 cups of yellow paint for each cup of blue paint.
-------------------------------------------------------------------------------------------------
Part B: The ratio of yellow to blue is 2:1 = 2/1. So, if for 2 yellow is 1 blue, then for 1 yellow is x:
2/1 = 1/x
x = (1*1) / 2
x = 1/2
For each cup of yellow paint, Greg should add 1/2 cup of blue paint.
-------------------------------------------------------------------------------------------------
Part C: 6 cups cost $54, then 1 cup cost:
54 / 6 = 9
The price per cup of yellow paint is $9.
A. The number of cups of yellow paint that Greg mixed with each cup of blue paint is (1/2) cup.
B. Greg should add 2 cups of blue paint to each cup of yellow paint.
C. The unit price of per cup of yellow paint is 9 dollars.
What is the ratio?The ratio compares similar quantities in simplest form.
Given that the ratio of the number of cups of yellow paint to the no. of cups of blue paint to make a green shade paint is 2:1.
This can also be written as
(yellow paint/blue paint) = (2/1).
∴ 1 cup of yellow paint and 2 cups of blue paint is required to make a green shade of paint.
A. The number of cups of yellow paint that Greg mixed with each cup of blue paint is (1/2) cup.
B. Greg should add 2 cups of blue paint to each cup of yellow paint.
C. The unit price of per cup of yellow paint is (54/6) = 9 dollars.
learn more about ratio here :
https://brainly.com/question/13419413
#SPJ2
Indira is climbing and starts at 182.5 meters above sea level each hour she descends 36.5 meters the table shows the function relating in inDara‘s height to the number of hours she mountain climbing
The function relating in indira‘s height to the number of hours she mountain climbing is: y = -36.5x + 182.5
A linear equation is given by:
y = mx + b;
where m is the slope(rate of change), b is the initial value of y, y is the dependent variable and x is the independent variable.
Let x represent the number of hours spent climbing the mountain and y represent the distance above see level.
She starts at 182.5 meters above sea level, hence; b = 182.5 meters
She descends 36.5 meters each hour, hence m = -36.5 meter per hour
Therefore the equation becomes:
y = -36.5x + 182.5
Find out more at: https://brainly.com/question/19586594
Simplify 4(12x−14y+3)
Answer:
48x - 56y +12
Step-by-step explanation:
Use the distributive property to simplify
(multiply each number in the parenthesis by 4)
4(12x−14y+3)
(4 * 12x)+ (4 * -14y) + (4*3)
48x - 56y +12
hope this helps :)
please crown me brainliest!!!
solve the following equation
3z + 14 = 5z - 18
solve the following equation
3z + 14 = 5z - 18
Solution:-3z + 14 = 5z - 183z = 5z - 18 - 143z - 5z = - 18 - 14-2z = -32z = -32/-2z = 16Answer:-[tex] \\ \tt \: Thus, \: { \boxed{ \tt{z = 16}}}[/tex]
what is 3 to the power of -4 as a fraction?
I need it ASAP.
The sum of three numbers is 95. The second number is 7 more than the first. The third number is 4 times the second. What are the numbers?
Answer:
I think the answer is 2,660 i am not really sure but that's my answer sorry if i got it wrong
WHICH NUMBER LINE MODEL REPRESENTS THE EXPRESSION: 2.5 + 4.5?
A)
B)
C)
The playing area of a board game is a rectangle with
the length of 14 inches and a width of 20 inches.
What is the area of the board game?
Three increased by twice a number is at least -7. Write the inequality and then try to solve it!
Answer:
Inequality: 3+2n≥-7
Solve for n: n≥-5
Step-by-step explanation:
3+2n≥-7
2n≥-10
n≥-5
Which of the following is equivalent to 2/5 x 3/8?
A. 3/8 / 2/5
B. 2/5 / 3/8
C. 2/5 / 8/3
D. 5/2 / 8/3
1. MATH CONNECTION: If a person were walking at the average speed of 2.5 mph from District 12 to District 13 and it takes a week to get there, how fast is the hovercraft traveling from District 12 to 13, which makes it there in 45 minutes?
Answer:
560 mph
Step-by-step explanation:
2.5(24 * 7) = 420 miles
420 miles = 45h
h = 420miles / ( 45 * 60)
420/0.75 = 560 mph
15. Matthew and some friends are going to a concert. They hire a car service for $60 to
drive them to a restaurant for dinner and then to the concert. They divide the $75 cost
of the dinner equally. However, since Matthew's dad provided concert tickets for the
group, the friends agree that Matthew doesn't have to help pay for the car service.
The friends divide this cost equally among themselves. If each friend spends a total of
$30, how many friends went to the concert with Matthew?
A4
B5
C6
D7
Answer:
7
Step-by-step explanation:
i got it correct on my test
PLEASE HELP i have no idea how to solve this L teacher for being rude when i asked for help
Answer:
I assume your teacher is asking you to prove how lines a and b are parallel. The given is the example: Line l and m are parallel because angles 1 and 2 are congruent. So I assume in the statement box you would write it like the given example and in the reason you would explain that statement. Hope this helps
x + 5 ≤ 13
PLEASE help!!!!
Answer:
x ≤ 8
Step-by-step explanation:
x + 5 ≤ 13
x ≤ 13 - 5
x ≤ 8
Feel free to mark this as brainliest! :D
Answer:
x ≤ 8
Step-by-step explanation:
x + 5 ≤ 13 (subtract 5 from both sides)
x ≤ 8
Write a formula that shows the dependent of the mass of a piece of cork on its volume note the density of the cork is 0.18 g/cm^3. Then use the formula to find the answer.
The volume of a piece of cork with a mass of 64.8g
Answer:
43.2 grams
Step-by-step explanation:
We will use density formula to solve our given problem:
he mass of a piece of cork with a volume of 240 cm³ is 43.2grams
The formula for calculating the density of a substance with mass "m" and volume "v" is expressed as:
m is the mass of the substance
v is the volume of the substance
Given the following parameters
Density = 0.18g/cm³
Volume = 240cm³
Substitute the parameters into the formula to get the mass:
Given are the points A(0,1) and B(4,-7). Find an equation (the point-slope form is perfectly acceptable) of the perpendicular bisector of line segment AB
Answer:
y + 3 = 1/2(x - 2)Step-by-step explanation:
Find the slope of the given line using the coordinates of A and B.
The slope:
m = (-7 - 1)/4 = -2Find the midpoint of segment AB:
x = (0 + 4)/2 = 2y = (1 - 7)/2 = -3The perpendicular line has a slope of 1/2 ( opposite-reciprocal of -2) and passes through the point (2, -3).
The equation of this line is:
y - (-3) - 1/2(x - 2)y + 3 = 1/2(x - 2)Slope-intercept form:
y = 1/2x - 4You start at (-2, -1). You move up 6 units. Where do you end?
Answer:
(-2,5)
Step-by-step explanation:
Since you're only moving up on the graph then only the Y axis will change and -1+6 is 5.
Answer:
(-2,4)
Step-by-step explanation:
When you move UP it changes the Y axis so you just add whatever number to there. But when you move down it subtracts the number of units your moving.
A. 0.15
B. an equal sign
C. a multiplication sign
D. a percent sign
Answer:
C.
Step-by-step explanation:
Sian invests £7000 for 3 years at 4% per annum compound interest. Find the compound interest earned in the 3 years.
Answer:
840.
Step-by-step explanation:
4%of £7000=£280
£280 x 3(years)=£840
Please help. Geometry!
Help how to do it because this is hard