Given the following information about the arithmetic sequence an, find a17.a3=13a13=43
Answers
Given:
The third term of an arithmetic progression is,
\(a_3=13\)The thirteenth term of the arithmetic progression is,
\(a_{13}=43\)The objective is to find the 17th term of the sequence.
Explanation:
The general formula for the nth term of an arithmetic sequence is,
\(a_n=a+(n-1)d\text{ . . . . . . (1)}\)The expression for the third term can be written as,
\(\begin{gathered} a_3=a+(3-1)d \\ 13=a+2d\text{ . . . . (2)} \end{gathered}\)Similarly, the expression for the thirteenth term can be written as,
\(\begin{gathered} a_{13}=a+(13-1)d \\ 43=a+12d \\ a=43-12d\text{ . . . . . .(3)} \end{gathered}\)To find d:
Now, substitute equation (3) in equation (2).
\(\begin{gathered} 13=(43-12d)+2d \\ 13-43=-10d \\ -30=10d \\ d=\frac{30}{10} \\ d=3 \end{gathered}\)To find a :
Now, substitute the value of d in equation (3).
\(\begin{gathered} a=43-12(3) \\ a=43-36 \\ a=7 \end{gathered}\)Thus, the value of a is 7 and the value of d is 3.
To find a17:
Now, the 17th term can be calculated from equation (1) as,
\(a_{17}=7+(17-1)3\)On further solving the above equation,
\(\begin{gathered} a_{17}=7+16(3) \\ =7+48 \\ =55 \end{gathered}\)Hence, the value of a17 of the arithmetic progression is 55.value of a17 of thear
Related Questions
Shade the plane that contains the given points.
Answers
Answer:
the bottom
Step-by-step explanation:
ehg are located on the bottom
Name the coordinates of M(-5, 8) under a translation along the vector < 3, -2 >.
Answers
If your base pay is 10000 your commission rate is 40% you sell 15 cars and you earn 40000 how much does each car cost
Answers
Answer: $4,000
Step-by-step explanation:
If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.
Since the commission rate is 40%, we can set up the equation:
40% x Total Sales = Commission Earned
We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:
40% x Total Sales = Commission Earned
40% x (15 x Price per Car) = $30,000
6 x Price per Car = $30,000
Price per Car = $5,000
However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:
Commission per Car = 40% x Price per Car
Commission per Car = 40% x $5,000
Commission per Car = $2,000
Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:
Amount earned per Car = Total Earnings / Number of Cars Sold
Amount earned per Car = $40,000 / 15
Amount earned per Car = $4,000
Julian belongs to a club that is marching in a parade. Each member of the club needs to wear one of the hats listed in the table below.
PARADE HATS
Straw Hat
25 red
20 white
40 blue
Cowboy Hat
30 red
25 white
10 blue
Julian chooses the first hat at random from all the hats. What is the probability the hat Julian chooses is blue? Show your work or explain your answer.
Answers
The probability Julian chooses a blue hat is 1/3.
What is the probability Julian chooses a blue hat?Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.
Total hat is:
= 25+20+40+30+25+1
= 150.
There are a total of 150 hats to choose from.
The number of blue hats to choose from is:
= 40 + 10
= 50.
The probability that Julian chooses a blue hat is:
= 50/150
= 1/3
= 0.33 or 33.33%.
Read more about probability
brainly.com/question/24756209
#SPJ1
Which is the graph of the inequality?
5y+x>−10
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
Answers
We can simplify the inequality to:
y > (-1/5)*x - 2
From that, we conclude that the correct option is the last one.
Which is the graph of the given inequality?
Here we have the inequality:
5y + x > -10
If we isolate y, we get:
y > (-10 - x)/5
y > (-1/5)*x - 2
Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.
From that we conclude that the correct option is the last one:
"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."
If you want to learn more about inequalities:
https://brainly.com/question/18881247
#SPJ1
Solve the system
x-y+z=-2
4x-y+2z=-3
2x-3y+2z=-7
Answers
z = 22
y = 11
I will mark you brainiest!
What is the length of LJ?
A) 23.0
B) 17.0
C) 4.7
D) 3.5
Answers
The the length of LJ is approximately 3.5.OptionD) is correct.
How to find the length of LJ?To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.
Let's denote the length of JL as x. Then, we can set up the following proportion:
sin(23°) / LJ = sin(89°) / KL
where KL is given as 9.
We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):
0.3919 / LJ = 0.0175 / 9
Multiplying both sides by x and then dividing both sides by 0.0175, we get:
LJ = 0.3919*9/ 0.0175
x ≈ 3.5
Therefore, the length of LJ is approximately 3.5.OptionD) is correct.
To know more about triangle visit:
brainly.com/question/2773823
#SPJ1
The graph shows China’s workforce from 2000 to 2019. A graph titled Percentage of Workers in Economic Sectors in China from 2000 to 2010 has year on the x-axis and percentage of workers on the y-axis, from 0 to 60 in increments of 10. Agriculture starts at 50 percent in 2000 and then decreases gradually to 37 percent in 2010. Industry starts at 23 percent and then slowly increases to 30 percent. Services starts at 29 percent and then slowly increases to 35 percent. Based on this graph, globalization has affected China’s workforce by creating a shift toward specialization in agriculture and away from services. services and away from agriculture. industry and away from services. agriculture, services, and industry.
Answers
Based on the graph, globalization affected China's workforce by creating a shift toward specialization in: B. services and away from agriculture.
What is globalization?Globalization is a strategic process that involves the integration of various markets across the world, in order to enhance and foster the continuous buying and selling of different goods and services between them.
This ultimately implies that, globalization helps in the creation of new forms of the following systems:
TransportationCommunicationTechnologyAgricultureBased on the given graph, we can logically deduce that globalization affected China's workforce by creating a shift toward specialization in services (increased from 29% to 35%) and away from agriculture (decreased from 50% to 37%).
Read more on globalization here: brainly.com/question/23711616
#SPJ1
Answer:
B. services away from agriculture
Step-by-step explanation:
5. Crackers were on sale 2
for $5.50 I bought three
packs. How much did I
spend?
Answers
Answer:
8.25
Step-by-step explanation:
Find the ratio
2 : 5.50
1 : 2.75
3 : 8.25
Hope it helps
Write the DECIMAL and FRACTION for ALL THE SHADED SQUARES
Answers
Answer:
56/100=0.56
Step-by-step explanation:
Total box=100
shaded=56
Robert is 40 years older than Brittany. the sum of their ages is 82. find their ages.
Answers
Answer:
brittany is 42
Step-by-step explanation:
if he is 40 years older than her and the sum of there ages is 82
82-40 = 42
1. Jon waits on tables and is paid $6.75an hour. In a 40-hour period, he earned $310.50 in tips. What were his total earnings?
Answers
Answer:
$617.25
Step-by-step explanation:
$617.25 Because, $310.50(tips) + $306.75(hourly wage)=$617.25
Answer:$580.50
Step-by-step explanation:
:)
One quarter has a mass of 5.67 grams. Which is the mass of 50 quarters?
Answers
The mass of 50 quarters is 283.5 grams.
A quarter could be a unit of currency utilized in a few nations, including the United States and Canada.
Mass could be a fundamental physical quantity that measures the sum of matter in an object. It is as a rule measured in kilograms (kg) or grams (g).
In the given question,
One quarter has a mass of \(5.67\) grams.
Mass of 50 quarters =?
To find out the mass of 50 quarters we have to multiply by the mass of one quarter.
Mass of 50 Quarter = \(5.67\) ×\(50\)
Mass of 50 Quarter = \(283.5 grams\)
Therefore, the mass of 50 quarters is 283.5 grams.
To learn more about mass,
https://brainly.com/question/28477696
Can someone please help me with this? Thank you. No links!
Answers
Answer: 2(mJKL)=mJL
Step-by-step explanation: The arc angle is double the inscribed angle
hello?! i need help what is the value of my dads duck farm?
Answers
Answer:
It’s worth a pair of cozy slippers with a nice warm bowl of milk
Step-by-step explanation:
A 2-yard roll of waxed paper coats $4.02. What is the price per foot
Answers
Answer: $0.67.
Step-by-step explanation:
To find the price per foot of the waxed paper, we need to convert the price from yards to feet and then divide the total cost by the length in feet.
Given:
Length of waxed paper roll = 2 yards
Cost of waxed paper roll = $4.02
1 yard is equal to 3 feet. Therefore, the length of the waxed paper roll in feet is:
Length in feet = 2 yards * 3 feet/yard = 6 feet
To find the price per foot, we divide the total cost by the length in feet:
Price per foot = Cost / Length in feet
Price per foot = $4.02 / 6 feet
Dividing gives us:
Price per foot = $0.67 per foot
Therefore, the price per foot of the waxed paper is $0.67.
1. Pool Dimensions. The area of a rectangular
swimming pool is 80 yd?. The length is 1 yd longer
than three times the width. Find the dimensions of
the swimming pool.
Answers
Answer: I think the length is 60.25 yd and the width is 19.75 yd
Step-by-step explanation: I formed a equation using the information that has been given.
Width : X
length : 1 + 3x
equation : (1 + 3x) + x = 80
Then, I added the like pairs ( 3x+x ). After, I subtracted 1 from 80 and got 79. Then I divided 79 and 4 (79/4) to get 19.75, which is my x value. later, I substituted the x value to the equation and received my answer.
Question 2
A laboratory did 36 blood tests on Monday, 43 on Tuesday,
29 on Wednesday, and 48 on Thursday. What is the mean
(average) number of blood tests the lab did each day?
answer choices :
o 45
o 42
o 39
0 33
Answers
Answer:
The answer is 39.
Step-by-step explanation:
The average is the total amount of blood tests divided by the number of days.
Total: 36 + 43 + 29 + 48 = 156 blood tests / 4 days = 39 blood tests per day.
Colin got 16 out of 80 correct in his test.
What fraction of the marks did he get wrong?
Give your answer in its simplest form.
Answers
Answer:4/5
Step-by-step explanation:
=80 out of 80 - 16 out of 80
=64 out of 80
Answer:
4/5
Step-by-step explanation:
substract the number of questions he got correctly from the total number of the questions to yield 80-16=64
then set the fraction as number of incorrect questions as the numerator and the total number of questions as the denominator
64/60=4/5
hope anyone help me please
Answers
9514 1404 393
Answer:
a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22
b) 30
c) 6
d) yes; no
Step-by-step explanation:
a) The values are read from the graph.
__
b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest
__
c) -2 -(-8) = -2 +8 = 6 . . . positive difference
(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)
__
d) -2 + 5 < 5 . . . . true
-2 + 5 < -2 . . . . false
Can someone please help me?
Answers
9514 1404 393
Answer:
x = 87°vertical anglesStep-by-step explanation:
The marked angles share a vertex and are formed from opposite rays. They do not share a side, so are not adjacent angles. The angles are vertical angles.
As such, they are congruent, so x = 87°.
can somebody please help me i’ll gift you 40 points
Answers
Answer:
B and D
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
she got 35 is positive 35
she bought something for 15 and something for 7 is negative 15 and 7
she got 10 is positive 10
+35 + (-15) + (-7) + 10
35-15-7+10
Prove the Converse of the Pythagorean Theorem
In this activity, you will prove and apply the converse of the Pythagorean theorem. Recall that the
converse states that if the square of the length of the longest side of a triangle is equal to the sum of
the squares of the other two sides, then the triangle is a right triangle.
Open the GeoGebra activity to complete each step below. For help, watch these short videos about
using GeoGebra to measure and create points, lines, and anglese.
Question 1
Part A
Draw AABC with vertices at A(1,6), B(1, 1) and C(5,1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E
Paste a picture of your drawing in the answer box.
= 90°, and EF
BC.
B I U X² X2 15px
AVA
E E g = = 三 四 V 田
=
Answers
The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.
To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.
AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5
BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4
AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)
Now, let's check if AB^2 + BC^2 = AC^2:
AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41
AC^2 = (2sqrt(10))^2 = 4(10) = 40
Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.
For more such questions on Pythagorean theorem:
https://brainly.com/question/28981380
#SPJ8
Blake measures the lengths, in inches, of 10 insects. He records the lengths of the insects on this line plot. He adds the lengths of the 3 longest insects.
Answers
Answer: 5 inches
Step-by-step explanation:
The x's denote the insects measured so the longest insects would be of lengths:
1³/₄ inch, 1³/₄ inch and 1¹/₂ inch.
Adding them together would require converting them to improper fractions first:
7/4, 7/4, 3/2
Pick a denominator that is both denominators' lowest common multiple = 4
Adding them:
Divide the LCM by the denominator of the fraction and multiply the result by the numerator:
= (7 + 7 + 6) / 4
= 20/4
= 5 inches
How do I solve this??
Answers
The length of leg is equal to 100 based on the length of hypotenuse and angle.
The length of leg will be calculated using Pythagoras theorem as the stated triangle is right angled triangle. Based on the theorem, se have side A is hypotenuse. So, sin theta = perpendicular/hypotenuse, where theta will be 90 degree and perpendicular is leg. Let us represent the leg as x.
sin 90 = x/ A
Keep the value of sin 90, which is 1
1 = x/100
Rearrange the equation in terms of x along with performing multiplication
x = 100
Hence, the length of leg is 100.
Learn more about right angled triangle -
https://brainly.com/question/64787
#SPJ1
\(\int\limits^{i/2}_i {e^{z/2}} \, dx\)
Answers
Ans: (i/2)xe^z/2 - ixe^z/2= -(i/2)xe^z/2
![[tex]\int\limits^{i/2}_i {e^{z/2}} \, dx[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Ffz4INfd5rhjDvAlU4FuQ8JDFmSkCWpm.png)
Answer this please I’ll give brainalist + points, please help!
Answers
Answer:
The answer is C because the largest mode is the longest set with the biggest numbers
Step-by-step explanation:
A total of 5000 tickets were sold for a raffle. the prizes are $1000, $500, $200, and $100. what price should be charged so there is a 60% profit per ticket?
Answers
Answer: $0.576
Step-by-step explanation:
The total amount in prizes is $1800.
For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).
Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)
HELP IM IN K12 AND THERS MORE OF THESE
Answers
Use differences to find a pattern in the sequence.
3,8,15,28,51,88,143
Assuming that the pattern continues, the eighth term should be
Answers
Answer:
220
Step-by-step explanation:
You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.
First differencesSubtracting each term from the next, we find the sequence of first differences to be ...
5, 7, 13, 23, 37, 55
Second differencesThe first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.
The second differences are the differences of the sequence of first differences. They are ...
2, 6, 10, 14, 18
Third differencesThe differences of the terms of the 2nd-difference sequence are constant: 4.
4, 4, 4, 4, 4
Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.
Next termSince we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.
next 2nd difference = 18 +4 = 22
next 1st difference = 55 +22 = 77
next sequence term = 143 +77 = 220
The eighth term should be 220.
__
Additional comment
The n-th term is ...
f(n) = 2/3n^3 -3n^2 +28/3n -4
