Given:
The sum of the first 15 terms of an arithmetic sequence is 480.
To find:
The 8th term of the sequence.
Solution:
We have,
[tex]S_{15}=480[/tex]
We know that, the nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
Putting n=8, we get the 8th term of the sequence.
[tex]a_8=a+(8-1)d[/tex]
[tex]a_8=a+7d[/tex]
The sum of first n terms is
[tex]S_{n}=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where, a is the first term and d is the common difference.
[tex]S_{15}=\dfrac{15}{2}[2a+(15-1)d][/tex]
[tex]480=\dfrac{15}{2}[2a+14d][/tex]
[tex]480=\dfrac{15}{2}[2(a+7d)][/tex]
[tex]480=15(a+7d)[/tex]
Divide both sides by 15.
[tex]\dfrac{480}{15}=a+7d[/tex]
[tex]32=a+7d[/tex]
[tex]32=a_8[/tex]
Therefore, the 8th term of the arithmetic sequence is 32.
Answer:
32
Step-by-step explanation:
32
Please help. Due today
Answer:
im sorry
Step-by-step explanation:
i dont know how
i am also doin triangles tho
Each bracelet needs 1 and ¾ feet of yarn. How many complete bracelets can be made from a piece of yar that is 9 and ½ feet long?
Answer:
56
Step-by-step explanation
3/4 x 1/2 =3/12 this aint right btw
The triangle shown below are similar. Solve for x. 
Answer:
x=16
Step-by-step explanation:
27/45=(2x+7)/(4x+1)
cross multiply
27(4x+1)=45(2x+7)
108x+27=90x+315
108x-90x=315-27
18x=288
x=288/18
x=16
Looking at the image, The triangle shown below are similar. The value for x is 16.
What is the triangle about?Note that in the triangle given, the shapes are similar. Therefore:
27/45 = 2x + 7/ 4x + 1
3/5 = 2x + 7/ 4x + 1
So:
3 (4x + 1) = 5 (2x + 7)
12x + 3 = 10x + 35
12x - 10x = 35-3
2x = 32
x = 32/ 2
x = 16
Therefore, the value of x is 16.
Learn more about triangle from
https://brainly.com/question/17335144
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PLZ HELP MEEEEEEEEEEEEEEEEEE
Please help!!!
Each circles radius diameter circumference and formula used needs to be found!!!! I need help urgently and I’ll give brainliest!
Answer:
Check bolded below
Step-by-step explanation:
1)radius = 10 in (given), diameter = 2*radius = 2(10 in) = 20 in
formula for circumference => 2πr => 2π(10)
circumference = 20π in
2)diameter = 12 ft (given), radius = 1/2*diameter = 1/2(12 ft) = 6 ft
formula for circumference => 2πr => 2π(6)
circumference = 12π ft
3)radius = 3 m (given), diameter = 2*radius = 2(3 m) = 6 m
formula for circumference => 2πr => 2π(3)
circumference = 6π m
4)diameter = 18 cm (given), radius = 1/2*diameter = 1/2(18 cm) = 9 cm
formula for circumference => 2πr => 2π(9)
circumference = 18π cm
1.
radius = 10 in
diameter = 10 × 2 = 20 in
formula = π × d
circumference = π × 20 = 62.83 in
2.
radius = 12 ÷ 2 = 6 ft
diameter = 12 ft
formula = π × d
circumference = π × 12 = 37.70 ft
3.
radius = 3 m
diameter = 3 × 2 = 6 m
formula = π × d
circumference = π × 6 = 18.85 m
4.
radius = 18 ÷ 2 = 9 cm
diameter = 18 cm
formula = π × d
circumference = π × 18 = 56.55 cm
I’m confused on my math someone help
Okay so we’re trying to find out if they are true or false I guess so the first question is HELP MEEE
Answer:
False, True, True are thr answers
On Robert’s shelf are 6 mystery books, 2 science fiction books, 3 adventure books, & 4 history books. Robert will randomly choose 1 book to read, not put it back and then grab another book to read. What is the probability that he chooses an adventure book and then a history book?
Answer:
2/35
Step-by-step explanation:
total of 15 books
P(Adv,Hist) = 3/15 · 4/14 = 1/5 · 2/7 = 2/35
Joel Bradley purchased a new cooler for his florist shop for $4,500. He wants to finance it with an installment loan from his bank. If he wants to finance only $2,800, what percent of the total cost should his down payment be?
Answer:
62.22% I think.
Step-by-step explanation:
Have a good day.
What is the missing value of 5x-2y=30 (8,)
Answer:
In this equation, we can start by understanding that "x" has a value of 8, as given in the ordered pair. When multiplied by 5, this leads to "40 - 2y = 30". Next, we can subtract 40 from both sides of the equation. This leads us to a value of "-2y = -10". The next step would be to divide both sides by -2 as a way of isolating "y", which leads us to a final value of "y = 5". The final ordered pair would be (8,5).
What is the slope of the line l ? (-2,9) (6,1)
In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?In ΔFGH, the measure of ∠H=90°, GF = 37, HG = 12, and FH = 35. What ratio represents the sine of ∠F?
[tex]tan \: j \: = \frac{opp}{adj} [/tex]
[tex]tan \: j \: = \frac{11}{60} [/tex]
[tex]sin \: f = \frac{opp}{hyp} [/tex]
[tex]sin \: f = \frac{12}{37} [/tex]
help me please how do i do this
Answer:
41 degrees
Step-by-step explanation:
In a parallelogram, opposite angles are equal, so:
[tex]3x+11=5x-9\\-2x = -20\\x=10\\\\E = 3x + 11\\E = 3 * 10 + 11\\E = 30 + 11\\E = 41[/tex]
What is the area on this?
Area of the rectangle is length x width = 5 x 10 = 50 sq. cm
Area of the triangle is 1/2 x base x height, base = 17-10 = 7, height = 5
Area = 1/2 x 7 x 5 = 17.5 sq.cm
Total area = 50 + 17.5 = 67.5 sq. cm.
3. Sheila is creating a graph of the outside temperatures, t, at her house for math class. Which
would be a reasonable range for Sheila's graph if she collected data throughout the year?
A.-98°F
B.-125°F
C. 100°F
D. 25°F
Answer:
Step-by-step explanation:
Answer:
29°F < t < 94°F
Step-by-step explanation:
HELP IF I DONT PASS THIS IS STAY IN THe GRADE I AM IN PLZZ
Answer:
2 1/9
Step-by-step explanation:
decimal 2.111111111111111111111111111
just cut 2 in half then 2/9 in half
Answer:
2 1/9
Step-by-step explanation:
turn the mixed number into an irregular fraction then divide.
38/9 ÷ 2
38/9 * 1/2 = 38/18 because you multiply by the reciprocal
2 1/9 is the answer
45 points fellas cmon
Answer:
4x + 4y
Step-by-step explanation:
Hopefully this is the correct answer and hope this helps
Answer:
YES YOU ARE CORRECT!!!
Because....
4x+2y=20
2x+y=10
4x2=8 2x y(1)=2
8+2=10
Step-by-step explanation:
hope that helped you! :)
An electric fan connected to a 220 V source. the current is 4A what is the power of the fan
Answer:
Voltage V=220V
Current I=4A
Now, rate at which the electrical energy transformed
P=V×I
P=220×4
P=880 watts
Now, the energy is transformed in 2 min
P=tE
E=P×t
E=880×120
E=105600J
Hence, the energy transformed is 105600 J
HELP DUE IN 10 MINS!
Attached is the Question.
Answer:
∠N ≅ ∠J - givenLN ≅ LJ - given∠L ≅ ∠L - reflexive propertyPostulate: ASA
Congruency Statement: ΔJML ≅ ΔNKL
Factoriza el siguiente trinomio 6x^2 – 26x – 200
Answer:
2 (x + 4)(3x - 25)
Step-by-step explanation:
[tex]6 {x}^{2} - 26x - 200[/tex]
[tex]3 {x}^{2} - 13x - 100[/tex]
[tex]2 (x + 4)(3x - 25)[/tex]
Tia cut 4-meter 8-cenimeter wire into 10 equal pieces. Martha cut a 540-centimeter wire into 9 equal pieces. How much longer is one of Marta's wires than one of Tia's?
Answer: 19.2 cm
Step-by-step explanation:
A meter is equal to 100 centimetres so the total length of Tia's wire in centimetres is:
= 4.08 * 100
= 408 cm
She cuts this into 10 equal pieces:
= 408 / 10
= 40.8 cm
Martha cuts her 540 cm wire into 9 pieces. Each piece is:
= 540 / 9
= 60 cm each
The difference is:
= 60 - 40.8
= 19.2 cm
Solve the equation by substitution y=x+1 and 2y=3x
Step-by-step explanation:
suby=x+1 in 2y=3x
2(x+1)=3x
2x+2=3x
2=3x-2x
2=x
descubre el número que falta
What is 2p²+6p-72 factored?
Answer:
(x+12)(x-6)
Step-by-step explanation:
when factoring an equation like this you want to find two numbers that multiply to make the third digit, and add to make the middle one.
12-6=6
12x-6=-72
26
24
10
HELP PLSSsSs
Answer:
what is the question? all I see is a drawing w labels
calculate 41% 0f 51kg
Answer:
20.91kg
Step-by-step explanation:
Amount = .41 * 51 = 20.91kg
i need someone thats good at math pls help me i dont have the dot plot but i need the mena answer the median sentence and median answer pls
Answer:
to work out the median you put the numbers in ascending order and then cross one number from the left and right side one at a time until you reach the middle, if you have lots of numbers then add one to the number of items in the data and divide by two.Evaluate (4-^2)^2. Help me now now
Answer:
aksksjjsjsjjsjsjejjssnehjejeejejkejjs
If it takes Charlie 45 minutes walking at 2.5 km/hr to get to the chocolate factory and it takes Willy Wonka 15 minutes walking at 3.5 km/hr then who lives closer and by how far?
Answer:
Willy Wonka
Step-by-step explanation:
Given data
it takes Charlie 45 minutes walking at 2.5 km/hr
speed = distance /time
distance= speed*time
distance= 2.5*45
distance= 112.5 km
it takes Willy Wonka 15 minutes walking at 3.5 km/hr
distance= speed*time
distance= 3.5*15
distance= 52.5 km
Hence Willy Wonka stays closer
The label on a 1.25 pound bag of wildflower seeds states that it will cover an area of 280 square feet. Based on this information, what is the number of square feet that 1 pound of wildflower seeds will cover?
Answer:
1 pound of sunflower seeds will cover about 187 square feet of land
Step-by-step explanation:
To solve this problem, we will have to assume that there is a linear relationship between the net weight of the wildflower seeds and the area of land it can cover when planted.
Based on this assumption, we can find the number of square feet that a 1 pound bag will cover, by setting up a simple relationship as shown below:
if 1.5 pounds covers 280 square feet
1 pound will cover x square feet.
by cross multiplying, we have that
x = (280 X 1) / 1.5 = 186.66 square feet.
Therefore, 1 pound of sunflower seeds will cover about 187 square feet of land
Solve for x
[tex]\frac{x}{7}[/tex] − [tex]\frac{x}{9}[/tex] =−1
Answer:
[tex]x = \frac{ - 63}{2} \: or \: - 31.5[/tex]
Step-by-step explanation:
[tex] \frac{x}{7} - \frac{x}{9} = - 1[/tex]
Lets take the L.C.M of 7 & 9.
L.C.M of 7 & 9 = 63
[tex] = > \frac{9x - 7x}{63} = - 1[/tex]
[tex] = > \frac{2x}{ 63} = - 1[/tex]
Now lets multiply 63 on both the sides.
[tex] = > \frac{2x}{ 63} \times 63 = (- 1) \times 63[/tex]
[tex] = > 2x = - 63[/tex]
Now lets divide both the sides by 2.
[tex] = > \frac{2x}{2} = \frac{ - 63}{2} [/tex]
[tex] = > x = \frac{ - 63}{2} = - 31.5[/tex]