Answers
Answer:
The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
Step-by-step explanation:
Third term of sequence is 18
Sixth term of sequence is 33
We need to find the explicit equation for the sequence.
The explicit sequence is [tex]a_n=a_1+(n-1)d[/tex]
We need to find a_1 the first term and common difference d
We have a₃=18
We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]
[tex]18=a_1+2d[/tex]
a₆=33
We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]
Now, solving these equation s we can find value of d
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
Subtract both equations
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]
So, we get common difference d = 5
Now finding a_1
Put value of d in equation [tex]18=a_1+2d[/tex]
[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]
So, we get a₁ = 12
Now, the explicit equation is:
[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]
So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
Related Questions
In three days, Karen ate 1/3 of a large bag of chips during
her lunch break. How many
days would it take her to
finish the bag of chips?
Answers
Answer:
Karen asked for the manager
Step-by-step explanation:
Karen asked for the maneger because that is what karens do. you’re lucky that you are not black, becuase she would falsely accuse you of murder after slightly bumping into her on accident.
These box plots show the basketball scores for two teams.
Which statement is the most appropriate comparison of the spreads?
Answers
Answer: The interquartile range (1QR) for the Bulldogs, 20, is less than the IQR for the Wolverines , 30.
Step-by-step explanation:
The table shows the balance of an account each year.
Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account?
Answers
Answer:
+2 each year. 40+(2+y), y being years.
this is part three of four
Answers
Answer:
D. 275
Step-by-step explanation:
400/2... So just do 550/2 and you will get your answer
Help please...........
Answers
Answer: A
Step-by-step explanation:
A
B
C
D
I NEED HELP ASAP
Answers
Answer:
D
Step-by-step explanation:
ΔCBA ≅ Δ BCD
∠A = ∠D = 90°
BC = CB {hypotenuse and reflexive property}
BA = CD
help me out :)) 2(5x-1)+3x !! simplify !!
Answers
Answer:
13x-2
lol :)
hope i could helped:)
Patrycja goes shopping in a supermarket.
Patrycja buys 12 bread rolls.
The bread rolls costs £4.44 altogether.
How much does one bread roll cost?
Answers
Answer:£0.37
Step-by-step explanation:
£4.44/12=£0.37
One less than the square of a number
Answers
Answer:
the number would be the same
Step-by-step explanation:
Melissa and Brian are at the base of a mountain. Melissa hikes to
a location 27 meters above sea level. Brian hikes to a
location 21 meters below sea level.
a. Write an integer to represent each hiker's location with respect
to sea level.
b. What is the difference of the hikers' altitudes?
c. Can the integers be subtracted in either order to find the difference? Explain.
Answers
Question 5
2 pts
(9x + 16)°
(5x - 14)
The value of
is
The measure of the exterior angle is
degrees
Answers
Answer:
Value is 15 and measure is 151
I know how to solve this so I just wanna give points away.
Emil was dividing his candy among 15 friends and himself. If each person received 4 pieces, how many pieces of candy did Emil have to start with? Define a variable and write an equation. Solve the equation and check your solution.
Answers
chile anyways so i just wanted the points
I'm so confused
At the beginning of the school year, the number of students in the band was the same as the number of students in the choir. Throughout the school year, the number of students in the band decreased by 8, and the number of students in the choir decreased by 4. At the end of the school year, the number of students in the choir was 25% more than the number of students in the band. How many students were in the band at the beginning of the school year?
At the beginning of the school year, _________ students were in the band
Answers
Answer: 16............................
Answer:
16
Step-by-step explanation:
4=25%
If the markup is 30% on a cell phone that has a
selling price of $520, what is the initial cost?
Answers
Answer:
The initial cost of the cell phone was $364
Step-by-step explanation:
Since there was a 30% markup, 70% of the new cost is the initial cost. Multiply 520 by 0.7 on a calculator and you get 364
A box of candy contains three times as many cherry pieces. It hasfour more grape pieces than cherry pieces. There are 46 total pieces in the box. How many cherry pieces are in the box
Answers
Answer:
The number of cheery pieces in the box are [tex]18[/tex].
Step-by-step explanation:
Let the number of orange pieces in the box be [tex]x[/tex].
The box contains three times as many cherry pieces as orange pieces.
So, the number of cherry pieces in the box be [tex]3x[/tex].
It has four more grape pieces than cherry pieces.
So, the number of grape pieces in the box be [tex]3x+4[/tex].
There are [tex]46[/tex] total pieces in the box.
So, [tex]x+3x+3x+4=46[/tex]
[tex]\Rightarrow 7x+4=46[/tex]
[tex]\Rightarrow 7x=46-4[/tex]
[tex]\Rightarrow 7x=42[/tex]
[tex]\Rightarrow x=\frac{42}{7}[/tex]
[tex]\Rightarrow x=6[/tex]
So, the number of cherry pieces [tex]=3x=3\times 6=18[/tex].
Hence, the number of cheery pieces in the box are [tex]18[/tex].
Please help! I need to do well on this!
Answers
Answer:
The answer is a
Step-by-step explanation:
help plz it's not dark blue
Answers
Answer:
YELLOW
Step-by-step explanation:
MY TEACHER MADE ME DO THIS LOL
HELP HELP PLEASE ASAP
Answers
A spinner is divided into 10 congruent sections. Each section is labeled with a number as shown. The spinner will be spun one time. What is the probability that the arrow will land in a section that is labeled with a number that is a multiple of 2? 1 A U 9 un 6 3 B 1 10 2 09 4 1 1 / 2 UN
Answers
Answer:
b
Step-by-step explanation:
Guys can y'all help me out D:
Answers
Answer: a
Step-by-step explanation: thanks for being my friend and sorry if im wrong
Solve: -6n + 5 < 11
Which graph shows the solutions?
Answers
Answer:
Step-by-step explanation:
If you follow the pythagorean therum you get a multiple of 6 then get the square root of six and that’s you answer
what will be the new coordinate of vertex b if the triangle is dilated with a center at the origin by a scale factor of 1/3
Answers
Answer:
6 , 3
Step-by-step explanation:
your welcome
The new coordinate of vertex B if the triangle is dilated with a center at the origin by a scale factor of 1/3 is (1,2) and this can be determined by using the given data.
Given :
Dilation Factor = 1/3Points - A(-2,2), B(3,6), and C(1,-2)After the dilation of 1/3 the coordinate of the triangle becomes:
[tex]\rm A(-2,2) \to A'(-2\times \dfrac{1}{3},2\times \dfrac{1}{3}) = A'\left(\dfrac{-2}{3},\dfrac{2}{3}\right)[/tex]
[tex]\rm B(3,6) \to B'(3\times \dfrac{1}{3},6\times \dfrac{1}{3}) = B'\left(1,2)[/tex]
[tex]\rm C(1,-2) \to C'(1\times \dfrac{1}{3},-2\times \dfrac{1}{3}) = C'\left(\dfrac{1}{3},\dfrac{-2}{3}\right)[/tex]
The new coordinate of vertex B if the triangle is dilated with a center at the origin by a scale factor of 1/3 is (1,2).
For more information, refer to the link given below:
https://brainly.com/question/20595275
A salesperson earns a commission of a certain percentage on the original price of any items he helps you buy. The salesperson helped you select a new jacket that was originally 90$. He eared 5.76$ commission on this sale. What percentage of the original jacket price did the salesperson earn
Answers
Answer:
5.18%
Step-by-step explanation:
5.76 x 100 = 576
576 ÷ 100 = 5.184
5.184 = 5.18%
Pls help and show workings
Answers
Answer:
22
Step-by-step explanation:
you would take 14 plus 8 and that would give you your answer. I've done this before. I'm positive its 22
A computer was on sale for 270 if the original price was cut by 40% what was the original price
explain.
Answers
Answer: 108
Step-by-step explanation: The 40% percent taken away from $270 would be $108, because I round it to 50% percent off and that would $135 but since it's 40% off not 50% so I took away 10% from $135, and that's how I found my answer .
What is the approximate what is the approximate area of the circle shown below?
A. 908 cm2
B. 53 cm2
c. 3630 cm2
D. 107 cm2
Answers
The area of the circle is around 908 square centimeters, so the correct option is A.
How to find the area of the circle?The area of a circle of radius R is given by:
A = pi*R²
Where pi is an irrational number, and we can write it as pi = 3.14
Here we can see that the radius of the circle is 17cm, then we can replace that in the area formula to get:
A = 3.14*(17cm)² = 908 cm²
Then the corret option is A.
Laern more about areas at:
https://brainly.com/question/24487155
#SPJ1
I NEED THIS FAST HELP!
Which mixed number is equivalent to the improper fraction 569?
569
629
789
849
Answers
Answer:
569 IS THE SAME NUMBER AS 569 AND THERE ARE NO FRACTIONS THERE are just numbers
Step-by-step explanation:
MAYBE 569????????????
The mixed number that is equivalent to the improper fraction 56/9 is
6(2/9)
Option B is the correct answer.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
A number is called an improper fraction if the denominator is less than the denominator.
Now,
56/9 is an improper fraction.
5(6/9) = 51/9
6(2/9) = 56/9
7(8/9) = 71/9
8(4/9) = 76/9
Thus,
6(2/9) is equal to 56/9.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ2
Sheldon purchased 289 sq ft of sod for his square-shaped yard.
What is the width of his yard?
Answers
Answer:
The width and the length are both 17 feet long.
Step-by-step explanation:
17 * 17 = 289
i need help please!1
Answers
Answer:
for the first picture, she cleans 30 windows
the second picture is 52/100 :)
Answer:
It's B for the first one.
For the second one, it is C
Step-by-step explanation:
30 * 0.3 = 9
So 30% of 30 is 9. She did 9 windows.
0.52 = 52/100
It's 52/100 because 0.52 = 52%. 52% then equals 52/100.
52/100 = 13/25
So the answer is 13/25
An artist mixes 25 ounce of blue paint with 115 ounce of green paint. Using the same ratio, how many ounces of green paint should she mix with 3 ounces of blue paint?
Answers
Answer:
Ounces of green paint needed = 13.8
Step-by-step explanation:
Blue paint : green paint = 25 : 115
how many ounces of green paint should she mix with 3 ounces of blue paint?
Let
Ounces of green paint needed = x
Blue paint : green paint = 3 : x
Equate both ratios
25 : 115 = 3 : x
25/115 = 3/x
25 * x = 115 * 3
25x = 345
x = 345/25
x = 13.8 ounces
Ounces of green paint needed = 13.8