Answer:
aₙ = 4n + 10Step-by-step explanation:
Given is the AP with
The first term of 14The common difference of 4Explicit rule for the sequence is
[tex]a_n=a_1+(n-1)d=14+(n-1)(4)=14+4n-4=4n+10[/tex]Answer:
[tex]\sf a_n=4n+10[/tex]
Step-by-step explanation:
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
Given recursive rule:
[tex]\begin{cases} \sf a_n=a_{n-1}+4\\ \sf a_1=14\end{cases}[/tex]
Therefore, the next two values in the sequence are:
[tex]\begin{aligned} \implies \sf a_2 & = \sf a_{2-1}+4\\& = \sf a_1+4\\& = \sf 14+4\\& = \sf 18\end{aligned}[/tex]
[tex]\begin{aligned} \implies \sf a_3 & =\sf a_{3-1}+4\\& = \sf a_2+4\\& = \sf 18+4\\& = \sf 22\end{aligned}[/tex]
Explicit formula
[tex]\sf a_n=a+(n-1)d[/tex]
where:
[tex]\sf a_n[/tex] is the nth terma is the first termn is the number of the termd is the common difference between termsGiven:
[tex]\sf a = a_1=14[/tex][tex]\sf d = 22-18=4[/tex]Substituting the given values into the formula:
[tex]\sf \implies a_n=14+(n-1)4[/tex]
[tex]\sf \implies a_n=14+4n-4[/tex]
[tex]\sf \implies a_n=4n+10[/tex]
Therefore, the explicit rule in simplified form for the sequence is:
[tex]\sf a_n=4n+10[/tex]
Learn more about arithmetic sequences here:
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what does -2/3 + 1/6 =
please show work
Answer: negative 1 over 2
− 1/2
=negative 0.5−0.5
Reason why:
Step 1 of 2: Add.
Add
(negative 2 over 3 − 2/3) + 1 over 6
1/6
= negative 3 over 6 −3/6
Simplify
negative 3 over 6−
3
6
= negative 1 over 2−
1/2
Step 2 of 2: Simplify, sub-step a: Reduce fraction to lowest terms.
Reduce fraction to lowest terms
negative 3 over 6 −3/6
= −( 3 ÷ 3 ) over ( 6 ÷ 3 )
3 ÷ 3 6 ÷ 3 = negative 1 over 2 −1/2
Which value for Y makes this sentence true?
y = 1/5
Answer:
[tex] \frac{1}{5} [/tex]
making both sides d same value makes d sentence true
Which expression has a simplifled expression of 5x - 12?
-3(4 x - 4) - 7 x
3(4 x-4) - 7 x
31-4x + 4) - 7 x
-31-4 x - 4) - 7 x
Answer:
The correct answer is A
Step-by-step explanation:
When you simplify it it's A
The possible outcomes for rolling a pair of fair dice are shown below.
What is the probability of rolling a sum that is a prime number?
Answer:
5/12
Step-by-step explanation:
"When two dice are thrown, the total number of sample spaces is 36.
Favourable outcomes = {(1,1),(1,2),(1,4),(1,6),(2,3),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}
Total number of favourable outcomes = 15
Hence, the probability of getting a sum of prime numbers = 15/36 = 5/12."
This was taken from a Byjus post.
Hope this helps.
what number is 90% of 140?
126
Step-by-step explanation:A percentage is a proportion of some whole number. There are 2 ways to find percentages. Firstly, you can multiply by a decimal, or you can use a shortcut.
Multiplying with Decimals
You can always rewrite percentages as decimals. To do this move the decimal point 2 digits to the left. This means that 90% becomes 0.90. Then multiply this decimal by the whole number to find the correct percentage.
0.90 * 140 = 126Shortcut
Because 90% is a multiple of 10%, we can use a shortcut. First off, find 10% of 140. To find 10% of any number, move the decimal 1 digit to the left. This means 10% of 140 is 14.0. Next, 90% is 10% less than 100%. So, subtract 10% from 140 to find 90%.
140 - 14 = 126Answer:
126
Step-by-step explanation:
We need to find 90% of 140.
90% is the same as 0.9 or 9/10.
140 can be written as 14 x 10.
Multiply 14 x 10 with 9/10.
⇒ 14 x 10 x 9/10
[The 10 and 1/10 cancel out by cross multiplication]
⇒ 14 x 9
⇒ 126
Can someone please help me with this
Answer:
1, 4, 6.
Step-by-step explanation:
[tex]\left(2n+8\right)\left(n+4\right)=2n^2+16n+32[/tex]
1. [tex]2(x+4)^2=2n^2+16n+32[/tex]
2. [tex]2\left(n+4\right)\left(n+4\right)=2(n+4)^2[/tex]
3. [tex]16n+32=16n+32[/tex]
4. [tex]2n^2+16n+32=2n^2+16n+32[/tex]
5. [tex]2n^2+8n+32=2n^2+8n+32[/tex]
6. [tex]2(n^2+8n+16)=2n^2+16n+32[/tex]
As you can see from the answers it is 1, 4, and 6.
What is the next term of the geometric sequence
Answer:
64/7
Step-by-step explanation:
Pattern = Multiplying by -4
-16/7 x -4/1
64/7
7x=7.7 How would i figure this out ?
which part of the cell makes proteins?
a) chromosomes
b) ribosomes
c) lysosomes
d) mitochondrion
18. Simplify the expression.
(5)10 - (5)13
Answer:
Answer:
-15 is the answer
Step-by-step explanation:
According to the BODMAS (bracket of Division Multiplication Addition Subtraction) rule
=5*10-5*13
=50-65
=-15
Find the value of y.
AABC = ADEF
A
17y - 8
B
(11x - 4)
D
23
117
12 + 13y
'C
E
Answer: 5
Step-by-step explanation:
HELP. WORTH 1 POINT
GIVING 10
Answer:
117
Step-by-step explanation:
well, if they are supplementary, and they are on the same line and a line is equal to 180 degrees, then its as easy as 180-63=117
find the valu of x 8: 10 =x:50
Answer:
40
Step-by-step explanation:
50 / 10 = 5
8 * 5 = 40
Both should be divisible by same amount and that is 5.
Answer:
40
Step-by-step explanation:
Answer this and i mark u branliest
Step-by-step explanation:
5a.
10 white squares
15 shaded squares
5b.
a1 = 1 = 2×1 - 1
a2 = a1 + 2×2 - 1 = 2×1 - 1 + 2×2 - 1 = 2×(1+2) - 2
a3 = a2 + 2×3 - 1 = 2×(1+2+3) - 3
...
an = 2×(1+2+...+n) - n = 2×n×(n+1)/2 - n = n²
so,
a350 = 350² = 122,500
figure350 has 122,500 squares.
5c.
a1 = 1
a2 = a1 = 1
a3 = a2 + 5
a4 = a3 = 6
a5 = a4 + 9
a6 = a5 = 15
a7 = a6 + 13
a8 = a7 = 28
...
a(2n) = a(2n - 1)
a(2n - 1) = a(2(n-1) - 1) + 1 + 4(n - 1) = n×1 + 4(0+1+2+...+n-1) =
= n + 4×(n-1)×n/2 = n + 2×(n² - n) = 2n² - n
therefore,
a350 = a349
a349 = a(2×175 - 1) = 2×175² - 175 = 61,075
figure350 has 61,075 shaded squares.
f(X)= 4X+8 g(X)= X+3, find f(X) • g(X)
Answer:
[tex]4x + 20[/tex]
Step-by-step explanation:
[tex]4(x + 3) + 8 = 4x + 12 + 8 = 4x + 20[/tex]
12x +15x² - 18x³
Factorise the expression
Answer:
-3x(2x+1)(3x-4)
Step-by-step explanation:
Add and subtract the second term to the expression and factor by grouping.
Anser and Explanation:
First, factor out an x to get:
[tex]x(-18x^2 + 15x + 12)[/tex]
Then, factor out a -3:
[tex]-3x(6x^2 - 5x - 4)[/tex]
Finally, factor by grouping:
[tex]-3x(6x^2 + 3x - 8x - 4)[/tex]
[tex]-3x(3x(2x + 1) - 4(2x + 1))[/tex]
[tex]-3x(3x - 4)(2x + 1)[/tex]
so -3x(3x - 4)(2x + 1) is the factored expression.
True or false?
The greater a fractional part of a circle an angle takes up, the smaller it’s measurement will be.
This is the Answer :
true
Determine the mean of the following data. Choose the correct option.
7, 8, 9, 2, 4, 5, 12, 9
Answer:
7
Step-by-step explanation:
mean means average
there are 8 numbers
add them all up
7+8+9+2+4+5+12+9=56
divide 56 by 8 = 7
Express in the form 1 : n , give n as a demical : 20 : 15
Answer:
1 : 0.75.
Step-by-step explanation:
15/20 = 0.75
So its 1 : 0.75
Answer:
1 : 0.75
Step-by-step explanation:
20÷20=1
15÷20=0.75
n=0.75
Find the value of m if 13m + 24m = 41m
Answer:
m=0
Step-by-step explanation:
Add
13m
and
24m
.37
m=
41m
Move all terms containing m
to the left side of the equation.
help me please.........
Answer:
um 21
Step-by-step explanation:
What is the length of LM?
Let see
KM²=LM×MJ6²=LM×3LM=36/3LM=12Option B
Using scales of 1cm to 30° on the x axis and 2cm to 1 unit on the y axis,draw the graph of y=sin 0 for 0°less than or equal to 0 less than or equal to 360°.Using the graph to a)find the equation b) solve the equation i)sin0=0.6 ii)4sin0=-3
Help me and will mark brainlest
Answer:
Attachment 1: graph of [tex]y=\sin(\theta)[/tex]
(using given scale)
Question (a) (Attachment 2)
[tex]\sin(\theta)=0.6[/tex]
Draw the line [tex]y=0.6[/tex] (shown in blue).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=37^{\circ},143^{\circ}\:\textsf{(nearest degree)}[/tex]
Question (b) (Attachment 3)
[tex]4\sin(\theta)=-3[/tex]
[tex]\implies \sin(\theta)=-\dfrac34[/tex]
Draw the line [tex]y=-\dfrac34[/tex] (shown in red).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=229^{\circ},311^{\circ}\:\textsf{(nearest degree)}[/tex]
Differentiate y = tan²x from first principle
Answer:
[tex]y'=2sec^2(x)tan(x)[/tex]
Step-by-step explanation:
Good people please don't leave me help!!!
Answer:
I hope it helped you
Step-by-step explanation:
Pls check the given attachment
I hope it helped you
please helpppppppppppppppp
A bag contains seven red balls, five green balls, four yellow balls, and two black balls. A ball is picked at random
from the bag. What is the probability that the ball will NOT be black?
Answer:
50/50 chance a black ball will be picked
HELPP ASAPP
FIRST PERSON GET BRAINIEST
Answer:
2,6 / Number 3
Step-by-step explanation:
Thats the right answer
Answer:
(2,6)
Step-by-step explanation:
moving 3units to the left gives (2,4) and 2units above gives (2,6) finally
The following can be deposited in a savings account: (check all that apply)
1. Jewels
2. Cash
3. Paycheck
4. Coin
5. Checks
Answer: cash, paychecks, checks
Step-by-step explanation:
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Which of of the following statements are true? Select all that.
Answer:
I think the answer is <1 and <4 are supplementary angles
