Can you identify the value of each digit ?

What is the coefficient of a in the expression 5a3 + 9a2 + 7a + 4 ?

vlada-n [284]

The coefficient is the number that's before the variable and is multiplying the variable.
In 9a2, the coefficient is 9.

3 0

2 years ago

Read 2 more answers

Show work and explain with formulas.

vova2212 [387]

Answer:

$\large\boxed{4.\ S_{13}=260}$

$\large\boxed{5.\ \sum\limits_{k=1}^7(2k+5)=91}$

$\large\boxed{6.\ a_1=17,\ a_2=26,\ a_3=35}$

Step-by-step explanation:

4.

We have:

$a_6=18,\ a_{13}=32$

These are the terms of the arithmetic sequence.

We know:

$a_n=a_1+(n-1)d$

Therefore

$a_6=a_1+(6-1)d\ \text{and}\ a_{13}=a_1+(13-1)d\\\\a_6=a_1+5d\ \text{and}\ a_{13}=a_1+12d\\\\a_{13}-a_6=(a_1+12d)-(a_1+5d)\\\\a_{13}-a_6=a_1+12d-a_1-5d\\\\a_{13}-a_6=7d$

Substitute a₆ = 18 and a₁₃ = 32:

$7d=32-18$

$7d=14$ divide both sides by 7

$d=2$

$a_6=a_1+5d$

$18=a_1+5(2)$

$18=a_1+10$ subtract 10 from both sides

$8=a_1\to a_1=8$

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{a_1+n_1}{2}\cdot n$

Substitute a₁ = 8, a₁₃ = 32 and n = 13:

$S_{13}=\dfrac{8+32}{2}\cdot13=\dfrac{40}{2}\cdot13=20\cdot13=260$

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5.

We have

$\sum\limits_{k=3}^7(2k+5)\to a_k=2k+5$

Calculate $a_{k+1}$

$a_{k+1}=2(k+1)+5=2k+2+5=2k+7$

Calculate the difference:

$a_{k+1}-a_k=(2k+7)-(2k+5)=2k+7-2k-5=2$

It's the arithmetic sequence with first term

$a_1=2(1)+5=2+5=7$

and common difference d = 2.

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute n = 7, a₁ = 7 and d = 2:

$S_7=\dfrac{2(7)+(7-1)(2)}{2}\cdot7=\dfrac{14+(6)(2)}{2}\cdot7=\dfrac{14+12}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)\\\\S_7=91$

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6.

We have:

$a_1=17,\ a_n=197,\ S_n=2247$

The formula for the n-th term of an arithmetic sequence:

$a_n=a_1+(n-1)d$

The formula of the sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute:

$(1)\qquad 197=17+(n-1)d\\\\(2)\qquad2247=\dfrac{(2)(17)+(n-1)d}{2}\cdot n$

Convert the first equation:

$197=17+(n-1)d$ subtract 17 from both sides

$180=(n-1)d$ Substitute it to the second equation:

$2247=\dfrac{34+180}{2}\cdot n\\\\2247=\dfrac{214}{2}\cdot n$

$2247=107n$ divde both sides by 107

$21=n\to n=21$

Put the value of n to the equation (n - 1)d = 180:

$(21-1)d=180$

$20d=180$ divide both sides by 20

$d=9$

Therefore we have the explicit formula for the nth term of an arithmetic sequence:

$a_n=17+(n-1)(9)\\\\a_n=17+9n-9\\\\a_n=9n+8$

Put n = 1, n = 2 and n = 3:

$a_1=9(1)+8=9+8=17\qquad\text{CORRECT :)}\\\\a_2=9(2)+8=18+8=26\\\\a_3=9(3)+8=27+8=35$

4 0

2 years ago

Matty jogs 9 km/hr. Compute Matty's speed in m/s.

PSYCHO15rus [73]

9 km/hr=
9000m/hr=
9000m/60mins=
9000m/3600seconds=
30m/12seconds=
10m/4seconds=
5m/2seconds
2.5m/1second

3 0

3 years ago

Eric and mark went t a ball game and visited the concession stand.They each got a hot dog,and mark got a large soda and a bag of

LenKa [72]

The soda was $1.00.

Hot Dog- $3.50
Peanuts- $4.00

3.50+4.00= 7.50

Total paid is $11.50-$7.50= $4.00-$3.00(coupon)= $1.00

8 0

2 years ago

Read 2 more answers

How do I find this, what’s the formula to find the 20th term and can anyone explain the formula? Will award brainliest

harina [27]

Answer:

f(n) = n^2 +1
f(20) = 401

Step-by-step explanation:

The first differences of the sequence are ...

5-2 = 3
10-5 = 5
17-10 = 7
26-17 = 9
37-26 = 11

Second differences are ...

5 -3 = 2
7 -5 = 2
9 -7 = 2
11 -9 = 2

The second differences are constant, so the sequence can be described by a second-degree polynomial.

We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...

f(n) = an^2 + bn + c

Then the first three terms of the sequence are ...

f(1) = 2 = a·1^2 + b·1 + c
f(2) = 5 = a·2^2 +b·2 + c
f(3) = 10 = a·3^2 +b·3 +c

Subtracting the first equation from the other two gives ...

3a +b = 3

8a +2b = 8

Subtracting the first of these from half the second gives ...

(4a +b) -(3a +b) = (4) -(3)

a = 1 . . . . . simplify

Substituting into the first of the 2-term equations, we get ...

3·1 +b = 3

b = 0

And substituting the values for a and b into the equation for f(1), we have ...

1·1 + 0 + c = 2

c = 1

So, the formula for the sequence is ...

f(n) = n^2 + 1

__

The 20th term is f(20):

f(20) = 20^2 +1 = 401

_____

Comment on the solution

It looks like this matches the solution of the "worked example" on your problem page.

4 0

3 years ago

Can you identify the value of each digit ? ​

Can you identify the value of each digit ?