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MA_775_DIABLO [31]

2 years ago

14

the second term in a sequence is 13. the term to term rule is "add 6". write an expression in terms of n, for the nth term of a

sequence

2 answers:

Genrish500 [490]2 years ago

6 0

Answer:

f(n)=6n+5

Step-by-step explanation:

since the second term is 13, we have to subtract 6 to get our first term, 5.

Then we put it together,

I hope this helps you

If it does a thanks (and brainliest trying to level up) would be appreciated, if wrong please leave a comment

NikAS [45]2 years ago

4 0

Answer:

$a_{n}$ = 6n + 1

Step-by-step explanation:

This is an arithmetic sequence with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = a₂ - 6 = 13 - 6 = 7 and d = 6, thus

$a_{n}$ = 7 + 6(n - 1) = 7 + 6n - 6 = 6n + 1

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Find the equation of the plane through the point (2,5,7) that is parallel to the line r=(3i+2j−2k)+t(i+2j+9k) and perpendicular

insens350 [35]

The plane we want to find has general equation

$a(x-2)+b(y-5)+c(z-7)=0$

with $a,b,c$ not equal to 0, and has normal vector

$\vec n=a\,\vec\imath+b\,\vec\jmath+c\,\vec k$

$\vec n$ is perpendicular to both the normal vector of the other plane, which is $4\,\vec\imath+5\,\vec\jmath+6\,\vec k$ , as well as the tangent vector to the line $\vec r(t)$ , which is $\vec\imath+2\,\vec\jmath+9\,\vec k$ .

This means the dot product of $\vec n$ with either vector is 0, giving us

$\begin{cases}4a+5b+6c=0\\a+2b+9c=0\end{cases}$

Suppose we fix $c=1$ . Then the system reduces to

$\begin{cases}4a+5b=-6\\a+2b=-9\end{cases}$

and we get

$(4a+5b)-4(a+2b)=-6-4(-9)\implies-3b=30\implies b=-10$

$a+2(-10)=-9\implies a=11$

Then one equation for the plane could be

$\boxed{11(x-2)-10(y-5)+(z-7)=0}$

or in standard form,

$\boxed{11x-10y+z=-21}$

The solution is unique up to non-zero scalar multiplication, which is to say that any equation $(11x-10y+z)k=-21k$ would be a valid answer. For example, suppose we instead let $c=2$ ; then we would have found $a=22$ and $b=-20$ , but clearly dividing both sides of the equation

$22(x-2)-20(y-5)+2(z-7)=0$

by 2 gives the same equation as before.

7 0

2 years ago

You decide to make milk a loss leader. You drop the price from its cost of $2.59 per gallon to $1.99 per gallon. What is the per

Veseljchak [2.6K]

Answer:

<u>The percentage loss per gallon is 23.17%</u>

Step-by-step explanation:

Original price per gallon = $ 2.59

Discounted price per gallon = $ 1.99

Now, let's calculate the percentage loss per gallon, using the Direct Rule of Three, as follows:

Price Percentage

2.59 100

1.99 x

*****************************

2.59 * x = 1.99 * 100

2.59x = 199

x = 199/2.59

x = 76.83

Percentage loss = 100 - 76.83

<u>Percentage loss = 23.17%</u>

4 0

2 years ago

Read 2 more answers

Nicole has nine dollars to spend on cards she finds friends with the same amount of money to split the cost of a set once it cos

anyanavicka [17]

Answer:

Each Friend will get $\frac{x}{3}$ cards.

Step-by-step explanation:

Let the number of cards be x.

Given:

Amount Nicole used to spend on cards = $9

Total cost of one set =$27

Also, she finds friends with the same amount of money to split the cost of a set.

So, Number of friends she finds can be calculated by dividing the Cost of 1 set with amount of money Nichole used to spend on cards.

Number of friends she finds = $\frac{27}{9} = 3$

Hence she finds 2 friends and 1 is nichole hence there are 3 persons carrying $9 to buy $27 set of card

Now, Number of cards each friend gets is equal to Total number of Cards in 1 set divided by number of people.

Number of cards each friend = $\frac{x}{3}$

Hence Each Friend will get $\frac{x}{3}$ cards.

4 0

2 years ago

Casey bought sandwiches and bags of chips. Each sandwich cost three times asmuch as a bag of chips. She bought 5 sandwiches for

Lerok [7]

Answer:

Casey Bought 6 bags of chips

Step-by-step explanation:

If each sandwich costs 3 times the amount of a bag of chips and the sandwich is 6 dollars, the chips are 2 dollars. Casey bought 5 sandwiches and spent $30 dollars on sandwiches. Since the total was $42 dollars you have $12 dollars left to get your total of $42. 2x6 = 12 so therefore Casey bought 6 bags of chips.

5 0

2 years ago

Kiran says that a solution to the equation x+4=20 must also be a solution to the equation 5(x+4)=100 Write a convincing explanat

Helen [10]

Answer:

x+4=20 is a solution to 5(x+4)=100.

Step-by-step explanation:

Following PEMDAS, divide 5 from both sides of the equation 5(x+4)=100, and you have x+4=20 remaining.

This means that both equations have the same solution.

8 0

2 years ago