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2 years ago

What is the explicit formula for the sequence {3,8,13,18,…}?

Mathematics

1 answer:

SVEN [57.7K]2 years ago

5 0

Answer:

3+5(n-1)

Step-by-step explanation:

first term (a)=3

common difference (d)=5

they an=a+(n-1)d

=>3+(n-1)5

=>3+5(n-1)

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Find the equation of quadratic function determined from the graph below?

Aleksandr [31]

Step-by-step explanation:

The x-intercepts are x = -1 and x = 5, so:

y = k (x + 1) (x − 5)

The vertex is (2, -3), so:

-3 = k (2 + 1) (2 − 5)

-3 = -9k

k = 1/3

y = 1/3 (x + 1) (x − 5)

Simplifying:

y = 1/3 (x² − 4x − 5)

y = 1/3 x² − 4/3 x − 5/3

3 0

4 years ago

Solve for x and y:<br> 3/x -1/y =13/10<br> 1/x + 2/y =9/10

harkovskaia [24]

Answer:

(x, y) = (2, 5)

Step-by-step explanation:

I find it easier to solve equations like this by solving for x' = 1/x and y' = 1/y. The equations then become ...

3x' -y' = 13/10

x' +2y' = 9/10

Adding twice the first equation to the second, we get ...

2(3x' -y') +(x' +2y') = 2(13/10) +(9/10)

7x' = 35/10 . . . . . . simplify

x' = 5/10 = 1/2 . . . . divide by 7

Using the first equation to find y', we have ...

y' = 3x' -13/10 = 3(5/10) -13/10 = 2/10 = 1/5

So, the solution is ...

x = 1/x' = 1/(1/2) = 2

y = 1/y' = 1/(1/5) = 5

(x, y) = (2, 5)

_____

The attached graph shows the original equations. There are two points of intersection of the curves, one at (0, 0). Of course, both equations are undefined at that point, so each graph will have a "hole" there.

3 0

3 years ago

Determine the geometric mean of 45 and 15

Alenkinab [10]

I believe 30 is the answer :)

7 0

3 years ago

Read 2 more answers

HELP PLEASE DUE NOW!! Does a line of best fit need to go through at least one point for there to be a correlation Also if a line

koban [17]

Answer:

For a line of best fit, it doesn't nessesarily have to land on a point, it just has to be in between them or on them whichever way you choose to do it. And also your second question, yes it is correlation if it lines up with the line and not somewhere else or if there are so many dots that they don't really form a line then it isn't a correlation.

Hope this helps!

6 0

3 years ago

Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant

Ksju [112]

Answer:

A(n) = L(n) × W(n) and $A(n)=0.5n^{2} +2n+2$

Step-by-step explanation:

We are given that the length of the rectangular garden is L and width is W.

Also, in terms of 'n',

Length is given by, L(n) = n + 2

Width is given by, W(n) = 0.5n + 1.

Now, we know that, Area of rectangle = Length × Width.

Therefore, area of Kirti's garden is given by, A(n) = L(n) × W(n).

Thus, formula of area in terms of L(n) and W(n) is A(n) = L(n) × W(n).

Moreover, as A(n) = L(n) × W(n).

i.e. A(n) = (n+2) × (0.5n+1)

i.e. $A(n)=0.5n^{2} +n+2 \times 0.5n+2$

i.e. $A(n)=0.5n^{2} +n+n+2$

i.e. $A(n)=0.5n^{2} +2n+2$

Hence, the formula for area in terms of 'n' is $A(n)=0.5n^{2} +2n+2$ .

5 0

4 years ago