Factor this 5rst-15ab + 7cd

What the recursive formula for the sequence

klemol [59]

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ a_n=2-5(n-1)\implies a_n=\stackrel{\stackrel{a_1}{\downarrow }}{2}+(n-1)(\stackrel{\stackrel{d}{\downarrow }}{-5})$

so, we know the first term is 2, whilst the common difference is -5, therefore, that means, to get the next term, we subtract 5, or we "add -5" to the current term.

$\bf \begin{cases} a_1=2\\ a_n=a_{n-1}-5 \end{cases}$

just a quick note on notation:

$\bf \stackrel{\stackrel{\textit{current term}}{\downarrow }}{a_n}\qquad \qquad \stackrel{\stackrel{\textit{the term before it}}{\downarrow }}{a_{n-1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{current term}}{a_5}\qquad \quad \stackrel{\textit{term before it}}{a_{5-1}\implies a_4}~\hspace{5em}\stackrel{\textit{current term}}{a_{12}}\qquad \quad \stackrel{\textit{term before it}}{a_{12-1}\implies a_{11}}$

8 0

4 years ago

Please solve this question

Alchen [17]

Answer:

(3, 4 )

Step-by-step explanation:

3x - y = 5 → (1)

x + y = 7 → (2)

adding the 2 equations term by term will eliminate y

4x + 0 = 12

4x = 12 ( divide both sides by 4 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (2)

3 + y = 7 ( subtract 3 from both sides )

y = 4

solution is (3, 4 )

4 0

2 years ago

Can you help with this please.

andrew-mc [135]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - two points P ( 5 , 10 ) and R ( 12 , 14 ) on the cartesian plane

To find - distance between the two points

Using the distance formula ~

$\qquad\underline{d(PR) = \sqrt{( x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} }} \\ \\$

we have ,

$\longrightarrow x_{1} = 5 \\ \longrightarrow x_{2} = 12 \\ \\ \longrightarrow \: y_{1} = 10 \\ \longrightarrow \: y_{2} = 14$

substituting the values in the formula , we get

$d(PR) = \sqrt{(12-5) {}^{2} + (14-10) {}^{2} } \\ \\ \implies \: d(PR) = \sqrt{(7) {}^{2} + ( 4) {}^{2} } \\ \\ \implies \: d(PR) = \sqrt{49 + 16} \\ \\ \implies \: d(PR) = \sqrt{65} \\ \\ \implies \: d(PR) = 8.1 \: units \: (approx)$

hope helpful :)

5 0

2 years ago

Read 2 more answers

Two ships leave a harbor at the same time. One ship travels on a bearing Upper S 14 degrees Upper W at 15 miles per hour. The ot

jekas [21]

Answer:

69.94 miles

Step-by-step explanation:

The distance d₁ the first ship moves after 3 hours is 3 hours × 15 miles per hours = 45 miles

The distance d₂ the second ship moves after 3 hours is 3 hours × 12 miles per hours = 36 miles.

The angle the first ship's direction makes in the North-East direction is 90° - 75° = 15°

The angle the second ship's direction makes in the South-West direction = 14°

The distance moved by the two ships form the side of a triangle. The angle, θ between the two ship directions is 14° + 90° + 15° = 119°

Using the cosine rule, we find the distance d between the two ships

d = √(d₁² + d₂² -2d₁d₂cosθ)

= √(45² + 36² -2×45×36cos119°)

= √(2025 + 1296- (-1570.78))

= √(3321 + 1570.78)

= √4891.78

= 69.94 miles

4 0

3 years ago

- Find the 7th term of the arithmetic sequence – 2x – 1, 4x – 5, 10x - 9, ... Help

nalin [4]

34x-25 is the answer

Explanation in image

6 0

2 years ago