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pav-90 [236]
2 years ago
8

Write an equation of the line, in slope intercept form.

Mathematics
2 answers:
MatroZZZ [7]2 years ago
7 0
Answer is Y = -3x + 6
DedPeter [7]2 years ago
4 0

Answer:

y = -3x + 6

Step-by-step explanation:

Slope-intercept form:

y = mx + b

m (slope) = \frac{-6}{2} or -3

b (y-intercept, or where the line crosses the y-axis) = 6

y = -3x + 6

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Find the general term of sequence defined by these conditions.
disa [49]

Answer:

\displaystyle  a_{n}  =     (2)^{2n -1}   -   (3) ^{n-1 }

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0  \:  \: where :  \:  \:a_1 = 1 \: ,a_2 = 5,

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

  • {x}^{n}  =  c_{1} {x}^{n - 1}  + c_{2} {x}^{n - 2}  + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}

the steps for solving a linear homogeneous recurrence relation are as follows:

  1. Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
  2. Solve the polynomial by factoring or the quadratic formula.
  3. Determine the form for each solution: distinct roots, repeated roots, or complex roots.
  4. Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

{x}^{2}  - 7x+ 12= 0

Step-2:Solve the polynomial by factoring

factor the quadratic:

( {x}^{}  - 4)(x - 3) =  0

solve for x:

x =  \rm 4 \:and \: 3

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

\displaystyle a_{n}  = c_{1}  {x} _{1} ^{n }  + c_{2}  {x} _{2} ^{n }

so substitute the roots we got:

\displaystyle a_{n}  = c_{1}  (4)^{n }  + c_{2}  (3) ^{n }

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

\begin{cases}\displaystyle 4c_{1}    +3 c_{2}    = 1  \\ 16c_{1}    + 9c_{2}     =  5\end{cases}

solve the system of equation which yields:

\displaystyle c_{1}  =  \frac{1}{2}     \\  c_{2}   =   - \frac{1}{3}

finally substitute:

\displaystyle  a_{n}  =  \frac{1}{2}   (4)^{n }   -  \frac{1}{3}  (3) ^{n }

\displaystyle \boxed{ a_{n}  =    (2)^{2n-1 }   -   (3) ^{n -1}}

and we're done!

7 0
3 years ago
Select the correct answer.
Ilia_Sergeevich [38]

Answer:b

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A test consists of 10
Alecsey [184]
I didn't understand your question. please repeat 
6 0
2 years ago
Seth's balcony is 7 feet wide and 14 feet long. Seth paid $4.00 per square foot to have the
BlackZzzverrR [31]

Answer:

392

Step-by-step explanation:

4 0
2 years ago
Help me pls math genius
Alecsey [184]

Answer:

x = -3

y = -1

Step-by-step explanation:

in the given question :-

=》x - 4y = 1

=》x = 4y + 1

now replacing the value of x as ( 4y + 1 ) in equation (2)

=》3x + 2y = -11

=》3 (4y + 1) + 2y = -11

=》12y + 3 + 2y = -11

=》14y = -11 - 3

=》y = -14 ÷ 14

=》y = -1

now, putting the value of y in equation (1)

=》x - 4y = 1

=》x - ( 4 × -1 ) = 1

=》x + 4 = 1

=》x = 1 - 4

=》x = -3

6 0
3 years ago
Read 2 more answers
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