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3 years ago

10

What is the equation of the parabola shown in the graph

1 answer:

Lapatulllka [165]3 years ago

3 0

Answer:

E. $x=\frac{y^{2}}{8}+\frac{y}{2} +\frac{9}{2}$

Step-by-step explanation:

I graphed each of the equations on a graph and found that equation E matched the graph. I graphed equation E on the graph below.

If this answer is correct, please make me Brainliest!

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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:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
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

On a snow day, Owen created two snowmen in his backyard. Snowman A was built to

faust18 [17]

Answer:

<u>The equations for each function:</u>

A(t) = 60 - 6t
B(t) = 42 - 3t

<em>The lines plotted, see attached</em>

<u>The point at which both the snowmen have same height:</u>

60 - 6t = 42 - 3t
6t - 3t = 60 - 42
3t = 18
t = 6

<u>The required interval is </u>

t = [0, 6)

7 0

3 years ago

The linear equation x=5 would be a graph of a..

Lelechka [254]

Thw answer to your Problem would be A

7 0

3 years ago

Combine like terms,<br><br> 1)c+19-4<br><br> 2)m+12-10

rewona [7]

1) Would be c+15 because you can combine 19-4

2) Would be m+2 because you can combine 12-10

8 0

3 years ago

Read 2 more answers

Mai has picked 1 cup of strawberries for a cake which is enough for 3/4 of the cake. How many cups does she need for the whole c

Vaselesa [24]

Answer:Mai has picked 1 cup of strawberries for a cake which is enough for 3/4 of the cake. How many cups does she need for the whole cake?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers