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3 years ago

What is four fifths more than a number is one third

Mathematics

2 answers:

LiRa [457]3 years ago

7 0

Answer:

1. 4/5+x=1/3

2. x=-7/15

Step-by-step explanation:

maks197457 [2]3 years ago

4 0

Answer:

a+4/5=1/3 because + means more than

Step-by-step explanation:

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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

Two dice are tossed. The probability that the total score is a prime number is:

andrew11 [14]

Step-by-step explanation:

50/50 it's random I think but I learned that in science

8 0

3 years ago

Read 2 more answers

What is 92.3 times 4 to the power of ten

steposvetlana [31]

I am pretty sure your answer will be 96783564.8, but it may need to be rounded. If I am wrong, I am sorry.

Hope this helps~!

5 0

3 years ago

Find the equation of the line

Gre4nikov [31]

Answer:

y= - 1/6x -1

Step-by-step explanation:

Given:

y= 6x -2

and point (6, -2)

Perpendicular line has slope of reciprocal opposite to the given: - 1/6, so the equation:

y= -1/6x + b

Finding b using the intersected point:

-2= -1/6*6 +b
b= -2 +1= -1

So the equation is:

y= - 1/6x -1

5 0

3 years ago

If a is a rational number and b is a rational number, then the product ab must be

alukav5142 [94]

The best way to answer this is to find counterarguments for each answer to eliminate them as a possibility. ab doesn't have to be an integer, 2.5*3=7.5 . That's also not an imaginary number so that's out. And that's also not an irrational number so that's out too. Only choice left is rational number.

8 0

3 years ago

Read 2 more answers