NO EXPLANATION NEEDED

Which table represents a direct variation? Table A x 4 6 8 10 y 7 9 11 13 Table B x 4 6 8 10 y 12 18 24 30 Table C x 4 6 8 10 y

Greeley [361]

Answer:

We conclude that 'Table B' represents a direct variation.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality.

Table A

x 4 6 8 10

y 7 9 11 13

Finding k for all the pairs of x and y

k = y/x

k = 7/4, k = 9/6 = 3/2, k = 11 / 8, k = 13/11

As constant of proportionality 'k' does not remain constant.

Hence, table A does not represent a direct variation

Table B

x 4 6 8 10

y 12 18 24 30

Finding k all the pairs of x and y

k = y/x

k = 12/4 = 3, k = 18/6 = 3, k = 24/8 = 3, k = 30/10 = 3

As the constant of proportionality remains constant.

Therefore, the value of k = 3 for all the points in the table.

Hence, table B represents a direct variation.

Table C

x 4 6 8 10

y 1 3 5 7

Finding k all the pairs of x and y

k = y/x

k = 1/4, k = 3/6 = 1/2, k = 5/8, k = 7/10

As the constant of proportionality 'k' does not remain constant.

Hence, table C does not represent a direct variation.

Table D

x 4 6 8 10

y 3 3 3 3

Finding k all the pairs of x and y

k = y/x

k = 3/4, k = 3/6, k = 3/8, k = 3/10

As the constant of proportionality 'k' does not remain constant.

Hence, table D does not a direct variation.

Therefore, we conclude that 'Table B' represents a direct variation.

8 0

2 years ago

Read 2 more answers

4. Multiply. Write each answer in simplest form: (-3/4)(1/2)(-2/3)

m_a_m_a [10]

Step-by-step explanation:

6/24

=1/4

;)

;(

;/

;]

;|

;[

8 0

2 years ago

Calculate the loan for $10,000, at an annual percentage rate of 5%, for a term of 5 years. What is the amount of accrued interes

nikdorinn [45]

Answer:

Step-by-step explanation:

I= P*r*T

Interest equals 10,000 times 5% times 5 years

$2500 is the total interest.

4 0

2 years ago

Determine the amplitude and period of each function without graphing.

Luba_88 [7]

Answer:

Step-by-step explanation:

We know for a function:

y = Asinωt

=> on comparison, A = 5 m

=> T = 2π / ω

=> T = 2π / 2

=> T = π seconds

5 0

1 year ago

Which geometric series diverges? Three-fifths three-tenths three-twentieths StartFraction 3 Over 40 EndFraction ellipsis Negativ

Sholpan [36]

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

<h3>What is geometric series diverges? </h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

$a+ar+ ar^2+ ar^3+...$

Here,

is the (a) first term of the sequence, and (r) is the common ratio.

To be a series as geometric series diverges, it should follow,

$|r| > 1$

First option given as,

3/5+3/10+3/20+3/40+ ...

Here, the common ratio is,

$r=\dfrac{\dfrac{3}{10}}{\dfrac{3}{5}}\\r=\dfrac{1}{2}$

The common ratio is less than one. Thus option a is not correct.

First option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

$r=\dfrac{4}{-10}\\r=\dfrac{-2}{5}$

For the option number two the common ratio is (-2/5) which is less than 1. This option is also not correct.

In the option number c, the value of common ratio is -4. The absolute value of common ratio is,

$|r|=|-4|\\|r|=4$

The absolute value of this common ratio is more than one. Thus, this is the correct option.

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

Learn more about the geometric sequence here;

brainly.com/question/1509142

7 0

1 year ago