Two points in a transformation are J'(-2, 5) and J'(0, 4). which of the following translations was used?

64, –48, 36, –27, ...<br><br> Which formula can be used to describe the sequence?

nordsb [41]

Answer:

$\boxed{a_n \: = \: 64 \: \times \: ( - \frac{3}{4} ) ^{n \: - \: 1} }$

Step-by-step explanation:

We first compute the ratio of this geometric sequence.

$r \: = \: \frac{ - 48}{64} \\ \\ r \: = \: \frac{36}{ - 48} \\ \\ r \: = \: \frac{ - 27}{36}$

We simplify the fractions:

$r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4}$

We deduce that it is the common ratio because it is the same between each pair.

$r \: = \: - \frac{3 }{4}$

We use the first term and the common ratio to describe the equation:

$a_1 \: = \: 64; \: r \: = \: - \frac{3 }{4}$

<h3>We apply the data in this formula:</h3>

$\boxed{a_n \: = \: a_1 \: \times \: {r}^{ n \: - \: 1} }$

_______________________

<h3>We apply:</h3>

$\boxed {\bold{a_n \: = \: 64 \: \times \: {( - \frac{3}{4} )}^{ n \: - \: 1} }}$

<u>Data</u>: The unknown "n" is the term you want

<h3><em><u>MissSpanish</u></em></h3>

4 0

2 years ago

Choose the equation of the line that is parallel to the y- axis.

Alex17521 [72]

The answer is x=-2 because its the only one thats parallel to the y axis

8 0

2 years ago

Read 2 more answers

Evaluate the following integral in cylindrical coordinates triple integral 1/(1+x^2+y^2) dzdxdy z=0..2 y=0..square root(1-x^2) x

sertanlavr [38]

In cylindrical coordinates, we take

$x=r\cos\theta$

$y=r\sin\theta$

$z=z$

so that $\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$ .

We have

$1+x^2+y^2=1+r^2$

and the integral is

$\displaystyle\int_0^2\int_0^\pi\int_0^1\frac r{1+r^2}\,\mathrm dr\,\mathrm d\theta\,\mathrm dz=\frac{\ln2}2\int_0^2\int_0^\pi\mathrm d\theta\,\mathrm dz=\boxed{\pi\ln2}$

8 0

3 years ago

Mr. Mole left his burrow and started digging his way down at a constant rate. Time (minutes) Altitude (meters) 666 -20.4−20.4min

Juli2301 [7.4K]

Answer:

$-6$ meters.

Step-by-step explanation:

We have been given Mr. Mole left his burrow and started digging his way down at a constant rate.

We are also given a table of data as:

Time (minutes) Altitude (meters)

6 -20.4

9 -27.6

12 -34.8

First of all, we will find Mr. Mole's digging rate using slope formula and given information as:

$m=\frac{y_2-y_1}{x_2-x_1}$ , where,

$y_2-y_1$ represents difference of two y-coordinates,

$x_2-x_1$ represents difference of two corresponding x-coordinates of y-coordinates.

Let $(6,-20.4)$ be $(x_1,y_1)$ and $(9,-27.6)$ be $(x_2,y_2)$ .

$m=\frac{-27.6-(-20.4)}{9-6}$

$m=\frac{-27.6+20.4}{3}$

$m=\frac{-7.2}{3}$

$m=-2.4$

Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.

$y=mx+b$ , where,

m = Slope,

b = The initial value or the y-intercept.

Upon substituting $m=-2.4$ and coordinates of point $(6,-20.4)$ , we will get:

$-20.4=-2.4(6)+b$

$-20.4=-14.4+b$

$-20.4+14.4=-14.4+14.4+b$

$-6=b$

Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is $-6$ meters.

6 0

2 years ago

Read 2 more answers

Determine the constant of proportionality,k,of Kevin’s wage.

ankoles [38]

Answer:

Kevin's constant of proportionality,k = $8.25 per hour

Greg's constant of proportionality,k = $9 per hour

Savannah's constant of proportionality,k = $9.5 per hour

Step-by-step explanation:

1. What is the constant of proportionality, k, of Kevin's wage? Greg's? Savannah's?

Solution

y = kx is a proportional variation

Where,

y and x are represent two different variables

k represent constant of proportionality

From the attached table,

Let

y = wages earned (in dollars)

x = hours worked

To find the constant of proportionality k of Kevin's wage, divide the variable y (total earned) by the variable x (number of hours)

Using any points on the table

Take (8,66.00) for example

constant of proportionality k of Kevin's wage = variable y (total earned) / variable x (number of hours)

= 66.00/8

= 8.25

k = $8.25 per hour

B. Constant of proportionality of Greg's wage = variable y (total earned) / variable x (number of hours)

Using (9, 81.00)

k = 81.00/9

= 9

Greg's k = $9 per hour

C. Constant if proportionality of Savannah's wage = variable y (total earned) / variable x (number of hours)

Using (6, 57.00)

k = 57.00/6

= 9.5

Savannah's k = $9.5 per hour

Therefore,

Kevin's constant of proportionality,k = $8.25 per hour

Greg's constant of proportionality,k = $9 per hour

Savannah's constant of proportionality,k = $9.5 per hour

7 0

3 years ago