All categories

3 years ago

What is the image of the point (6,-1) after a rotation of 270 counterclockwise about the origin

Mathematics

1 answer:

Sav [38]3 years ago

4 0

Answer:

(- 1, - 6 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (y, - x ), thus

(6, - 1 ) → (- 1, - 6 )

You might be interested in

A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many na

ira [324]

Answer:

Approximately $58.2\; \text{nautical miles}$ (assuming that the bearing is ${\rm S$29^{\circ}$W}$ .)

Step-by-step explanation:

Let $v$ denote the speed of the ship, and let $t$ denote the duration of the trip. The magnitude of the displacement of this ship would be $v\, t$ .

Refer to the diagram attached. The direction ${\rm S$29^{\circ}$W}$ means $29^{\circ}$ west of south. Thus, start with the south direction and turn towards west (clockwise) by $29^{\circ}$ to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of $v\, t$ . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly $29^{\circ}$ .

Since the hypotenuse is of length $v\, t$ , the dashed line segment opposite to the $\theta = 29^{\circ}$ vertex would have a length of:

$\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}$ .

Substitute in $\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}$ and $t = 6\; \text{hour}$ :

$\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}$ .

7 0

2 years ago

If the data in the stem-and-leaf graph below were shown in a line plot, which statement’s would be true of the line plot? Please

lukranit [14]

Answer:

1) THE TOTAL NUMBER OF MARKS TELLS YOU THE SIZE OF THE DATA SET.

2)hISTOGRAM

Step-by-step explanation:

3 0

3 years ago

Someone who's good at math please help me!!!

timurjin [86]

#1.
Here what you do is cross multiply.
$\frac{8x}{13x}$
#2.
Same as #1, just cross multiply.
$\frac{9x}{12}$

You get the gist?

8 0

3 years ago

Connie Harris, in charge of office supplies at First Capital Mortgage Corp., would like to predict the quantity of paper used in

Amiraneli [1.4K]

Answer:

y = 0.325X + 7.5 ;

21.5 ;

R^2 = 0.7655 ;

r = 0.8749

Step-by-step explanation:

No. of loans originated ____ sheets of p/paper

45 ______________22

25 ______________ 13

50 _____________ 24

60 _____________ 25

40 _____________ 21

25 _____________ 16

35 _____________ 18

40 _____________ 25

Using the linear regression calculator : the linear model obtained is:

y = 0.325X + 7.5

y = predicted variable = sheets of photocopy paper

X = number of loans originated

0.325 = slope

Intercept = 7.5

B.)

X = 42

y = 0.325(42) + 7.5

y = 21.15

C.)

The Coefficient of determination as determined using the correlation coefficient calculator is :

R^2 = 0.7655 ; this means that about 76.55% of change in number of photocopy performed is explained by the number of loans originated.

D.) The correlation Coefficient (r) :

r = sqrt(R²)

r = sqrt(0.7655)

r = 0.8749

This shows that a strong positive correlation exists between the number of loans originated and the volume of photocopying done.

3 0

3 years ago

Translate the given phrase to an expression. The quotient of 10 and 5 3/4<br> The expression is:

JulijaS [17]

Quotient means to divide.

10 / 5.75 = 1.74

5 0

4 years ago