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3 years ago

If P=(2,-1),find the image of P under the following rotation. 180 degrees counterclockwise about the origin

Mathematics

1 answer:

vichka [17]3 years ago

3 0

9514 1404 393

Answer:

(-2, 1)

Step-by-step explanation:

Rotating a point 180° about the origin in either direction is equivalent to reflecting it across the origin. The effect is to negate both coordinates.

(x, y) ⇒ (-x, -y) . . . . . rotation 180°

(2, -1) ⇒ (-2, 1) . . . . . P' rotated 180° from P

The coordinates of the rotated point are (-2, 1).

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On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapid

Elza [17]

Answer:

$L(t)=7600e^{0.2273t}$

Step-by-step explanation:

-The locust population grows by a factor and can therefore be modeled by an exponential function of the form:

$P=P_oe^{rt}$

Where:

$P$ is the population after t days.
$P_o$ is the initial population given as 7600
$r$ is the rate of growth
$t$ is time in days

-Given that the growth is by a factor of 5( equivalent to 500%), the r value will be 5

-The population increases by a factor of 5 every 22 days. therefore at any time instance, t will be divided by 22 to get the effective time for calculations.

Hence, the exponential growth function will be expressed as:

$P=P_oe^{rt},\ \ \ P=L(t)\\\\\therefore L(t)=7600e^{5\frac{t}{22}}\\\\=7600e^{0.2273t}$

7 0

3 years ago

a small table is 2 feet by 3 feet a large table is twice as long and rwice as wide as the small table. Whats the area of the lar

Scorpion4ik [409]

Answer:

The area of larger table is 24 square feet.

Step-by-step explanation:

Given are the length and width of small table

$l_s = 2\ ft\\w_s = 3\ ft$

The area of a rectangular table is calculated by multiplying the length and width. It is also given that the length and width of the larger table is double the length and width of small table

So the length and width of larger table will be:

$l_l = 2*2 = 4\ feet\\w_l = 3*2 = 6\ feet$

The area of larger table will be:

$A_l = l_l*w_l\\= 4 * 6\\=24\ ft^2$

Hence,

The area of larger table is 24 square feet.

7 0

3 years ago

How to rewrite 3x4-1+2

igomit [66]

If you want to solve it the answer is 13...
If you want multiple ways to write that here are some:
3x4+2-1
3x4+1
12+2-1
12+1
Etcetera

4 0

3 years ago

a 32m tall building cast a shadow. the distance from the top of the building to the tip of the shadow is 35m. find the length of

icang [17]

The length of the shadow is 14.2 m

Right angle triangle:

Right angle triangle has one of its sides as 90 degrees.

The height of the building is the opposite side of the triangle.

The distance from the top of the building to the tip of the shadow is 35 m is the hypotenuse side.

The length of the shadow is the adjacent side of the triangle.

Therefore,

c² = a² + b²

b² = 35² - 32²

b² = 1225 - 1024

b² = 201

b = √201

b = 14.17

b = 14.2 m

Hence the length of the shadow is 14.2 m.

learn more about right triangle here:

brainly.com/question/4278699

#SPJ9

3 0

1 year ago

Solve: |2(x-5)|+11=17

Otrada [13]

Answer:

Step 1

Use the distributive property to multiply 22 by x-5x−5.

|2x-10|+11=17∣2x−10∣+11=17

Hint

Expand using distributive property.

Step 2

Subtract 1111 from both sides.

|2x-10|=17-11∣2x−10∣=17−11

Step 3

Subtract 1111 from 1717 to get 66.

|2x-10|=6∣2x−10∣=6

Hint

Subtract one term from another.

Step 4

Use the definition of absolute value.

2x-10=62x−10=6 2x-10=-62x−10=−6

Step 5

Add 1010 to both sides of the equation.

2x=162x=16 2x=42x=4

Step 6

Divide both sides by 22.

x=8x=8 x=2x=2

Solution

x=2x=2

x=8x=8

Step-by-step explanation:

pa brainliest

6 0

2 years ago