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2 years ago

J'K'L'M' is a translation of JKLM by vector (-6/2). What are the coordinates of K'? What are the coordinates of M'?

Mathematics

1 answer:

pochemuha2 years ago

7 0

By applying the concept of rigid transformation and the equation of translation we conclude that the coordinates of points K' and M' are (-2, 3) and (-4, 1).

<h3>How to apply a translation to a point on a Cartesian plane</h3>

Rigid transformations are transformations applied onto geometric loci such that Euclidean distance is conserved at every point of the loci. Translations are an example of rigid transformations, whose formula is defined by the following expression:

$P'(x, y) = P(x, y) + \vec v$ (1)

Where:

P(x, y) - Original point
P'(x, y) - Resulting point
$\vec v$ - Translation vector

If we know that K(x, y) = (4, 1), M(x, y) = (2, -1) and $\vec v = (-6, 2)$ , then the coordinates of points K' and M' are:

Point K'

K'(x, y) = (4, 1) + (-6, 2)

K'(x, y) = (-2, 3)

Point M'

M'(x, y) = (2, -1) + (-6, 2)

M'(x, y) = (-4, 1)

By applying the concept of rigid transformation and the equation of translation we conclude that the coordinates of points K' and M' are (-2, 3) and (-4, 1).

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Calculate the number of ways that the coach can assign the 4 positions to his 16 players.

Natali5045456 [20]

The number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways

<h3>How to calculate the permutation</h3>

The formula for permutation is given as;

Permutation = $\frac{n!}{(n - r)!}$

n = 16

r =4

Permutation = $\frac{16!}{12!}$

Permutation = $\frac{16 *15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1}$

Permutation = 43, 680 ways

Thus, the number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways

Learn more about permutation here:

brainly.com/question/12468032

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8 0

2 years ago

Sophia buys an apple that weighs 0.45 pound, a grapefruit that weighs pound, a navel orange that weighs pound, and a pear that w

Tanzania [10]

Answer:

The order of fruit from least to greatest weight is -

Apple , pear, navel orange, grapefruit

Step-by-step explanation:

P.S - The exact question is -

Given - Sophia buys an apple that weighs 0.45 pound, a grapefruit that weighs $\frac{3}{4}$ pound, a navel orange that weighs $\frac{5}{8}$ pound, and a pear that weighs 0.5 pound.

To find - What is the order of the fruit from least weight to the greatest weight ?

Proof -

Weight of apple = 0.45 pound

Weight of grapefruit = $\frac{3}{4}$ pound = 0.75 pound

Weight of navel orange = $\frac{5}{8}$ pound = 0.625 pound

Weight of a pear = 0.5 pound

As,

0.45 < 0.5 < 0.625 < 0.75

So, The order of fruit from least to greatest weight is -

Apple , pear, navel orange, grapefruit

8 0

3 years ago

A bookstore costs $96 a day to keep open, and it spends $12 for each book that it sells. If each book sells for $18, what is the

asambeis [7]

Answer: The break even point is when they have sold 16 books and have made $288

Step-by-step explanation: The costs are modeled in the equation y = 12x + 96. x is the number of books sold.

The earnings are modeled by he equation y = 18x.

Substitute 18x for y and solve for x.

18x = 12x + 96 Subtract 12x from both sides.

6x = 96 Divide both sides by 6

x = 16

Substitute into the original equations to solve for y

y = 12(16) + 96

y = 192 + 96

Y = 288

y = 18(16)

y = 288

7 0

3 years ago

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

3 years ago

Which of the following statements are true? Select all that apply.

kap26 [50]

b (?) and c

m and n have the same slope (-2/5) so m//n

8 0

3 years ago