Each home room has to have the same number of girls and boys in each home room.

AlekseyPX

9514 1404 393

Answer:

B.

as x increases, f(x) decreases;
as x decreases,f(x) decreases

Step-by-step explanation:

The function is of even degree with a negative leading coefficient. f(x) will tend toward negative infinity as x gets larger or smaller. That is ...

as x increases, f(x) decreases;
as x decreases,f(x) decreases

_____

<em>Even degree</em> means the end behaviors are the same for both large and small x. <em>Negative leading coefficient</em> means the function value decreases for larger x.

8 0

2 years ago

Given the system of equations:

uranmaximum [27]

Answer:

x=4

y=2

Step-by-step explanation:

2x+2y=12

x−y=2

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+2y=12,x−y=2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+2y=12,2x+2(−1)y=2×2

Simplify.

2x+2y=12,2x−2y=4

Subtract 2x−2y=4 from 2x+2y=12 by subtracting like terms on each side of the equal sign.

2x−2x+2y+2y=12−4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

2y+2y=12−4

Add 2y to 2y.

4y=12−4

Add 12 to −4.

4y=8

Divide both sides by 4.

y=2

Substitute 2 for y in x−y=2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2=2

Add 2 to both sides of the equation.

x=4

The system is now solved.

x=4,y=2

Correct choice is B) x=4.

8 0

1 year ago

Read 2 more answers

Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C' (C' = kC)

taking exponents of both sides, we have

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$