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1 year ago

Fill in the table using this function rule. y=-4x+2 x y -1 0 1 2

1 answer:

7 0

All you have to do is substitute all the Xs to and get a final y output.

for example:
if we take the number x is -1 all you do is:

y=-4(-1)+2
y=4+2
y=6
thats the first one done

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David made a class banner out of a large rectangular piece of paper. He cut a

Irina18 [472]

Answer:

100 in²

Step-by-step explanation:

The area of the banner is equal to the area of the initial rectangle minus the area of the cutout triangle.

The rectangle has a height of 8 inches and width of 14 inches, so its area is:

A = (8 in) (14 in) = 112 in²

The triangle has a base of 8 inches and a height of 3 inches, so its area is:

A = ½ (8 in) (3 in) = 12 in²

So the area of the banner is 112 in² − 12 in² = 100 in².

6 0

2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

1 year ago

On any given day, Juan will break even if he earns as much money as he spends. On day 5, he records the expression 16 + (–16). D

viktelen [127]

Yes

I’m assuming 16 is the amount he earned and (-16) is the amount he spent

16 + (-16) = 16-16 = 0

Juan spent the same amount of money as he earned that day and broke even

5 0

2 years ago

Read 2 more answers

What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation? What

alexandr402 [8]

Answer:

1. Multiply (2) by 2 to eliminate the x-terms when adding

2. Multiply (2) by 3 to eliminate the y- term

Step-by-step explanation:

Use this system of equations to answer the questions that follow.

4x-9y = 7

-2x+ 3y= 4

what number would you multiply the second equation by in order to eliminate the x-terms when adding the first equation?

4x-9y = 7 (1)

-2x+ 3y= 4 (2)

Multiply (2) by 2 to eliminate the x-terms when adding the first equation

4x-9y = 7

-4x +6y = 8

Adding the equations

4x + (-4x) -9y + 6y = 7 + 8

4x - 4x - 3y = 15

-3y = 15

y = 15/-3

= -5

what number would you multiply the second equation by in order to eliminate the y- term when adding the second equation?

4x-9y = 7 (1)

-2x+ 3y= 4 (2)

Multiply (2) by 3 to eliminate the y- term

4x - 9y = 7

-6x + 9y = 12

Adding the equations

4x + (-6x) -9y + 9y = 7 + 12

4x - 6x = 19

-2x = 19

x = 19/-2

= -9.5

x = -9.5

6 0

1 year ago

Read 2 more answers

Use complete sentences to describe the range of the sine function.

MA_775_DIABLO [31]

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle,

$-1 \leq sinx \leq 1$ ,

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function.

So the Range of the sine function is [-1, 1]

3 0

2 years ago