After purchasing a home for $160,00 the homeowner noticed the suggested value of her house was depreciating by 5% each year.

What is the decay factor for this situation?



A
0.05

B
0.50

C
0.95

D
1.05

Solution :

Let x, y, z be the dimensions of the rectangle.

Volume of the rectangle (V) = xyz

Given that the vertex should lie on ellipse [tex]$4x^2 + y^2+4z^2=4$[/tex] .......(i)

So here the volume xyz must be maximum with constraints above.

We solve this using Lagranches method with variable λ

Lagranches function is

[tex]$F : xyz + \lambda(4x^2+y^2+4z^2-4)=0$[/tex] .....(ii)

To find λ, [tex]$\frac{dF}{dx}=0; \frac{dF}{dy}=0;\frac{dF}{dz}=0$[/tex]

[tex]$\frac{dF}{dx}=0 \Rightarrow yz+\lambda(16x)=0 \Rightarrow \lambda = -\frac{yz}{16x}$[/tex] .............(iii)

[tex]$\frac{dF}{dy}=0 \Rightarrow xz+\lambda(2y)=0 \Rightarrow \lambda = -\frac{xz}{2y}$[/tex] ..................(iv)

[tex]$\frac{dF}{dz}=0 \Rightarrow xy+\lambda(16z)=0 \Rightarrow \lambda = -\frac{xy}{16z}$[/tex] ...............(v)

Equating (iii) and (iv)

[tex]$-\frac{yz}{16x}=-\frac{xz}{2y} \Rightarrow y^2=8x^2 \Rightarrow y = \sqrt8 x$[/tex] ...............(vi)

Equating (iii) and (v)

[tex]$-\frac{yz}{16x}=-\frac{xy}{16z} \Rightarrow z^2=x^2 \Rightarrow z = x$[/tex] ....................(vii)

Substitute (vi) and (vii) in (i),

From (i),

[tex]$4x^2 + (\sqrt8 x)^2+4x^2 = 4$[/tex]

[tex]$\Rightarrow 4x^2 +8x^2+4x^2 = 4 \Rightarrow x = \frac{1}{4}$[/tex]

From (vi),

[tex]$y = \sqrt8 x$[/tex]

[tex]$\Rightarrow y= \sqrt8 \times \frac{1}{4} \Rightarrow y =\frac{\sqrt8}{4}$[/tex]

[tex]$\Rightarrow y =\frac{\sqrt{2\times4}}{4} \Rightarrow y = \frac{1}{\sqrt2}$[/tex]

From (vii),

z = x

[tex]$z =\frac{1}{4}$[/tex]

Therefore, for maximum volume the dimensions of a rectangle box are

[tex]$x =\frac{1}{4} ; y = \frac{1}{\sqrt2} ; z =\frac{1}{4}$[/tex]

Answer:

[tex]\frac{5}{14}[/tex]

Step-by-step explanation:

First subtract the two terms by setting the first term as a fraction.

3 * [tex]\frac{5}{5}[/tex] = [tex]\frac{15}{5}[/tex]

Then subtract the terms.

[tex]\frac{15}{5}[/tex][tex]-\frac{1}{5}[/tex] = [tex]\frac{14}{5}[/tex]

Finally, flip the numerator and the denominator.

Answer:

C

Step-by-step explanation:

Domain (and range) don't necessarily have to be in smallest to largest order unless your teacher requires it, so don't worry about the order.

Let's remind ourselves that the domain is the input value, or the x value, and y is the output value, or the y value. We know that in an ordered pair, the first # is x and the second # is y (because x comes before y in the alphabet). Lets look at our ordered pairs and see what the x values are.

{(8, -2), (4, -2), (-3, 2), (-5, -3)}

The x values are 8, 4, -3, and -5, therefore:

Domain: {8,4,-3,-5}

Range would equal all the y values. Remind yourself that if an x value is repeated to only write it down ONCE.

Remember, the order does not matter, so the answer would be C.

Hope this helped!

The speed of the robot from the graph is m = 10 feet per minute

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let y represent the distance of the robot

Let x represent the time taken

Let the first point be P ( 1 , 10 )

Let the second point be Q ( 2 , 20 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line will give the speed of the robot

Substituting the values in the equation , we get

Slope m = ( 20 - 10 ) / ( 2 - 1 )

m = 10 feet per minute

Hence , the speed is 10 feet/min

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The complete question is attached below :

This graph shows the distance that a robot walks. What is the robot's speed?

Walking Time and Distance

2 3 4 5

Time (minutes)

A) 10 feet per minute

B) 5feet per minute

C) 30 feet per minute

D) 20 feet per minute

Answer:

4996.875 or 39975/8

Step-by-step explanation:

brainly pls

Answer:

9 raffle tickets

Step-by-step explanation:

Because  3 raffle tickets are $5

and to find out the number of tickets you can buy with $15 you have to

divide $15 by $5 which is 3

then multiply the 3 times 3 to get 9 raffle tickets

Have a great day, I hope this is helpful to you.

Answer:

9

Step-by-step explanation:

3=5 6=10 9=15

Answer:

[tex]m=-2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-3, 5)

Point (0, -1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Answer: B

Step-by-step explanation:

Step-by-step explanation:

(1 point)

No, there isn't a more efficient way to solve this system.

Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.

Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.

Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.

Answer:

The lungs

Step-by-step explanation:

becuase biology

Answer:

Y-3/5x+2

Step-by-step explanation:

Answer:

12950

Step-by-step explanation:

Answer:

1<x<4

Step-by-step explanation:

this helps me out a lot in my math class

Answer:

x=4 and thats your answer thanks for helping you but if using the z-score it's 0

Step-by-step explanation:

1<x<4

Answer:

w to r to a

Step-by-step explanation:

e to c to p

Answer:

w to r to a

Step-by-step explanation:

Answer:

I don't understand make is more simplify

Answer:

one-ninth of 54

Step-by-step explanation

54*1/9=6

36*1/4=9

Answer:

1/9 of 54  is smaller than 1/4 of 36

Step-by-step explanation:

1/9 of 54 is 54/9 and that is 6

1/4 of 36 is 36/4 and that is 9.

Please mark brainliest

Answer:

-4/3

Step-by-step explanation:

y=mx+b

3y=-4x+15

y= -4/3 x +5

m is slope b is y intercept

Answer: pretty sure it's the number you multiply by 4 is 17

Step-by-step explanation:

when you multiply 4 and 16 you'll get 64 then you subtract 19 and get 45 which is less than 47 so by reasoning if you were to multiply 4 and 17 you'll get 68 then you subtract 19 from 68 and you should get 49 ( you didn't include how much greater than 47 the number should be but the safest bet would be to use 17)

Answer:

v = 2

Explanation:

8(2 − 6v) + 19 = −61

[ Simplify both sides of the equation ]

8(2 − 6v) + 19 = −61

(8)(2) + (8)(−6v) + 19 = −61 (Distribute)

16 + −48v + 19 = −61

(−48v) + (16 + 19) = −61 (Combine Like Terms)

−48v + 35 = −61

−48v + 35 = −61

[ Subtract 35 from both sides ]

−48v + 35 − 35 = −61 − 35

−48v = −96

[ Divide both sides by -48 ]

−48v / -48 = −96 / -48

v = 2

- PNW

Answer:

x = -3 + i√6 and x = -3 - i√6

Step-by-step explanation:

Let's apply the "completing the square" method to find the roots of this equation.

Take half of the coefficient 6 of x, square it and add this result to x^2 + 6x.  Then subtract the same quantity:

x^2 + 6x + 15 becomes

x^2 + 6x + 3^2 - 3^2 + 15 = 0

Rewriting the first three terms as the square of a binomial, we ge:

(x + 3)^2 - 9 + 15 = 0, which simplifies to:

(x + 3)^2 + 6 = 0, or (x + 3)^2 = -6

Taking the square root of both sides:

x + 3 = ±i√6

Then the two roots are complex:

x = -3 + i√6 and x = -3 - i√6

Answer:

32 ft tall

Step-by-step explanation:

24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32

Answer:

B

Step-by-step explanation:

Answer:

25.92

Step-by-step explanation:

Fuel efficiency is the measure or effort that is required to convert the chemical energy in the fuel to the kinetic energy which the cars needs to move. It is meant by how good or effectively the fuel is utilized by the vehicle. It is the ability of the engine to extract more energy from the fuel.

In the context, the size of the engine is 2.5 cubic liters. Then the predicted value of the fuel efficiency will be 25.92 miles per gallon.

Answer:

I'm guessing that when you graph it, the graph changes direction when it's not on the x-axis. the "real zeros" of a graph are the ones that go through the x-axis and then imaginary ones are the ones that don't.

Step-by-step explanation:

Answer:

=  -24576/7

or

-3510.857142

both are the correct answer

Answer:

irrational decimal

Step-by-step explanation:

It can't be repeated, can't go on forever, so it is an irrational decimal.

Answer:

as x → -∞, y → ∞ and as x → ∞, y → -∞

Step-by-step explanation:

Just check the first quadrant of the given graph.

In the first quadrant, when x gets smaller, the value of y is increasing to positive infinity.

In other words, as x → -∞, y → ∞

Now, observe the behavior of the graph in the 4th quadrant.

In the 4th quadrant, when x gets larger, the value of y is decreasing to negative infinity.

In other words, as x → ∞, y → -∞

Therefore, the behavior of f(x):

as x → -∞, y → ∞ and as x → ∞, y → -∞

Therefore, option (C) is true.

The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.

End behaviour of given graph is,  x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

Since, here a  graph is attached.

From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.

So, when  x tends negative infinity then y tends to positive infinity.

when x tends to positive infinity then y tends to negative infinity.

Therefore, end behaviour of given graph are,

                    x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

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