Solve the difference equation Yx+2 + 4yx+1 + 3yx = 3* , yo = 0, y1 = 1 using Z-transforms

Answer:

Step-by-step explanation:

H

A statement which best describes the function that represents the situation include the following: A) It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope or ratio of change and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we have the following linear function;

F = 0.75x

where:

F represents the final cost in dollars.

x represents the price on the tag in dollars.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.

Here,

It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.

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Complete question:

How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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awnser for a: d

awnser for b: a

anything else ?

John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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Answer:

16 × 10^11= 1.6e+12

8 × 10^5= 800000

Step-by-step explanation:

Observations can you make from a comparison of the number of water supply stoppages reported by owner-occupied units versus renter-occupied units 1.

Total no. of times owner-occupied units had a water supply stoppage lasting 6 or more hours

547000 + 5012000 + 6110000 + 2544000 + 557000 = 14770000

x = no. of times owner-occupied units had a water supply stoppage.

P(x=0) = 547000/14770000

P(x=0) = 0.0370

Similarly, we have at x=1

P(x=1) = 5012000/14770000

P(x=1) = 0.3393

P(x=2) = 6110000/14770000

P(x=2) = 0.4137

P(x=3) = 2544000/14770000

P(x=3) = 0.1722

P(x=4) = 557000/14770000

P(x=4) = 0.0378

x           f(x)

0             0.0370

1              0.3393

2         0.4137

3              0.1722

4         0.0378

Total     1

Observations can you make from a comparison of the number of water supply stoppages reported by owner-occupied units versus renter-occupied units 1.

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Answer is D) $300

Step-by-step explanation:

First find the rate of how many dollars she earns in 1 hour = $180/18

Mabel earns $10/h so 30 hours x $10 = $300/30 hours

Step-by-step explanation:

here's the answer to your question

The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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Answer:

y = 3x + 4

Step-by-step explanation:

Given:

Coordinates

(-3 , -5)

Slope m = 3

Find;

Equation of slope

Computation:

Given, x1 = -3 and y1 = -5

Equation of slope = y - y1 = m(x - x1)

Equation of slope = y - (-5) = 3(x + 3)

Equation of slope = y + 5 = 3x + 9

Equation of slope = y = 3x + 9 - 5

Equation of slope = y = 3x + 4

y = 3x + 4

Their ages are given below:

The sum of their ages would be 57 years.

The current age of Nico is 27 - 7 = 20 years.

Therefore, Maria and Luis's current ages would be 8 years older than when they were 10 and 11 respectively,

so Maria is currently 18 years old and Luis is currently 19 years old.

Therefore, the sum of their current ages is 18 + 19 + 20 = 57 years.

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8 years ago, Maria was 10 years old and Luis was 11 years old. In 7 years Nico will be 27 years old, what is the sum of the current ages of Maria, Luis and Nico?

Answer:

y = -5/9x

Step-by-step explanation:

Two points on the line; (4,-2) & (-5,3)

Finding the slope (m):

m = (3-(-2))/(-5-4)

= 5/-9

= -5/9

y = -5/9x + c

Since it passes through the origin, c = 0.

Hence, y = -5/9x

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The simplified expressions and their products can be written as follows:

A. 2/36 = 1/18

B. 20/40 = 1/2

C. 15/ 56 = 15/56

D. 6/36 = 1/6

To simplify the expression, we can start by multiplying the numerators and the denominators and then dividing by the greatest common factor.

In the first question, the numerators can be multiplied to give us 2 while the denominators can be multiplied to give us 36. On dividing these two, we will have 1/18. So, the simplified form of this expression is 1/18.

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Answer:

5/4

Step-by-step explanation:

I think this makes sense, if this is what ur asking for.

The correct statement regarding the congruence is given as follows:

1) Distance is preserved under reflection.

Examples of transformations are given as follows:

Congruent segments are those with the same length, and the dilation is the only transformation that has a loss of congruence.

The diagram is not necessary, as for every reflection the effect will be the same.

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Another method to represent this solution set is as {x | x ≤ 4.5} .

Open set example: What is it?

What does a closed set look like?

Then number-line shows a closed dot at 4.5. This shows that x is a number that is less than or equal to 4.5.

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The solution to the inequality (x + 5) / (x - 3) ≤ 0 is an empty set. There are no values of x that satisfy the inequality. In interval notation, we represent this as an empty interval: ∅.

To solve the inequality (x + 5) / (x - 3) ≤ 0, we need to find the values of x that make the expression less than or equal to zero.

First, we identify the critical points where the expression becomes zero or undefined. In this case, the denominator x - 3 becomes zero at x = 3.

Next, we create a sign chart by testing intervals on the number line. We choose test points within each interval and determine the sign of the expression.

Test x = 0:

(0 + 5) / (0 - 3) = -5 / -3 = 5/3 > 0 (positive)

Test x = 4:

(4 + 5) / (4 - 3) = 9 / 1 = 9 > 0 (positive)

Test x = 10:

(10 + 5) / (10 - 3) = 15 / 7 > 0 (positive)

Based on the sign chart, the expression is positive (greater than zero) for all tested values of x. Therefore, the solution to the inequality (x + 5) / (x - 3) ≤ 0 is an empty set. There are no values of x that satisfy the inequality.

In interval notation, we represent this as an empty interval: ∅.

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The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.

First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:

Distance Yq = \(\sqrt{[(10-8)^2 + (5-10)^2] }\)

Distance Yq = \(\sqrt{8 + 25 }\)

Distance Yq =\(\sqrt{ 33}\)

Distance 5B = \(\sqrt{[(3-2)^2 + (2-3)^2] }\)

Distance 5B = \(\sqrt{2}\)

Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:

x = (33/2)

Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,

Slοpe Yq = (10-5)/(8-10) = -5/2

Slοpe B-missing vertex = -5/2

write the equatiοn οf the line passing thrοugh B and the missing vertex:

y - 2 = (-5/2)(x - 3)

Simplifying, we get:

y = (-5/2)x + (19/2)

Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.

Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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the dimensions of the dumpster that will minimize its surface area

length l = 6.32

width w =  1.58

height h = 0.39

Length = l

width = w

height = h

given that length is four times its width

l = 4w

Now, the formula for the surface area of a cube is;

S = 2lh + 2lw + 2wh

substitute l = 4w in the above equation

S = 2(4w)h+2(4w)w+2wh

S = 8wh+8\(w^{2}\)+2wh

S = 10wh + 8\(w^{2}\)

formula for the volume of a cube is;

V = lwh

now substitute l=4w in the above equation

V = (4w)wh

V = 4\(w^{2}\)h

h = 4\(w^{2}\)/V

Put V/2w² for h in the surface area equation to get;

S= 8w² + 10w(V/4w²)

 = 8w² + 5V/2w

given that volume V = 25.6 substitute that in the above equation

S = 8w² + 5(25.6)/2w

  = 8w² + 128/2w

Since we want to minimize the surface area, let us find the first derivative of S to get;

S' = 16w - 128/2w²

At S' = 0

0 = 16w-  128/2w²

16w =  128/2w²

32w³ = 128

w³ = 128/32

w³ = 4

w = \(\sqrt[3]{4}\)

w = 1.58 yds

since l = 4w substitute the value of w in that

l = 4(1.58) = 6.32

h = 4\(w^{2}\)/V = 4(\(1.58^{2}\))/25.6

h = 0.39

the dimensions are

length l = 6.32

width w =  1.58

height h = 0.39

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

175 ; 5

Step-by-step explanation:

Supplementary angles sums up to 180

10x + 2x - 30 = 180

12x - 30 = 180

12x = 180 + 30

12x = 210

x = 210/12 = 17.5

10x = 10*17.5= 175

2*17.5 - 30 = 35 - 30 = 5

Answer:

Area of the square: 36

Step-by-step explanation:

6.1+8.2+9.7=24. Squares have 4 sides so 24/4=6. Area= base times highet, Base=6 Highet=6. 6 times 6=36!

Answer:

A=36 cm²

Step-by-step explanation:

the perimeter of triangle=a+b+c

P=6.1+8.2+9.7

P= 24 cm

P of triangle = P of square ( square has 4 equal sides):

24=4a

a=24/4=6

Area of square : a²

A=6² = 36 cm²

Answer:

4 t shirts.

Step-by-step explanation:

Given that money available with Sam = $150

Price for pants = $90

Price of each t shirt = $12.50

To find:

How many t shirts can he expect to purchase?

Solution:

Price for 2 pants = $180 which is more than $150.

Therefore, he can not buy more than 1 pants.

The remaining amount after buying pants = $150 - $90 = $60

This amount will be used for buying t-shirts.

Number of t-shirts that can be bought:

\(\dfrac{60}{12.5} \approx 4.8\)

But answer in decimal points for number of t shirts is not possible and he does not have more money.

It means, he can buy at most 4 t-shirts.

The absolute increase is 900 people, and the relative (percent) increase is 27.27%.

We will first find the absolute increase and then the relative (percent) increase.
Absolute increase:
Subtract the initial population from the final population: 4200 (2009 population) - 3300 (2006 population)
Calculate the absolute increase: 4200 - 3300 = 900
Absolute increase:

900 people
Relative (percent) increase:
Calculate the absolute increase (which we found earlier): 900 people.

Divide the absolute increase by the initial population: 900 / 3300
Multiply the result by 100 to find the percentage: (900 / 3300) * 100
Calculate the relative (percent) increase: (900 / 3300) * 100 = 27.27%
Relative (percent) increase: 27.27%.

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Answer:

(-2, -4)

Step-by-step explanation:

Since both equations are equal to y, you can set them equal to each other:

\(\frac{3}{2}x-1=\frac{1}{2}x-3\)

Next, solve for x:

\(\frac{3}{2}x-1=\frac{1}{2}x-3\\x-1=-3\\x=-2\)

Finally, substitute the solution for x in one of the equations (or both) to find y:

\(y=\frac{3}{2}(-2)-1\\y=-3-1\\y=-4\)

\(y=\frac{1}{2}(-2)-3\\y=-1-3\\y=-4\)

Therefore, the solution to the system of equations is (-2, -4).

Expand the square. Remember that

(a - b)² = a² - 2ab + b²

With a = 5√3 and b = √27, we have

(5√3 - √27)² = (5√3)² - 2 (5√3) √27 + (√27)²

… = 25•3 - 10√81 + 27

… = 75 - 10√(9²) + 27

… = 102 - 10•9

… = 102 - 90

… = 12