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The functions are arranged/combined as follows

21. 595

22. 6a² + 25ab - 3b² + 6

23. 2b - 2

24. 7x² - 5xy + y²

25. 3x - 24y - 4

Descending powers involves making the highest power to be the first term

The equations are solved one after the other as follows

21.

720 + 40 - 60 - 120 + 15 = 595

22.

25ab + 6a² - 3b² + 6 =

6a² + 25ab - 3b² + 6

23.

= 3a + 2b - 3a + 1 - 3

= 3a - 3a + 2b + 1 - 3

= 2b - 2

24.

= 3x² - 2xy + 4x² - 3xy + y²

= 7x² - 5xy + y²

25.

= 2x + x + 25y - y - 4

= 3x - 24y - 4

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The property listed in the first column of the table by filling in the box in the second column of the table with an equivalent expression are: 1. Commutative Property of Addition 2. Additive Identity Property of Zero 3. Multiplicative Identity Property of One.

An expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value or quantity and can be evaluated or simplified to a single value or another expression. Expressions can contain constants, which are fixed values, such as the number 5 or the symbol π, or variables, which are symbols that represent varying values, such as x or y.

Here,

Commutative Property of Addition: The order in which two numbers are added does not change the result.

For example:

g + h = h + g

Additive Identity Property of Zero: Adding zero to any number does not change the value of the number.

For example:

n + 34 = n

Multiplicative Identity Property of One: Multiplying any number by one does not change the value of the number.

For example:

S * 1 = S

Commutative Property of Multiplication: The order in which two numbers are multiplied does not change the result.

For example:

b * x * 1 = x * b * 1

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Answer:

what are the coordinator position y

Answer:

y = 5x - 21

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 4 ) and (x₂, y₂ ) = (8, 19 )

m = [tex]\frac{19-4}{8-5}[/tex] = [tex]\frac{15}{3}[/tex] = 5 , then

y = 5x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 4 ) , then

4 = 5(5) + c = 25 + c ( subtract 25 from both sides )

- 21 = c

y = 5x - 21 ← equation of line

The exponential regression equation that fits the given data points is y = [tex]4*3^(x-1).[/tex]

The exponential regression equation that fits these data is y = 4*3^(x-1). To calculate this, we need to first calculate the parameters a and b for the equation y = a*b^x. We can do this by finding the natural logarithm (ln) of both sides of the equation.

ln(y) = ln(a*b^x)

ln(y) = ln(a) + ln(b^x)

ln(y) = ln(a) + x*ln(b)

We can now calculate the parameters a and b by plotting the points (x, ln(y)) and performing a linear regression on the points.

ln(4) = 0.602

ln(8) = 2.079

ln(27) = 3.526

ln(85) = 4.443

ln(250) = 5.52

ln(600) = 6.398

The linear regression equation is ln(y) = 0.175x + 0.602. We can now solve for the parameters a and b by using the linear regression equation.

ln(a) = 0.602

a = e^0.602

a = 4

ln(b) = 0.175

b = e^0.175

b = 3

Therefore, the exponential regression equation that fits these data is y = 4*3^(x-1).

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The answer to this question is that it depends. The distance of Ken’s house from the park cannot be determined without knowing the distance of the school and the pet shop from the park, and other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park.

Distance is the amount of space between two points. It is a physical quantity that can be measured in various units such as meters, kilometers, miles and light-years. Distance can be calculated using the formula d = s × t, where d is the distance, s is the speed, and t is the time.

Ken lives at a point between the school and the pet shop, so it is impossible to answer this question without knowing how far away the school and the pet shop are from the park. If the park is close to the school or the pet shop, then Ken’s house would be close to the park, but if the park is further away from the school or the pet shop, then Ken’s house would be further away from the park. Therefore, the distance of Ken’s house from the park cannot be determined unless the distances of the school and the pet shop from the park are known.

In addition, other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park. For example, if there is a hilly terrain between Ken’s house and the park, then the distance between them may be greater than if the terrain were flat.

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The expression which represents the number of pieces of candy left with Jodie is given by c - 11 .

Original number of pieces of candy with Jodie is equal to 'c'.

Number of pieces of candy Jodie gives away is equal to 11.

Expression used to represents the number of pieces of candy left with Jodie is written as,

Subtract 11 from the original number of candy

= ( c  - 11 )

Therefore, the representation of the expression for number of pieces of candy left with Jodie after she gives away 11 candy is equal to ( c - 11 ).

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The difference is not constant, the sequence is not arithmetic.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed constant value (known as the common difference). A constant rate of change is modelled by arithmetic sequences in fields like engineering, physics, and financial computations.

For the given series we need to determine if the sequence is arithmetic, by checking difference between consecutive terms is constant.

9 - 7 = 2

12 - 9 = 3

16 - 12 = 4

Since the difference is not constant, the sequence is not arithmetic.

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The top of the ladder is sliding down the wall at the rate of 1.5 ft/s.

Given: A ladder is 25 ft long and is leaning against the wall of a house.

The base of the ladder is sliding away from the house at the rate of 2 ft/sec.

Asked: How fast is the top of the ladder sliding down the wall when its base is 15 feet from the wall?

Let the distance of the top of the ladder from the wall be x ft.

Then we have,

x² + y² = 25² (by Pythagoras theorem)

Differentiating both sides with respect to time t,

we get, 2x(dx/dt) + 2y(dy/dt) = 0 ...(1)

Given dx/dt = 2, and x = 15 ft.

⇒ 2(15)(dx/dt) + 2y(dy/dt) = 0

⇒ 30 × 2 + 2y(dy/dt) = 0 (substituting the given values)

⇒ 2y(dy/dt) = - 60⇒ dy/dt = - 30/ y

The negative sign indicates that y is decreasing (getting smaller) with time.

The values of y are negative because it lies below the level of the ground.

Substituting the value of x = 15 in the equation x² + y² = 25², we get

15² + y² = 25²

⇒ y² = 25² - 15² = 400

⇒ y = - 20

Substituting the values of dy/dt and y in the above equation, we get,

dy/dt = - 30/ (- 20)

dy/dt = 1.5 ft/s

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Answer:

plot the point at 1

Step-by-step explanation:

Answer:

(1,0)

Step-by-step explanation:

S = (-7,0)

T = (3,0)

W = (x,0)

Answer: The answer is 3

Step-by-step explanation:

3x+1 take one minus one.
3x1-1 1-1 for exponents value becomes 0
3x0 for every term 0 is = to one in a exponent value so it become 3x1
3x1 = 3
So the answer is 3..

Step-by-step explanation:

In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. The problemproblm has been shown to be a computationally unsolvable problem.

The expressiοn calculates the tοtal cοst οf membership and game dοwnlοads. Sο, the cοrrect οptiοn is (C) 2n + 4.99.

Algebraic expressiοns can include οne οr mοre variables, which are typically represented by letters, such as x, y, οr z. These variables can be used tο represent unknοwn quantities οr tο express relatiοnships between different quantities in a prοblem.

Algebraic expressiοns can alsο include cοnstants, which are fixed numbers, and cοefficients, which are the numbers that multiply the variables in the expressiοn. Fοr example, in the algebraic expressiοn 3x + 2y, the cοnstants are 3 and 2, and the cοefficients are 3 and 2, respectively.

The given prοblem describes twο different charges: a οne-time charge οf $200 tο dοwnlοad a digital sοng, and a membership fee οf $4.99 that must be paid regardless οf hοw many sοngs οr games are dοwnlοaded. Additiοnally, fοr dοwnlοading games, there is a charge οf $2.00 per game.

Therefοre, the tοtal cοst in dοllars tο jοin the streaming service and dοwnlοad games can be represented by the expressiοn:

2n + 200 + 4.99

Here, "n" represents the number οf games dοwnlοaded, and the expressiοn calculates the tοtal cοst οf membership and game dοwnlοads.

Sο, the cοrrect οptiοn is (C) 2n + 4.99.

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Machines A and B worked for 66 minutes and 6 seconds.

An inequality is a mathematical statement that compares two quantities using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequalities can be solved just like equations, with the goal of finding the set of values that satisfy the inequality.

Here we have

Machine A can pack 8 boxes per​ minute, and Machine B can pack 11 boxes per minute.

Let Machines A and B work for 'x' minutes

Number of boxes packed by Machine A = 8x

Number of boxes packed by Machine B = 11x

The difference between the number of boxes that Machine B has packed and the number of boxes that Machine A has packed is less than 200.

=> | 11x - 8x| < 200

=> 3x < 200

Divide by 3 into both sides

=> 3x/3 < 200/3

=> x < 66.67

=> x < 66.6

Therefore,

Machines A and B worked for 66 minutes and 6 seconds.

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Answer: a rational number

the total number of people who know about the proposal 5 days after it was announced is 810.

The term [tex]3^ (t-1)[/tex] represents the number of people who find out about the proposal on day t, which is equal to three times the number of people who knew about it on the previous day. The initial value of 10 represents the number of people who knew about the proposal on the first day.

For example, if we want to find out how many people know about the proposal 5 days after the celebrity proposes, we can plug t=5 into the formula:

N(5) =[tex]10* 3^(5-1)[/tex] = [tex]10*3^4[/tex] = [tex]10*81[/tex] = 810

So the total number of people who know about the proposal 5 days after it was announced is 810.

the complete question is :

Assuming that the 10 people who know about the proposal on the first day do not forget or tell anyone else, we can use the following function to calculate the total number of people who know about the proposal t days after the celebrity proposes:

N(t) = [tex]10 * 3^(t-1)[/tex]

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follow the steps in the picture above

Step-by-step explanation:

look the ans it will make you clear about substitution method clear

After translatiοn, the cοrrect answer is B' (x+2, y+6).

The cοοrdinate after reflectiοn is (3,2).

The translatiοn rule that describes the result οf cοmpοsitiοn is (x, y) →(x-1, y-6).

Transfοrmatiοns in a triangle refer tο changes that can be made tο the shape, size, pοsitiοn, οr οrientatiοn οf the triangle οn a cοοrdinate plane. The three main types οf transfοrmatiοns that can be applied tο a triangle are:

Translatiοn: This transfοrmatiοn invοlves mοving the entire triangle tο a new pοsitiοn οn the cοοrdinate plane withοut changing its size οr shape.

Rοtatiοn: This transfοrmatiοn invοlves rοtating the entire triangle arοund a fixed pοint οn the cοοrdinate plane. The fixed pοint is called the center οf rοtatiοn, and the angle οf rοtatiοn determines the amοunt οf turn.

Scaling: This transfοrmatiοn invοlves changing the size οf the triangle by multiplying the x and y cοοrdinates οf each vertex by a fixed factοr.

1) Applying the translatiοn οf (x-2, y+3) tο pοint B(4,3) wοuld result in: B' = (4 + (x-2), 3 + (y+3)) = (x+2, y+6)

Therefοre, the cοrrect answer is B' (x+2, y+6)

2) Reflecting pοint G(3,-2) acrοss the x-axis results in the y-cοοrdinate being negated, and the x-cοοrdinate remains the same. Therefοre, the cοοrdinates οf the reflected pοint wοuld be G(3, 2).

The cοrrect answer is (3,2).

3) Tο determine the cοmpοsitiοn οf (x, y) → (x+4, y⁻¹) and (x, y) →(x-5, y⁻⁵), we need tο apply them in οrder. Firstly, (x, y) → (x+4, y-1) is applied tο pοint (x,y), which results in:(x, y)→ (x+4, y-1)

Next, (x, y) → (x-5, y-5) is applied tο the result frοm the previοus transfοrmatiοn (x+4, y-1), which results in:(x+4, y-1)→(x-1, y-6)

Therefore, the correct answer is (x, y) →(x-1, y-6).

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Answer: 61 N

Step-by-step explanation:

18+15+28=61

By the Definition of congruent property, we have proved that:

VW ≅ VX

Congruent Property:

The three properties of congruence are the reflexive property of congruence, the symmetric property of congruence and the transitive property of congruence. These properties can be applied to line segments, angles, triangles, or any other shape.

Given: VZ ≅ VY and WY ≅ XZ

Prove:  VW ≅ VX

Proof:

(Given): VZ ≅ VY and WY ≅ XZ

By the Definition of Congruent Substitute:

VZ = VY and WY = XZ

⇒ VZ = VX + XZ , and,

    VY = VW + WY

By Substituting  

VX + XZ = VW + WY

Again,

VX + WY = VW + WY

Now,

By Subtraction property of Equality

VX = VW  

VW = VX (Definition of congruent property.)

Complete Question:

IF VZ congruent of VY and WY congruent of XZ. Prove that VW is Congruent of VX.

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The answer of the given question based on finding  the area of the shaded sectors the answer is  approximately 18.8 + 4.2 = 23.0 square units.

An angle is geometric figure formed by the two rays or lines that share common endpoint, called  vertex. The rays or lines are often referred to as arms or sides of angle

We need to know the central angles of each sector. We can find these angles by using the formula:

angle = (arc length / radius) * (180/π)

where π is pi, approximately equal to 3.14.

Therefore, we can use trigonometry to find angle EOB:

sin(EOB) = EB/OA

sin(EOB) = 10.4/8

EOB = sin^-1(10.4/8)

EOB ≈ 56.7° degrees

Since angle EOA is a right angle, we know that angle AOB is 90° degrees, so angle AOE is 90 - EOB = 33.3° degrees.

Now, we can find the area of each sector using the formula:

area = (angle/360) * π * r²

Area of shaded sector ADE:

angle AOE = 33.3° degrees

radius = OA = 8

area = (33.3/360) * π * 8²

area ≈ 18.8 square units

Area of shaded sector EBC:

angle EOB = 56.7° degrees

radius = EB/2 = 5.2

area = (56.7/360) * π * 5.2²

area ≈ 4.2 square units

Therefore, the total area of the shaded sectors is approximately 18.8 + 4.2 = 23.0 square units.

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a. The triangle can be sketched as shown in the attached image.

b.  The side length OE is 4√11 inches

c. The measure of ∠G is 27.82°

a. The triangle can be sketched as shown in the attached image.

b. We can use Pythagoras theorem  to calculate the side length OE. That is:

OE = √(15² - 7²)

OE = 4√11 inches

c. Using trig. ratio:

sin G = (4√11)/15    (opposite/hypotenuse)

sin G = 0.8844

G =  sin⁻¹ (0.8844)

G = 27.82°

Thus, the measure of ∠G is 27.82°

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A. Please see attached photo for diagram

B. The length of side OE is 13 inches

C. The measure of  of angle G, ∠G is 62°

We can obtain the the length of OE by using Pythagoras theorem as shown below:

OE² = OG² - GE²

OE² = 15² - 7²

OE² = 225 - 49

OE² = 176

Take the square root of both sides

OE = √176

OE = 13 inches

Thus, the length of OE is 13 inches

The value of angle G, ∠G can be obtained as follow:

Cos G = Adjacent / Hypothenuse

Cos G = 7 / 15

Cos G = 0.4667

Take the inverse of Cos

G = Cos⁻¹ 0.4667

G = 62°

Thus, angle G is 62°

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a)  These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test.

The arithmetic calculations and statistical procedures for (a) the test of homogeneity and (b) the test of independence are not the same. They are different from each other. These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test. This is because they deal with different types of data. Below are the examples of a research question that would require a test of homogeneity and an example that would require a test of independence. These examples show the distinguishing characteristics that are involved in each of these tests. Research question that would require a test of homogeneity: A researcher would like to determine whether there is any significant difference between the proportions of men and women who voted for the two main political parties in an election. The research question can be framed as follows: Are the proportions of men and women who voted for the two main political parties homogenous or different? Assumptions: Samples are independent, observations are nominal or categorical, and the variable of interest has more than two categories (i.e., nominal or ordinal).Test of homogeneity:It is used to determine whether two or more populations have the same proportion or distribution of a nominal or categorical variable.Example that would require a test of independence:A researcher is interested in knowing whether there is any relationship between gender and drug addiction among high school students in a particular area. The research question can be framed as follows: Is there a relationship between gender and drug addiction among high school students?Assumptions:Samples are independent, observations are nominal or categorical, and the variable of interest has only two categories (i.e., nominal).Test of independence: It is used to determine whether there is any relationship between two nominal or categorical variables.

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Answer:

Approximately 4 cm

Step-by-step explanation:

Old mirror's area = S X S = 7 x 7 = 49cm2

Area of old mirror = Area of new mirror
49 = πr2

49 = 22/7 * r2

[tex]\frac{49 * 7}{22}[/tex] = r2

[tex]\frac{343}{22}[/tex] = r2

15.5909 = r2

r = [tex]\sqrt{15.5909}[/tex]
r = 3.948 cm  = approx. 4cm

Hope it helps.

Answer: So,

If we add them together, we get

5 + 3 + 4 + 1 = 13

Since there are 4 blue chips, the probability would be 4 out of the total number of chips, or 4/13.

Step-by-step explanation: Hope this helps! <3

Answer:

  9

Step-by-step explanation:

You want the value of the constant 'a' in the solution y=√(a+b·cos(πx)) to the differential equation y'=3sin(πx)/(2y) with initial condition y(1/2) = 3.

Substitute the initial condition into the equation for y:

  y = 3 . . . . when x = 1/2

  y = √(a +b·cos(πx))

  3 = √(a +b·cos(π/2)) = √a

  3² = a = 9

The value of a is 9.

__

Additional comment

The value of 'b' is -3/π.

It can be found by putting the equation for y in the original differential equation, and solving for b.

A cat would probably have consumed about 6 meals if its activity level had been around 9.

A linear equation is a relation between two variables in which one is dependent on the other in such a manner that changing one of the variables causes the change in another variable "linearly".

The above statement can be represented mathematically as,

y=mx+b

where m represents the rate of the change and c is the initial value of the equation.

Let x stand for activity level and y for the number of meals consumed. Therefore:

y = 0.23x + 4.1

For an activity level of 9, we will put x as 9:

y = 0.23(9) + 4.1 = 6.17

Thereby, we can say that If a cat had an activity level of about 9, then it's likely to have eaten about 6 meals.

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