The product of the polynomials (2ab + b) and (a2-b2) is _____.If this product is multiplied by (2a + b), the result is a polynomial with ____ terms.

      Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

Similar shapes are enlargements of each other using a scale factor.

All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

The scale factors for length, area and volume are not the same.

From the given diagram,

 Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

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The amount of the loan is $11000 (this is also called the principal)

the loan is for 5 years (so time is 5), and the annual interest reat is 6% (which in math form becomes: 0.06.

So, we use the formula for the Total value of the loan (also known as ACCRUED value), which is the following exponential function:

Here we replace: P (principal) with 11000

r with 0.06 (annual interest rate)

and t with 5 (number of years), and we get:

Therefore the total to be paid for the loan is $14720.48. Now, in order to find the amount to be paid per month during the 5 years of the loan, we reacall that there are 12 months in a year, therefore we are going to have 5 * 12 = 60 monthly loan payments to complete the total loan amount. Then each loan payment per month will be:

$14720.48 / 60 = $245.34

Answer:

3/5=0.6

_

4/9=0.4

_

11/12=0.916

Answer:

The Answer/Quotient is x+3

The number of fish food cubes that will fill the shipping box is: 2,340.

Volume of the Shipping Box:

Volume = 3.75 × 3 × 3.25 = 36.5625 ft³

Volume of the Fish Food Cube:

Volume = 0.25 × 0.25 × 0.25 = 0.015625 ft³

Number of Fish Food Cubes that will contain the shipping box:

= Volume of shipping box / volume of fish food cube

= 36.5625 / 0.015625

= 2,340 fish food cubes.

Therefore, the number of fish food cubes that will fill the shipping box is: 2,340.

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Answer:

i cant understans the quedtoion its worng bro

Answer:

Step-by-step explanation:

total sum of Triangle's angles is 180 deg:

than: x = 180 -61-56 = 63

Answer:

63 degrees

Step-by-step explanation:

All three angles in a triangle is always 180, so 180-61-56=63 degrees

Please mark Brainliest.

Have a great weekend!

Step-by-step explanation:

f(x) = 3√x /4

x=0 => y = 0

x=1 => y = 0.75

x=4 => y = 1.5 ==> (4, 1.5)

x=16=>y= 3

the right answer is the second graph

Answer:

\(x=5\)

Step-by-step explanation:

The perimeter of a figure is the sum of all its sides.

The sides are x, (x+3), and (2x). The perimeter is 23, so the sum of the expression equates to 23. Thus:

\(x+(x+3)+(2x)=23\)

Combine like terms:

\(4x+3=23\)

Subtract 3 from both sides:

\(4x=20\)

Divide both sides by 4:"

\(x=5\)

And we're done!

The right answer is No solution.

Look at the attached picture

Hope it will help you

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Answer:

The center is ( -2, 7) and the radius is 6

Step-by-step explanation:

A circle is written in the form

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x+2)^2+(y-7)^2=36

(x -  -2)^2+(y-7)^2=6^2

The center is ( -2, 7) and the radius is 6

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

Answer: i think 16

Step-by-step explanation:

Answer:

\(\alpha = 35º\)

Step-by-step explanation:

Primeiro, vamos dizer que essa folha tem extremidades nos pontos \(A, B, C, D\).

E vamos chamar os vértices do triângulo que contém o ângulo \(\alpha\) de \(E, F, G\).

Na semireta de baixo, formada por \(DC\), a gente tem um ângulo de \(70º\) e um outro ângulo de \(90º\) (porque ele indica um ângulo reto).

Vamos dizer que estes dois ângulos se encontram no ponto \(E\), que combinamos antes, como vértice (extremidade) do triângulo de cima.

Como os dois ângulos, estão num mesmo ponto, \(E\), podemos dizer que existe um terceiro ângulo para o qual sua soma seja \(180º\). E tem, seria o ângulo à esquerda de

Vamos chamar este ângulo de \(\beta _{I}\). Portanto:

\(\beta _{I} + 90º + 70º = 180º\\\beta _{I} = 180º - 160º\\\beta _{I} = 20º\)

Agora, temos um outro triângulo no canto inferior esquerdo da folha, cujos ângulos são \(\beta x_{I}\), \(90º\) e um outro ângulo, que vamos chamar de \(\beta x_{II}\)

Esse último vai ser o ângulo superior deste triângulo, tá legal?

Então, vamos ter que:

\(\beta _{I} + 90º + \beta _{II} = 180º\\\beta _{I} + \beta _{II} = 90º\\\)

Como \(\beta _{I} = 20º\),

\(\beta _{I} + \beta _{II} =20º + \beta _{II}\)

\(20º + \beta _{II} = 90º\\\beta _{II} = 90º - 20º\\\beta _{II} = 70º\)

Ou seja, o ângulo superior do triângulo no canto inferior esquerdo, é 70º.

Vamos concordar, que este mesmo triângulo tem vértices nos pontos \(F, D, E\). Onde \(F\) é o ponto superior, \(D\) é a extremidade inferior esquerda do retângulo e \(E\) é aquele mesmo ponto em que se encontram os ângulos de \(90º\)e \(70º\).

Mais à frente, você vai entender o porquê é importante nomear estes pontos, eu fiquei 40 minutos tentando fazer essa questão sem fazer isso e  não conseguia porque empacava numa parte da resolução.

Então, agora, sabemos que o ângulo \(\beta _{II}\), que é o encontro dos seguimentos \(FD\) e \(EF\) vale \(70º\).

Até aqui, foi só aplicar propriedades. Mas, a partir desse ponto, você vai precisar usar a criatividade.

Então, você entende que o ângulo \(\beta _{II}\) está inserido numa reta com outros dois ângulos concentrados no ponto \(F\).

Então, pode dizer que esse ângulo externo é o suplemento de \(\beta _{II}\).

Vamos chamar todo ele de \(\beta _{III}\)

\(\beta _{II} + \beta _{III} = 180º\\70º + \beta _{III} = 180º\\\beta _{III} = 180º - 70º\\\beta _{III} = 110º\)

Agora, vamos elevar o nível de criatividade no raciocínio e ver também que temos um quadrilátero formado pelos pontos \(A, G, F, E\)

A soma dos ângulos de qualquer quadrilátero é 360º.

E temos que esse mesmo quadrilátero é formado por dois ângulos retos, além do ângulo de 110º que calculamos.

A última extremidade que falta é um ângulo formado pela soma de \(\alpha\) a um outro ângulo, que vamos chamar de \(\beta _{IV}\).

Então, temos que:

\(90º + 110º + 90º + \alpha + \beta _{IV} = 360º\\\alpha + \beta _{IV} +290º = 360º\\\alpha + \beta _{IV} = 360º + 290º\\\alpha + \beta _{IV} = 70º\\\)

De todas, as etapas dessa resolução essa é a mais importante de entendermos os pontos que definimos. Eu refiz ela várias vezes porque não fiz isso antes.

Mas, veja, quando a gente dobra a folha, pegamos um formato qualquer e destacamos do resto dela.

Isso quer dizer que o formato que ficou dobrado é o mesmo que falta na folha. Do contrário, estaríamos criando folha ou excluindo matéria, o que não é possível no caso de uma simples dobra.

Em outras palavras, os triângulos \(AGF\) e \(EFG\) são os mesmos. (Eu recomendo que você construa esse desenho e coloque as letras em cada ponto, pra visualizar melhor.)

Isso é o mesmo que dizer que os ângulos de um vão ser os ângulos do outro.

Portanto, os ângulos são equivalentes. (Mesmos ângulos para ambos os triângulos, mudando só de posição.)

Assim, você pode afirmar que \(\alpha\) = \(\beta _{IV}\)

Se subirmos um pouco a resolução, vamos lembrar que encontramos que \(\alpha + \beta _{IV} = 70º\\\)

Se \(\alpha = \beta _{IV}\)

Temos:

\(\alpha + \alpha = 70º\\2\alpha = 70º\\\alpha = \frac{70º}{2} \\\)

e TCHARAAN!

\(\alpha = 35º\)

-------------------------

Força, guerreiro(a). Sucesso e que Deus te abençoe nos estudos.

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

12 girls

28 boys

Step-by-step explanation:

Multiply 40 by 30/100 to get 12 girls.

Subtract 12 from 40 to get 28 boys.

The book has a lower cost per minute than the movie.

To find the cost per minute of the book, we divide the cost by the number of minutes:

cost per minute of book = $15 / 200 minutes = $0.075 per minute

To find the cost per minute of the movie, we need to convert the time to minutes.

2 hours and 39 minutes is equal to:

2 hours x 60 minutes/hour = 120 minutes

39 minutes = 39 minutes

Total minutes = 120 + 39 = 159 minutes

cost per minute of movie = $14 / 159 minutes = $0.088 per minute

Therefore, the book has a lower cost per minute than the movie.

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.

A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.

To create a whisker plot, follow these steps:

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Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 144 millimeters, and a variance of 49.

This means that \(\mu = 144, \sigma = \sqrt{49} = 7\)

Sample of 46:

This means that \(n = 46, s = \frac{7}{\sqrt{46}}\)

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}\)

\(Z = -1.94\)

\(Z = -1.94\) has a p-value of 0.0262

2*0.0262 = 0.0524

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

2

Step-by-step explanation:

29 % 3 = 9

3x9 = 27

29 - 27 = 2

Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

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Answer:

3003 ways

Step-by-step explanation:

We are in a combination or permutation exercise, the difference between them is if the order matters (permutations) or does not matter (combinations),

in this case the order does not matter, since they only ask us for the ways to choose 10 of 15 roller coasters, therefore it would be a combination:

nCr = n! / (r! * (n-r)!

we know that n = 15 and r = 10, we replace:

15C10 = 15! / (10! * (15-10)!

15C10 = 3003

In other words, there are 3003 ways to choose 10 of the 15.

Answer:

x < -3

Step-by-step explanation:

x + 6 < 3

Subtract 6 from both sides

x + 6 - 6 < 3 - 6

x < -3

If you need to graph it on a number line, you need a open circle over the -3 with an arrow pointing left <---------