a. Explain why the area of the large rectangle is 2a + 3a + 4a.
b. Explain why the area of the large rectangle is (2 + 3 + 4)a.

Answer:

the - are the x or y

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf f(2) = 8}\)

Step-by-step explanation:

\(\sf Given \ that \ f(x) = 3x + 2 \\\\Put \ x = 2 \\\\f(2) = 3(2) + 2\\\\f(2) = 6+2\\\\\bold{f(2) = 8}\\\\\rule[225]{224}{2}\)

Hope this helped!

The required result of the identity is \(x^{2} =-y^{2}-2x+16y-56\).

To isolate the algebraic expression given below we need to simplify it and then make \(x^{2}\) the subject of the equation,

For that we must know the identity \((a+b)^{2}=a^{2}+2ab+b^{2}\).

We will break the given equation on the basis of the given identity.

Now, \((x+1)^{2} +(y-8)^{2}=9\\\)

     ⇒\(x^{2} +2x+1+y^{2}-16y+64=9\\\)

     ⇒ \(x^{2} =-y^{2}-2x+16y-56\)

So, the required result of isolating the above given equation is as above.

The correct answer is option B.

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Considering the vertical asymptote and the intercepts, the rational function is given by:

\(r(x) = \frac{4(x - 2)}{(x + 2)(x - 4)}\)

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

From the graph, there are vertical asymptotes at x = -2 and x = 4, hence the denominator is given by:

(x + 2)(x - 4).

The x-intercept of a function f(x) is the value of x when y = 0. For a rational function, they are the zeroes of the denominator.

For this problem, there is a x-intercept at x = 2, hence the numerator is given by:

a(x - 2).

Then the function is:

\(r(x) = \frac{a(x - 2)}{(x + 2)(x - 4)}\)

When x = 0, r(x) = 1, hence we use it to find a.

-2a/-8= 1

2a/8 = 1

2a = 8

a = 4.

Hence the function with the leading coefficient is:

\(r(x) = \frac{4(x - 2)}{(x + 2)(x - 4)}\)

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Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

Answer:

\( \frac{29}{2} \)

Answer:

so I dont understand Spanish sorry I just need the points ㅠㅠ

Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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Answer: x= 3π/2

Hope this helps.... Stay safe and have a great rest of the weekend!!! :D

The rate at which a particular animal grows is proportional to the difference between its adult height and current height. As the animal grows, the difference between the adult height and current height decreases. T

Therefore the rate of growth decreases. This is because, as the animal grows, it reaches a point where it cannot grow any taller and the rate of growth slows down. In other words, the rate of growth is proportional to the difference between the adult's height and current height. the rate of growth is also related to the age of the animal.

Younger animals tend to grow faster than older animals because their adult height is still far away, so the difference between their current height and adult height is greater.As the animal gets older and closer to its adult height, the rate of growth decreases.

furthermore, the rate of growth is also affected by the animal's diet and overall health. If the animal is malnourished or unhealthy, then its rate of growth will be slower than if it had a healthy diet and lifestyle. In conclusion, the rate of growth of  a particular animal is proportional to the difference between its adult height and current height

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Answer:

26y

Step-by-step explanation:

26y and 52y.

13*2*y and 13*2*2 *y

Common is 13*2*y

or 26y

Hope this helps!

Answer:

\(\displaystyle \frac{7}{3-15i}=\frac{7}{78}+\frac{35}{78}i\)

Step-by-step explanation:

\(\displaystyle \frac{7}{3-15i}\\\\\frac{7}{3-15i}*\frac{3+15i}{3+15i}\\\\\frac{21+105i}{9-225i^2}\\\\\frac{21+105i}{9+225}\\\\\frac{21+105i}{234}\\\\\frac{21}{234}+\frac{105}{234}i\\ \\\frac{7}{78}+\frac{35}{78}i\)

We can see that, when the input is 5, the output is 24.

Here we have the equation:

\(y = x^2 - 1\)

Where y is the output and x is the input.

We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:

\(y = 5^2 - 1 = 24\)

Then we can see that, when the input is 5, the output is 24.

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Showing that this need not be true if f is continuous but not uniformly continuous.

Given :

let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).

( 1 )

If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,

then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,

then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.

( 2 )

Let E = {1, 1/2, 1/3, · ·  } and f(1/n) = 1 is n is odd, f(1/n) = −1 if

n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the

sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.

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Answer:

S=9

Step-by-step explanation:

10\(\frac{1}{2}\) - 1\(\frac{1}{2}\) = 9

Answer:

s=9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

s+3/2=21/2

Step 2: Subtract 3/2 from both sides.

s+3/2−3/2=21/2−3/2

s=9

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

Step-by-step explanation:

\(\frac{3x^4}{(\frac{1}{x^2})^2} \\= 3x^8\)

Answer:

\(3x^{8}\)

Step-by-step explanation:

\((x^{-2})^{2}\) is equal to \(x^{-4}\). Whenever an x has a negative exponent, it means that you can put it to the other side, whether it be from denominator to numerator or numerator to denominator. In this case, because it is in the bottom it goes from denominator to numerator. You will end up with something like \(3x^{4} x^{4}\) but you can add the X's and end up with the answer.

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

65

Step-by-step explanation:

Answer: 65

Step-by-step explanation:

x = -2

6(8-(-2))+5

6(10)+5

60+5

65

Answer:

blue line: 20

black line: -20

Step-by-step explanation:

use rise (y) over run (x)! as the blue line goes from points (8,80) to (9,100) the difference in the x or run is 1 while the difference in the y or rise is 20 which makes it 20/1 = 20. for the black line, because it's going down it indicates it will be a negative slope, use the same trick as last time, our first point is (5,20) and our next point is (6,0) the difference in x is 1 and the difference in y is -20, so -20/1 = -20! hope this helped :-)

Answer:

A) Q(t) = 4e^-(0.0079t)

B) t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Step-by-step explanation:

a)

to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.

so given that; half-life of ²³⁸Pu is 87.7 years,

∴ t =  87.7 years , Q(t) = 0.5Q₀

Now we substitute these value in the form  Q(t)= Q₀e⁻^kt

Q(t)= Q₀e⁻^kt

0.5Q₀ = Q₀e^ -(87.7k)

0.5 = e^ -(87.7k)

now we take the natural logarithm of both sides

In(0.5) = Ine^ -(87.7k)

Now using the property logₙnᵃ = a

-87.7k = In(0.5)

k = - In(0.5) / 87.7

k = 0.0079

ALSO it was given that Q₀ = 4.0 kg

Therefore , model quality Q(t) of ²³⁸pu left after t years is:

Q(t) = 4e^-(0.0079t)

b)

to find the time left after 1.6kg of ²³⁸pu

we simple substitute  Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)

so we have

1.6 = 4e^-(0.0079t)

e^-(0.0079t) = 1.6/4

e^-(0.0079t) = 0.4

again we take the natural logarithm of both sides,

Ine^-(0.0079t) = In(0.4)

again using the property logₙnᵃ = a

-0.0079t = In(0.4)

t = - in(0.4) / 0.0079

t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Answer:

if we take the number of quarters Barrett have to be x we know Penelope has twice that ie 2x. so in total they have 2x+x = 60, 3x = 60; so x= 60/3 = 20.

Barrett has 20 quarters.

Responder:

Explicación paso a paso:

De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...

Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.

El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;

a es el primer término

n es el número de términos es la diferencia común

De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2

Tₙ = 4+ (n-1) 2

abre el paréntesis

Tₙ = 4 + 2n-2

Tₙ = 2n + 4-2

Tₙ = 2n + 2

Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2

Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Step-by-step explanation:

In a circle

Diameter (d) = 22 cm

radius (r) = d / 2 = 22 /2 = 11 cm

Hope it will help :)

Answer:

11 1/2 years old

Step-by-step explanation:

Let Amanda's age be a.

Let the company's age be c.

The company is 24 years older than Amanda. This means that:

c = 24 + a ______(1)

The sum of Amanda's age and the company's age is 121 years. This means that:

c + a = 121 ________(2)

Put (1) in (2):

24 + a + a = 121

2a = 121 - 24

2a = 97

a = 97 / 2 = 48 1/2 years

She has been there for 37 years, therefore, her age when she started working there is:

48 1/2 - 37 = 11 1/2 years old

NOTE: This age doesn't seem right but I worked based on the parameters given.

Answer:

b

Step-by-step explanation:

the square root of 9 is 3 because 3*3=9

3+6=9

Answer:

a)10

Step-by-step explanation: