Find the constant of proportionality (r) in the equation y=rx

Hello,

We have :

27 = 3³ = 3 × 3 × 3

[tex]x[/tex]³ = [tex]x[/tex] × [tex]x[/tex] × [tex]x[/tex]

So :

The cube root of 27[tex]x[/tex]³ is :

3 × [tex]x[/tex] = 3[tex]x[/tex]

(  because : (3[tex]x[/tex])³ = 27[tex]x[/tex]³ )

We have :

8 = 2³ = 2 × 2 × 2

So :

The cube root of 8 is : 2

[tex]a^{3} +b^{3} = (a+b)(a^{2} -ab+b^{2} )[/tex] with [tex]a=3x[/tex] and [tex]b=2[/tex]

We have :

[tex](3x)^{3}+2^{3}=(3x+2)((3x)^{2} -(3x)(2)+(2 )^{2} )[/tex]

Have a nice day :)

Answer:

soln,

set A ={ 1,2,3}

set B ={2,3}

9514 1404 393

Answer:

  4^4·6^5·7^7 = 1,639,390,814,208

Step-by-step explanation:

Taking the cube root multiplies each exponent by 1/3.

  ((4^12)(6^15)(7^21))^(1/3) = (4^(12/3))·(6^(15/3))·(7^(21/3)) = (4^4)(6^5)(7^7)

Answer:

Bro a normal speed of a human is 3km/hr

And I don't know the speed of jo

Because u haven't written full question

Step-by-step explanation:

Please Mark me brainliest

The common ratio of the geometric sequence is: B. r = 2/3.

The common ratio of a geometric sequence is determined by taking the last term and divide by the preceding term.

Given the geometric sequence, 6,4,8/3,16/9,..., the common ratio is calculated as follows:

16/9 ÷ 8/3 = 16/9 × 3/8 = 2/3 × 1/1 = 2/3

Or

8/3 ÷ 4 = 8/3 × 1/4 = 2/3

Or

4/6 = 2/3

Therefore, the common ratio of the geometric sequence is: B. r = 2/3.

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Answer:

50kg de café torrado

30kg de café arábico

Step-by-step explanation:

Queremos obtener un total de 80kg de café molido.

Se utilizarán:

Café arábico, que cuesta $18 el kg

Café torrado, que cuesta $10 el kg

Queremos que el precio, por kilo, de la mezcla de 80kg sea $13.

Ok, primero debemos definir las variables:

Definamos:

x = cantidad de café arábico usado

y = cantidad de café torrado usado.

Entonces, como la mezcla deberá tener 80kg en total, tenemos:

x + y = 80kg

Y el costo total de esta mezcla será:

x*$18 + y*$10

Si lo dividimos por el peso total, tendremos el costo por kilo, que es:

(x*$18 + y*$10)/80kg

Y queremos que esto sea igual a $13, entonces tenemos la ecuación

(x*$18 + y*$10)/80kg = $13

Ok, ahora tenemos dos ecuaciones, es decir, tenemos un sistema de ecuaciones:

x + y = 80kg

(x*$18 + y*$10) = $13*80kg

(donde reescribimos levemente la segunda ecuación)

Ok, para resolver este sistema trataremos de reemplazar variables, para ello, el primer paso es aislar una de las variables en una de las ecuaciones.

Aislemos x en la primera:

x = 80kg - y

Ahora reemplazamos esto en la otra ecuación:

(x*$18 + y*$10) = $13*80kg

(( 80kg - y)*$18 + y*$10) = $13*80kg

Ahora podemos resolver esto para la variable y:

$18*80kg - $18*y + $10*y = $13*80kg

$18*80kg - $13*80kg = $18*y - $10*y

($18 - $13)*80kg = ($18 - $10)*y

$5*80kg = $8*y

($5*80kg)/$8 = y

50kg = y

Se usan 50kg de café torrado.

y como:

x + y = 80kg

x = 80kg - y

x = 80kg - 50kg = 30kg

Entonces los 30kg restantes serán de café arábico.

y la estrategia utilizada fue el remplazo de variables.

Answer:

True

Step-by-step explanation:

This is the case when the result is True. The substituted variables in the argument must equal a conclusion that is also True. For example, if the premises are True, then the conclusion of the valid argument form needs to output a True conclusion as well. This makes the argument valid. Otherwise, the argument would be invalid if two True premises output a conclusion that is equal to False.

Answer:

x=13

y= -9

(13, -9)

Step-by-step explanation:

If we are solving using the substitution method, we can take the first equation and set it to y so y=4-x.

Then, we can take that equation and plug it into the bottom one so

3x+4(4-x)=3

Simplify:

3x+16-4x=3

-x=-13

x=13

We can then plug 13 into any of the two given equations (I am just going to plug it into the top one)

So, 13+y=4 which y= -9

Answer:

180

Step-by-step explanation:

Answer:

40/30

Step-by-step explanation:

Since tan∅= o/a, 40 is opposite, and 30 is adjacent to angle A, 40/30 is the ratio for tanA.

Answer:40/30

Step-by-step explanation:

....

Answer:

The minimum value of f(x) is greater than the minimum value of g(x).

Step-by-step explanation:

Given

[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)

[tex]g(x) = 4(x - 4)^2 + 3[/tex] --- g(x) equation

Required

Which of the options is true

First, we identify the vertex of g(x)

A quadratic function is represented as:

[tex]g(x) =a(x - h)^2 + k[/tex]

Where:

[tex](h,k) \to[/tex] vertex

So, we have:

[tex](h_2,k_2) = (4,3)[/tex]

[tex]a = 4[/tex]

If [tex]a>0[/tex], then the curve opens upward

From the question, we understand that f(x) also open upward. This means that both functions have a minimum

The minimum is the y (or k) coordinate

So, we have:

[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)

[tex](h_2,k_2) = (4,3)[/tex] --- vertex of g(x)

The minimum of both are:

[tex]Minimum = 4[/tex] ----  f(x)

[tex]Minimum = 3[/tex] ----  g(x)

By comparison:

[tex]4 > 3[/tex]

Hence, f(x) has a greater minimum

Answer:

The minimum value of f(x) is greater than the minimum value of g(x).

Step-by-step explanation:

Answer:Monday, Wednesday and Friday.

Step-by-step explanation:

It’s the other weekdays.

Yes

Replace x in the equation with the x in the solution and see if t equals the y in the solution:

Y = 7-5 = 2

The answer is yes.

Answer:

The surface area of the pyramid is 16.65 m^2.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Use the form asin(bx−c)+d

a=3

b=2

c=4

d=0

Phase Shift: c/b

Phase Shift: 4/2 = 2

Answer:

14 or 10.4

Step-by-step explanation:

I don’t really understand the question but here I go I’ll try;

The height is 4 and the width is 10, so I think it’s 14 or 10.4.

The Constant that relates the height and width is 5/2.

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Given:

we have the coordinates as (10, 4)

The coordinates shows that when the height of the rectangle is 4 unit then the width of the rectangle is 10.

Using Constant of Proportionality

y= k x

10 = k(4)

k = 10/ 4

k = 5/2

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1 and -1 are the only rational numbers which are their own reciprocal.[tex] \: [/tex]

Given:

The limit problem is:

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

It can be written as:

[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]

Applying limit, we get

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]

Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].

Hello!

8y + 3 > 15y + 52 <=>

<=> 8y - 15y > 52 - 3 <=>

<=> -7y > 52 - 3 <=>

<=> -7y > 49 <=>

<=> y < -7 => y ∈ { -∞; -7 }

Good luck! :)

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Explanation:

It might help to draw it out. See the diagram below.

The base is JK which is 7 units long. I'm picking this as the base because this segment is completely horizontal.

Notice how the base JK spans from x = -3 to x = 4, which we can use subtraction and absolute value to get |J-K| = |-3-4| = 7.

The height is always perpendicular to the base. If the base is JK = 7, then the height is the vertical distance from K (or J) to L. This vertical distance is also 7 units. Subtract the y coordinates and apply absolute value. The base and height aren't always the same number.

Now we can find the area of the triangle

area = base*height/2

area = 7*7/2

area = 49/2

area = 24.5 square units

Answer:

The slope is 9.

Step-by-step explanation:

Answer:

Slope = 9

Step-by-step explanation:

Slope intercept form is y = mx +b (where m is slope and b is y intercept).

Here, m= 9 (slope) and b=0 (y intercept)

Answer: B

Step-by-step explanation:

To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.

Equation 1: y=2|x+6|-4

Equation 2: y=6

Now, we can substitute.

2|x+6|-4=6

Let's solve for x.

2|x+6|-4=6        [add both sides by 4]

2|x+6|=10          [divide both sides by 2]

|x+6|=5              [subtract both sides by 6]

x=-1

Now that we know x=-1 is one of the solutions, we can eliminate C and D.

We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.

|x+6|=-5              [subtract both sides by 6]

x=-11

Therefore, we know that B is the correct answer.

Answer:

2/5√2

Step-by-step explanation:

2/√ 25 * 2

further:

ans (1/5)(√2)

Hi,

[tex]2\sqrt{50}\\\\=2\sqrt25*2}\\\\=2*5\sqrt{2}\\\\=10\sqrt{2}[/tex]

Answer:

18

Step-by-step explanation:

18

Answer:

I believe it would be 6.5184*10^-3

Step-by-step explanation:

If wrong please tell me

Answer:

see explanation

Step-by-step explanation:

Using the Pythagorean identity

cos²A + sin²A = 1 ( divide terms by cos²A )

[tex]\frac{cos^2A}{cos^2A}[/tex] + [tex]\frac{sin^2A}{cos^2A}[/tex] = [tex]\frac{1}{cos^2A}[/tex] , that is

1 + tan²A = sec²A ← as required

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute the 3

3(x) = 3x

3(1) = 3

We now have 45 = 3x + 3

Subtract 3 from both sides

45 - 3 = 42

3 - 3 cancels out

We now have 42 = 3x

Divide both sides by 3

42/3 = 14

3x / 3 = x

We're left with x = 14

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute

45 = 3x + 3

-3           -3

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

42 = 3x

----    ----

3       3

14   =  x

Answer:

4c+10t

Step-by-step explanation:

c= car

t= time/ hour

Answer:

Trey = 9 text messages

Rachel = 19 text messages

Juan = 57 text messages

Step-by-step explanation:

Let

Number of messages Trey sent = x

Number of messages Rachel sent = x + 10

Number of messages Juan sent = 3(x + 10)

Total messages = 85

Total = Trey + Rachel + Juan

85 = x + (x + 10) + 3(x + 10)

85 = x + x + 10 + 3x + 30

85 = 5x + 40

85 - 40 = 5x

45 = 5x

x = 45/5

x = 9

Number of messages Trey sent = x = 9 text messages

Number of messages Rachel sent = x + 10

= 9 + 10

= 19 text messages

Number of messages Juan sent = 3(x + 10)

= 3(9 + 10)

= 3(19)

= 57 text messages