If the volume of a cube increases at rate of 3 cm^3/sec what is the rate of increase of the length of its side ?

Answer:5

Step-by-step explanation:

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

From the question, we are to order the equations from least to greatest by the value of the slope

The given equations are

y = (-3/4)x + 2

3x - 4y = 7

y = 12(x - 19) + 5

y - 3 = 1/2(x - 4)

To determine the slopes of the line, we will compare the equations to the general form of the equation of a line

The general form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = -3/4

∴ Slope = -3/4

First, rearrange

3x - 7 = 4y

4y = 3x - 7

y = (3/4)x - 7/4

By comparison,

m = 3/4

∴ Slope = 3/4

First, simplify

y = 12x - 228 + 5

y = 12x - 223

By comparison,

m = 12

∴ Slope = 12

y - 3 = 1/2(x - 4)

First, simplify

y - 3= (1/2)x - 2

y = (1/2)x -2 + 3

y = (1/2)x + 1

By comparison,

m = 1/2

∴ Slope = 1/2

Now,

The slopes ordered from the least to greatest is

-3/4 < 1/2 < 3/4 < 12

Thus,

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

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Answer:

Simplify the expression, Your answer would be :

Step-by-step explanation:

And to find the Value of the following expression, Your answer would be :

hopefully this helps you ! ~

Raíz cuadrada de 864

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

The general equation of ellipse is given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , where, a is length of semi-major axis and b is length of semi-minor axis.

centro: (0,0)

focus : (0, -√28) , (0, √28)

eje conjugado = 2√3

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

de los focos podemos obtener que: √28

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

b = √3

podemos utilizar la siguiente fórmula para obtener a:

si despejamos a en la ecuación obtenemos lo siguiente:

ahora podemos sustituir los valores:

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

si graficamos la hipérbola, queda como en el documento adjunto.

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I just think this way if it is wrong sry but at least I try

297 mm is  nearest millimetre complete this statement .

The definition of convert units?

1 cm = 10mm

the length of a sheet of paper = 29.7 cm

the nearest millimetre = 29.7 * 10 = 297 mm

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Answer:

-1, 2

Step-by-step explanation:

Plug the "x" on the top row into the "x" on the equation.

y = 3(0) - 1 = -1

y = 3(1) - 1 = 2

The area of the rectangular-shaped building is 2448 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-

Area of rectangle = Length x width

Area of rectangle = 34 x 72

Area of rectangle = 2448 square feet

Therefore, the area of the rectangular-shaped building is 2448 square feet.

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Answer: 29°

Step-by-step explanation:

(2x-2)° + (x+5)° + 90° = 180°

(2x-2)° + (x+5)° = 90°

(2x + x)° = 87°

(3x)° = 87°

x° = 29°

The answer is option C, No; the graph fails the vertical line test.

The graph given doesn't show a function.

The method that is used to determine whether a given graph is a function or not is called the vertical line test. In this test, a vertical line is drawn at an arbitrary point x. If this line touches the given graph at more than 2-points, then the given graph is not a function.

In the given graph, if we draw a vertical line for any x > -1, then this vertical line touches the graph at more than two points.

In other words, for any value x > -1, the corresponding value of y is not unique.

So, the answer is option C, No; the graph fails the vertical line test.

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Answer:

C= [tex]\frac{AD}{B}[/tex]

Step-by-step explanation:

the answer is c because I said it c and the way you get the answer is by dividing the equality of the fraction

For the functions in this problem, we have that:

a) The function is exponential, and the table is completed as follows.

b) The function is linear, and the table is completed as follows.

c) The function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

A function with initial value 1 and where the y-value is computed by multiplied the previous y-value by 5, as in item a, is an exponential function with parameters a = 1 and b = 5, hence the rule is:

[tex]y = 5^x[/tex]

Then:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

A proportional relationship is also classified as linear with a intercept of 0. For item b, since each y-value is the x-value multiplied by 5, the rule is:

y = 5x.

Hence the table is:

For item c, when x changes by 1, y is always multiplied by 1/2, and due to the multiplication, the function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

The -16 is because when x = 0, y = -16.

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The x- and y-intercepts of the function both are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The relationship between the quantity of Fun Pass tickets sold and the amount of the overall sales are represented on the given graph.

Positive and negative functions are performed here, and the meanings are interpreted in the context of the situation.

Therefore, the x- and y-intercepts of the function are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

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Answer:

Step-by-step explanation:

Answer: closed circle on -2 with the arrow to the left

               open circle on 1 with the arrow to the right

The volume required for a 5% solution is 5.7 L, while a 40% solution requires 4.3 L for the experiment.

A percentage is a fraction of a whole represented as a number ranging from 0 and 100.

The equation should be as follows:

If 'x' is the volume of a 40% solution, then the volume of a 5% solution is:

10 L = 40% solution volume + 5% solution volume

10 L = x + 5% volume of solution

10 L - x = 5% solution volume

The volume would then be calculated as follows:

(volume 20% × concentration 20%) = (volume 40% × concentration 40%)           + (volume 5% × concentration 5%)

10 litre × 20% = x litre × 40% + (10- x) litre × 5%

10 L ×  20% = x litre  × 35% + 10 litre × 5%

x litre × 35 = 10 L × 20 - 10 L × 5

                 = 10 L × 15

x litre = 10 L × 15/35

x litre = 4.28 L

x litre = 4.3 L

40% solution volume = 4.3 L

The volume of 5% solution is equal to 10 L - 4.3 L = 5.7 L.

Thus, the volume of 5% solution  requires is 5.7 L and volume of 40% solution required is 4.3 L.

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The ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.

In mathematics, Ratio is a term that is used to compare two or more numbers.

Given that their are 20 sports drinks in a cooler out of which 8 are orange flavored. Therefore, we can write that -

Number of orange flavored bottles = n[O] = 8

Total number of bottles = n[T] = 20

We can calculate the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler as follows -

Total number of non - orange flavored bottles will be -

n[C] = n[T] - n[O]

Now, the ration of non - orange bottles to the total number of bottle's can be written as -

n[C] / n[T]

(n[T] - n[O]) / n[T]

(20 - 8) / 20

12 / 20

3 / 5

Assume that the ratio is denoted by R. Therefore -

R = 3 : 5

Hence, the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.

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These forecasts illustrate bias.

Therefore, these forecasts illustrate bias.

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Answer:

0

Step-by-step explanation:

As x aproaches a, (x-a) will aproach 0, so the numerator will aproach 0, and because 0 divided by anything=0, the whole function will become 0. So, the answer is 0.

Miranda made error by combining unlike terms, She added 5x and 9y then subtracted 4 from the answer. Answer is already in simplified form, it cannot be simplified further.

Like terms are ones whose exponent power and variables are the same. These variables' coefficients could differ. Terms that are comparable to one another are known as algebraic terms. As an illustration, consider the algebraic statement 8y + 2y, where y is the same variable as in the expression but has different coefficients.

Terms that have variables and exponents that differ from one another are said to be unlike terms. In contrast to terms, an expression is known to obtain when the coefficient, variables (in this case, two variables), and exponent powers (if any) are all distinct. Contrary to algebraic terms, the algebraic formula 3x + 9y is known as, where x and y are two separate variables with different coefficients.

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The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.

For Example , Derivative of [tex]3x^{2} =6x[/tex].

Product Rule of Differentiation

Let f(x) and g(x) be any two function. The derivative of their will be

F(x)=f(x)*g(x)

[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]

Given y=(sin(7x))ln(x)

[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]

[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]

[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]

Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

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Answer:

16

Step-by-step explanation:

Answer:

[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]

[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]

[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]

[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]

[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]

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

Question 2

[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]

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

Question 3

[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]

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

Question 4

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]

Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.

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

Question 5

[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

The midpoint of line segment AB is (2, 5)

The coordinates are given as:

A= (-1,3)

B = (5.-7)

The midpoint of line segment AB is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-1 + 5, 3 + 7)

Evaluate

Midpoint = (2, 5)

Hence, the midpoint of line segment AB is (2, 5)

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Answer:  b

Step-by-step explanation:

I think

Answer:

Graph in the picture

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))

Given the function

f(x)= 5-3x/2 and

g(x)= 5-2x/3

f(g(x)) = f(5-2x/3)

Substitute

f(g(x)) = 5-3(5-2x)/3)/2

f(g(x)) = (5-5+2x)/2

f(g(x)) = 2x/2

f(g(x)) = x

Similarly

g(f(x)) = 5-2(5-3x/2)/3

g(f(x)) = 5-5+3x/3

g(f(x)) = 3x/3

g(f(x)) =x

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

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Answer:

60.2 is the average

Step-by-step explanation:

add all numbers together to get: 301

divide 301 by 5 because there are 5 numbers total to get: 60.2

Answer: ≈578 cm²

Step-by-step explanation:

[tex]V_{cyl}=1056\ cm^3\ \ \ \ H=21\ cm\\V_{cyl}=\pi R^2H\\1056=\pi *R^2*21\\1056=21\pi *R^2\\[/tex]

Divide both parts of the equation by 21π:

16=R²

4²=R²

4=R

[tex]S{tot\ sur}=\pi R^2+2\pi RH\\S{tot\ sur}=\pi R*(R+2H)\\S{tot\ sur}=\pi *4*(4+2*21)\\S{tot\ sur}=4\pi *(4+42)\\S{tot\ sur}=4\pi *46\\S{tot\ sur}=184\pi \\S{tot\ sur}\approx578\ cm^2[/tex]

Answer:

-3

Step-by-step explanation:

4+(-7), In math you always have to do parentheses first. But, 4+(-7) equals -3 because -7 is bigger than 4. So it equals -3.