the rectangle prism below has a volume of 464 3/4 cubic meters. a- write an equation that could be used to find the length of the prism b- find the length, show your work.

PLEASE HELP!!

The new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function f(x) shown in the coordinate plane.

The function g(x) = f(2x)

As we can see in the new function g(x) it is the transformation of the f(x).

Transformation is applied as below:

x → 2x   (x is replaced by the twice of it)

= f(x)

= f(2x)

= g(x)

When the function is multiplied by a positive number it will be stretched or compressed according to that factor vertically and in the given function the factor is 2 which means the g(x) will be stretched or compressed according to that factor.

Thus, the new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.

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Therefore , the solution of the given problem of function comes out to be the interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

The math lesson includes a variety of subjects, such as math, integers, but one's subdivisions, as well as architecture, construction, and that both real but rather fictitious geographic locations. A work covers the connections between different variables that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinctive results for each input.

Here,

First, we assess f(x) at the interval's endpoints:

=> f(-3) = 2(-3)^3 - 7(-3) + 4 = -43

=> f(3) = 2(3)^3 - 7(3) + 4 = 44

There must be at least one root in each of the gaps between (-3, r) and (r, 3), where r is the function's root, because the function changes sign at x = -3 and x = 3. To find the function's roots numerically,

we can use the bisection technique or Newton's method.

We can plot the function using a graphing calculator or computer software and see that there is one root in the range (-3, -2), one root in the range (-2, 0), and one root in the range (-3, -2). (0, 3).

Consequently, the periods where the function is positive on the range (-3, 3) are as follows:

=> (-3, -1.3233) and (0.7838, 3) (0.7838, 3)

The interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

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Answer:

4 12/25

Step-by-step explanation:

4.48 can be written as 4 48/100

Simplify

4 24/50

Simplify some more.

4 12/25

Hope this helped :)

The answer is the last option (2x -3)/(5-2x)

Explanation

Since f(x)= 2x-3 and g(x0) = 5-2x,

f/g(x)

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➺ \( {x}^{2} = 64\)

➺ \( \: x = \sqrt{64} \)

➺ \( \: x = \sqrt{8 \times 8} \)

➺ \( \: x = \sqrt{ ({8})^{2} } \)

➺ \( \: x = ±8\)

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We know that z varies directly as √√x and inversely as y, which can be written as:

z = k(√√x)/y

where k is the constant of proportionality.

To find the value of k, we can use the values given when x = 25 and y = 7:

179 = k(√√25)/7

179 = k(5/7)

k = (179*7)/5

k = 250.6

Now we can use this value of k to find z when x = 64 and y = 4:

z = 250.6(√√64)/4

z = 250.6(2)/4

z = 125.3

Therefore, z ≈ 125.3 when x = 64 and y = 4.

9514 1404 393

Answer:

  115°

Step-by-step explanation:

Angle CHF has a measure equal to the average of the arcs the chords intercept.

  angle CHF = (arc CDF +arc AB)/2 = (190° +40°)/2

  angle CHF = 115°

Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

length = 26 cm

width = 4 cm

Step-by-step explanation:

A = 104 cm²

A = length x width

ratio of length and width = 13 : 2

total ratio of length and width is 15 = a

so ratio of length is (13/15)a and width (2/15)a

A = length x width = (13/15)a x (2/15)a = (26/225)a² = 104

a² = 104 x 225 : 26 = 900

a = 30cm

length = (13/15)a = 13/15 x 30 = 26 cm

width = (2/15)a = 2/15 x 30 = 4 cm

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The equation is:

(x-5)^2+(y-(-7))^2=36

I hope it helps!

Answer:  \(\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\)

=========================================

Work Shown:

\((h,k) = (5,-7) = \text{center}\\\\r = 6 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - 5)^2 + (y - (-7))^2 = 6^2\\\\\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\\\\\)

It will take the acrobat 1/4 of a second to land safely on the net.

Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: \(h=-16t^2+4t+25\).
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
\(h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4\)
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
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Answer:

x=40°

Step-by-step explanation:

x=180-75-65=40°

Answer:

1. y = 18

2. x = 5

3. y = 2

Step-by-step explanation:

Rule: y = 2x

y = 2 ( 9 )

y = 18

10 = 2x

x = 5

y = 2 ( 1 )

y = 2

Answer:

x - y

9 - 18

5 - 10

1 - 2

Step-by-step explanation:

if there is a number in the x column, multiply it by 2, if there is a number in the y column, then divide it by 2.

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

On solving the provided question we can say that the answer is third one , that equation is 3 x = 0.

Any equation that can be written in standard form, with x denoting an unknown value and a, b, and c denoting known integers, is referred to as a quadratic equation in algebra. In general, it is assumed that a > 0; equations with a = 0 are thought to be degenerate since they become linear or even more basic.

Here,

thus ,the given equation :

x - 5 = 4

6 x + 4 = 4

3 x = 0

x + 9 = 9

Thus , the given equation  3 x = 0  have 0 as its solution.

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The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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