What is the solution to the equation 2x + 4 = 23x?

Based on the above,  Frank will need to have about 533 water stations per kilometer for the 30-kilometer trail run.

If each runner is said to have about 250 milliliters (0.25 liters) of water per station and there are said to be 4000 liters of water available in total, we have to calculate the total number of water stations  by:

4000 liters of water ÷ 0.25 liters of water per station

= 16000 stations

we have 30-kilometer run, we have to divide the total number of stations by the distance and it will be:

16000 stations ÷ 30 kilometers

= 533.33 stations per kilometer

Therefore, about 533 water stations per kilometer for the 30-kilometer trail run is needed by Frank.

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see full question below

frank is designing a 30-kilometers trail run water that will be given to runners. if 4000 liters of water is available,  each runner was given about 250 milliliters (0.25 liters) of water per station.  how many water stations will there be 30-kilometer run.

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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The factored form of the polynomial is f(x) = (x + 2)(x + 10)(x - 6) .

The given polynomial is f(x) = x4 + x3 + 2x2 - 22x - 60.

To find the zeros of the polynomial, set f(x) = 0 and solve for x. This gives us the following equation:

x4 + x3 + 2x2 - 22x - 60 = 0

The given zero is -2. To factor the polynomial, use the zero(-2) as one factor. To find the other factors, set (x + 2) = 0 and solve for x. This gives us the following equation:

x3 + 2x2 - 22x - 60 = 0

To solve this equation, use the Quadratic Formula. This gives us two factors, (x + 10) = 0 and (x - 6) = 0. Therefore, the factored form of the polynomial is:

f(x) = (x + 2)(x + 10)(x - 6)

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Mae's walking speed is 10 miles per hour. This is calculated by considering the given information.

Let's assume Mae's walking speed is represented by the variable "x" (in miles per hour). According to the given information, her jogging speed would then be "x + 12.5" miles per hour.

To calculate Mae's exercise time, we can use the formula: time = distance / speed.

Mae jogs 27 miles at a speed of "x + 12.5" miles per hour, so her jogging time can be calculated as:

jogging time = 27 / (x + 12.5)

Mae walks an additional 3 miles at a speed of "x" miles per hour, so her walking time can be calculated as:

walking time = 3 / x

The total exercise time is given as 3 hours. Therefore, we can set up the equation:

jogging time + walking time = 3

Substituting the calculated values, we get:

27 / (x + 12.5) + 3 / x = 3

To solve this equation, we can start by multiplying all terms by x(x + 12.5) to eliminate the denominators:

27x + 27 * 12.5 + 3(x + 12.5) = 3x(x + 12.5)

Simplifying the equation:

\(27x + 337.5 + 3x + 37.5 = 3x^2 + 37.5x\)

Combining like terms:

\(30x + 375 = 3x^2 + 37.5x\)

Rearranging the terms to set the equation equal to zero:

\(3x^2 + 7.5x - 375 = 0\)

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(\(b^2\) - 4ac)) / (2a)

In this case, a = 3, b = 7.5, and c = -375. Substituting these values into the quadratic formula:

x = (-7.5 ± √(\(7.5^2\) - 4 * 3 * -375)) / (2 * 3)

x = (-7.5 ± √(56.25 + 4500)) / 6

x = (-7.5 ± √(4556.25)) / 6

Calculating the square root:

x = (-7.5 ± 67.5) / 6

Simplifying further:

x = (60 / 6) or x = (-75 / 6)

Since Mae's walking speed cannot be negative, the solution is x = 10.

Therefore, Mae's walking speed is 10 miles per hour.

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The complete question is:

For exercise, Mae jogs 27 miles then walks an additional 3 miles to cool down. If her jogging speed is 12.5 miles per hour faster than her walking speed and her total exercise time is 3 hours, what is her walking speed? The athlete's walking speed is

Answer:

-2592, -15552, -93312

Step-by-step explanation:

Just multiply the number by 6

Answer

-2,592

Step-by-step explanation:

Each number of the sequence is multiplied up by 6

-2x6= -12, -12x6= -72, -72x6= -423. To get your solution you do -432x6 = -2,592

Answer: 5x^3 + 4x^2 – (6x^2 – 2x – 9) =

5x^3 + 4x^2 – 6x^2 + 2x + 9 =

5x^3 – 2x^2 + 2x + 9

Step-by-step explanation: We have to find the difference (5x^3 + 4x^2) - (6x^2 - 2x - 9)

On distributing the minus over the parenthesis, we get

5x^3 + 4x^2 - 6x^2 + 2x + 9

Now, we group the like terms and combine them

5x^3 + (4x^2 - 6x^2) + 2x + 9

=5x^3-2x^2 + 2x +9

Therefore, the last expression is the correct option.

The difference of the polynomial is 5x^3-2x^2 + 2x +9

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ c=\sqrt{ 2^2 + 8^2}\implies c=\sqrt{ 4 + 64 } \implies c=\sqrt{ 68 }\implies c\approx 8.2\)

Answer:

8.3

Step-by-step explanation:

The equation to find the length of the hypotenuse from the legs is a² + b² = c². This means that you will need to square the lengths of the legs and then add them together to get the length of the hypotenuse squared. The lengths of the legs of this triangle are 2 and 8. 2 squared is 4, and 8 squared is 64. Add 64 + 4 to get 68. Now we know that 68 equals the hypotenuse squared. The square root of 68, 8.246, is the measurement of the hypotenuse. Now you just need to round up the number to the nearest tenth to get 8.3.

The residual of the data point (-1, -2) is approximately -4.649. The regression line equation given is: y = 2.0972 - 0.552x

To determine the residual of a data point, we need to calculate the difference between the observed value and the predicted value based on the regression line.

We are given the data point (-1, -2), where x = -1 and y = -2. Let's substitute these values into the equation to calculate the predicted value:

y_predicted = 2.0972 - 0.552*(-1)

= 2.0972 + 0.552

= 2.6492

The predicted value based on the regression line for the data point (-1, -2) is 2.6492.

The residual is then the difference between the observed value (-2) and the predicted value (2.6492):

Residual = Observed value - Predicted value

= -2 - 2.6492

= -4.6492

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer:

81.25

Step-by-step explanation:

Because you want to know the total distance, calculate how many digits -49.75 is away from 0. It is 49.75 digits away from 0.

Now calculate how many digits 31.5 is away from 0. It is 31.5 digits away from 0.

Finally, add those two distances together so that you know the total distance:

49.75+31.5 = 81.25

Answer:

in the picture

HOPE ITS HELP

Answer:

Step-by-step explanation:

Given points

Midpoint formula

Midpoint is (2, 2)

Standard trigonometry texts typically do not include formulas for the cotangent, secant, and cosecant of the sum and difference of two numbers or angles due to several reasons.

Firstly, these functions can be easily derived from the well-known trigonometric identities involving sine, cosine, and tangent. Including separate formulas for the cotangent, secant, and cosecant would result in redundancy and unnecessary complexity.

Secondly, the cotangent, secant, and cosecant are not as commonly used as sine, cosine, and tangent in practical applications, so their inclusion may not be prioritized.

Moreover, space limitations in textbooks also play a role, as providing comprehensive formulas for all trigonometric functions could make the texts excessively lengthy.

Therefore, students are encouraged to understand the relationships between trigonometric functions and employ the existing identities to derive the values they need.

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

3rd option: f(x)⇒ +∞ as x⇒-∞ and f(x)⇒ -∞ as x⇒ +∞

Step-by-step explanation:

This is a negative cubic graph, therefore:

Looking at the graph, as x goes towards negative infinity, the y values go toward positive infinity.

On the other hand, as x goes towards positive infinity, the y values go towards negative infinity.

Answer:

14) -123

15) 144

16) 3303

Step-by-step explanation:

Answer:

x = 9

y = 14

Step-by-step explanation:

If we observe the two figures, the bigger one is increased by 1.5 because 12/9 = 1.5.

Smaller side = 6

Larger side = x

=> 6 x 1.5

=> x = 9

Smaller side = y

Larger side = 21

=> 21 / 1.5

=> y = 14

The complex conjugate of z, denoted as z*, refers to the reflection of z across the real axis. In general, \(e^z*\) is not analytic everywhere.

To show this, let's consider the Cauchy-Riemann equations for a function f(z) = u(x, y) + iv(x, y), where u and v are real-valued functions representing the real and imaginary parts of f, respectively. The Cauchy-Riemann equations are as follows:

∂u/∂x = ∂v/∂y (1)

∂u/∂y = -∂v/∂x (2)

If a complex function is analytic, it satisfies these equations for all points in its domain. Let's examine \(e^z* = e^{(x - iy)} = e^x * e^{(-iy),\) where x and y are real numbers.

Considering equation (1), we have

∂u/∂x = ∂/∂x(e^x * cos(y)) = e^x * cos(y), and ∂v/∂y = -∂/∂y(e^x * sin(y)) = -e^x * sin(y).

For equation (1) to hold, e^x * cos(y) must be equal to -e^x * sin(y) for all values of x and y. However, this is not true, as the exponential term e^x is always positive, while the sine term sin(y) can take both positive and negative values.

Therefore,\(e^z*\) does not satisfy the Cauchy-Riemann equations and is not analytic everywhere.

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Answer:

length- 28 width- 7

Step-by-step explanation:

7 times 4 is 28, so 28 times 2 is 56, 7 times 2 is 14, 56+14 is 70

Answer as a fraction:  x = 5/2

Answer in decimal form:   x = 2.5

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

Explanation:

Replace f(x) with 5

So we go from f(x) = 2x to 5 = 2x

Now isolate x. We do so by dividing both sides by 2 (this undoes the multiplication of 2 on x)

So we get

5 = 2x

5/2 = 2x/2 ... divide both sides by 2

5/2 = x

x = 5/2

x = 2.5

Answer:

10 x 5 = 50 10 x 3= 30 So we could write this as 50 + 30 can be our expression in 2 number

Constant of variation for given quadratic equation is 2/3

Correct option is a.

The ratio between two variables in a direct variation or the product of two variables in an inverse variation.

In the direct variation equations = k and y = k x,

and the inverse variation equations x y = k and

k is the constant of variation.

Given,

quadratic equation,

15y = 10x²

y = (10/15)x²

y = (2/3)x²

Comparing it with general form y = kx²

k = 2/3

Hence, 2/3 is constant of variation for the quadratic equation.

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If the diagonal of a rhombus id x-4d and x+ 4d then the area of rhombus is (x² - 16d²) / 4 unit²

In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Let's call the length of one half of the diagonal "a" and the length of the other half of the diagonal "b". So we have:

a = (x - 4d) / 2

b = (x + 4d) / 2

The area of a rhombus can be calculated as half the product of its diagonals, or as half the product of its side lengths:

Area = (1/2) × a × b × 2

Area = a × b

Substituting the expressions for "a" and "b" from above, we get:

Area = [(x - 4d) / 2] × [(x + 4d) / 2]

Area = (x² - 16d²) / 4

Therefore, the area of the rhombus is (x² - 16d²) / 4 square units.

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\(c = 15d\)

Step-by-step explanation:

find the value of the constant of proportionality k

\(k = \frac{v}{d} \)

c =total cost

d =days

The distance between two points is given as;

The number beneath the radical symbol is 58.

Answer:

Programmed

Step-by-step explanation:

Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.

Answer:anyone here watch anime

Step-by-step explanation:

EREN JEAGER

The minimum amount of wrapping paper needed, in square feet, to wrap all 3 boxes is  12.5 square feet.

Side of each cube = 10 inches

Number of cubes =3

As we know The minimum amount of wrapping paper needed, in square feet, to wrap all 3 boxes will be the total surface area of all 3 boxes.

The total surface area of a cube with side a is 6a².

So, the total surface area of a cube with a side of 10 inches will be 6*10² = 6*100 = 600 square feet.

So, the total surface area of 3 cubes with a side of 10 inches will be 600*3 = 1800 square inches.

As we know that 1 square inch = 0.00694444 square feet

So, 1800 square inches = 1800*0.00694444 = 12.5 square feet.

Therefore, the minimum amount of wrapping paper needed, in square feet, to wrap all 3 boxes is  12.5 square feet.

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Deep foundations are recommended for larger or hillside developments , or those on poor soil .

Foundation Systems in Building

There are two classifications of foundations in building shallow foundations and deep foundations . These categories refer to the depth of soil in which the foundation is formed .

Shallow Foundations : Shallow foundations are usually located less than six feet below the lowest finished floor of a structure.

Deep Foundations : Deep foundations are structural elements that are used to transfer loads from weak and compressible soils to a stronger layer, usually located at a significant depth below the ground.

Recommendation

A shallow foundation can be constructed in as little as a one-foot depth , whereas a deep foundation is formed at a depth of 10 - 300 feet . Deep foundations are recommended for larger or hillside developments , or those on poor soil .

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Answer:

Step-by-step explanation: A shallow foundation distributes loads from the building into the upper layers of the ground.

Shallow foundations perform very well on sites with strong soils, sufficiently thick natural gravel rafts overlying weaker soils or where robust, engineered ground improvement is carried out.

Deep foundations can provide a good foundation for houses on sites with poor soil conditions near the surface,

Answer:

The correct set of data is D.

Answer:

-24

Step-by-step explanation:

steps are in the picture above.

Note:if you need to ask any question please let me know.

Answer:

x=(6,0)     y=(0,-2)

Step-by-step explanation:

hope it helped:)