A woman standing on a hill sees a flagpole that she knows is 40 ft tall. the angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. find her distance x from the pole.

The expression v^3 + 27 can be factored as a sum of cubes using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2). In this case, it factors to (v + 3)(v^2 - 3v + 9).

To factor the expression, v^3 + 27, we recognize it as a sum of cubes. The formula for factoring a sum of cubes is:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, a = v and b = 3 since 27 is 3 cubed (3^3).

Identify the cube roots of each term

Apply the sum of cubes formula:

Substitute the values into the formula:

Hence, we get v^3 + 27 = (v + 3)(v^2 - 3v + 9)

So, v^3 + 27 factors to (v + 3)(v^2 - 3v + 9).

Neil has approximately 21/30 gallon of paint in total.

To find out how much paint Neil has in total, we need to add up the amounts of paint in each can.

The first can contains 1/3 gallon of paint, the second can contains 1/5 gallon of paint, and the third can contains 1/2 gallon of paint.

To add fractions, we need to find a common denominator. In this case, the common denominator is 30. We can convert the fractions to have a denominator of 30 and then add the numerators:

1/3 gallon + 6/30 gallon + 15/30 gallon = 21/30 gallon.

Therefore, Neil has approximately 21/30 gallon of paint in total.

Final answer:

Neil has a total of 31/30 gallons of white paint when his three cans containing 1/3, 1/5, and 1/2 gallon are added together, which is slightly more than 1 gallon.

Explanation:

Neil has three partially full cans of white paint with quantities of 1/3 gallon, 1/5 gallon, and 1/2 gallon. To find the total amount of white paint Neil has, we simply need to add these fractions together. Adding fractions involves finding a common denominator and then adding the numerators.

In this case, the common denominator for 3, 5, and 2 would be 30, so the fractions would be equivalent to 10/30, 6/30, and 15/30, respectively. Now, we add the numerators:

10/30 + 6/30 + 15/30 = 31/30 gallons

So Neil has 31/30 gallons of white paint in total, which is a little more than 1 gallon when converted from an improper fraction to a mixed number (1 gallon and 1/30 of a gallon).

The volume of a basketball with a radius of 12.5 inches is calculated using the formula for the volume of a sphere (4/3πr³). The result approximates to 8177.083 cubic inches.

The volume of a sphere, like a basketball, can be calculated using the formula 4/3πr³. Here, r is the radius of the sphere. As specified, the radius of the basketball is 12.5 inches. So, we just need to plug that into our formula:

Volume = 4/3 * π * (12.5)^3  , value of  π is 3.14 approximately.

When you calculate the above expression, you'll find the volume of the basketball is approximately 8177.083 cubic inches.

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Value of x is 2, can be determined by algebraic equation.

It’s a equation for of known and not known constant and we have to find the not known constant value .

3(5x+4) - 20 -13x

= - 4 15x + 12 - 20 - 13x

= - 4 2x -8

= - 4 2x

= 8 - 4 2x

= 4 x

= 2

Hence , the value of x will be 2 .

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In the given scenario above, the one who will be named as the external stimulus is the action of having to use the sense of sight when you have seen the fruit of bowl. The internal stimulus will be the action of having to feel the hunger.

Isolating L, it is found that the solution for L is given by:

[tex]L = 2(S - B)[/tex]

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The equation is:

[tex]S = B + \frac{1}{2}L[/tex]

Leaving everything with L on one side, everything without on the other.

[tex]\frac{L}{2} = S - B[/tex]

[tex]L = 2(S - B)[/tex]

Which is the solution for L.

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Answer:

-12 or 8

Step-by-step explanation:

Answer:  The required value of the variable c is 18 and that of YZ is 72.

Step-by-step explanation:  Given that Y is in between X and Z, where

XY= 11, YZ=4c and XZ=83.

We are to find the value of the variable c and YZ.

Since the point Y is in between X and Z, so we must have

[tex]XY+YZ=XZ\\\\\Rightarrow 11+4c=83\\\\\Rightarrow 4c=83-11\\\\\Rightarrow 4c=72\\\\\Rightarrow c=\dfrac{72}{4}\\\\\Rightarrow c=18.[/tex]

And,

[tex]YZ=4c=4\times 18=72.[/tex]

Thus, the required value of the variable c is 18 and that of YZ is 72.

The given problem is a segment addition problem in geometry. It can be solved by creating an equation based on the Segment Addition Postulate, simplifying and solving it to find the value of the variable c equal to 18. Substituting this value into the equation for YZ gives a result of 72.

The subject of this question is a segment addition problem in geometry. From the given values, we can create an equation based on the Segment Addition Postulate, which states that the length of the whole line segment (XZ in this case) is equal to the sum of the lengths of the two segments it is split into (XY and YZ in this context).

With XZ = 83, XY = 11, and YZ = 4c, the equation becomes XY + YZ = XZ, or 11 + 4c = 83. To solve for the value of the variable c, subtract 11 from both sides, giving 4c = 72. Finally, divide each side by 4 to find that c = 18.

To find the value of YZ, substitute c = 18 back into the YZ equation: YZ = 4c = 4*18 = 72.

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Answer: There are 42 products he can have at maximum.

Step-by-step explanation:

Since we have given that

Number of products displays = 12

Number of shelves six products have = 4

Number of shelves six products have = 3

So, total number of shelves first six products have

[tex]6\times 4=24[/tex]

Total number of shelves next six products have

[tex]6\times 3\\\\=18[/tex]

So, the maximum number of products that he can have is given by

[tex]24+18=42[/tex]

Hence, there are 42 products he can have at maximum.

After translating words to numerical form, it is equal to 135.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the value provided in the question,

Product of 15 and another number.

Another number is negative 3 decreased by 12 which means that (12 - 3) = 9

Product in numeric form = 15 × 9 = 135

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Parallel lines have the same slope, so if we find the slope of the line shown, the slope of the line parallel to it will be the same.

To find the slope, we find the rise divided by the run, or the change in x values divided by the change in y values.

slope = m = (y1 - y2)/(x1 - x2) = (3-2)/(0-3) = 1/(-3) = -1/3

Therefore, the slope is -1/3, and so the slope of the parallel line is also -1/3.

Your answer is -1/3.

Hope this helps!

divide 3 by 4 = 3/4 = 0.75

so Cody jogs 3/4 mile for every 1 mile Vanessa runs

Answer:

The point best approximates √45 is C = 6.72

Step-by-step explanation:

We have to show the approximate square value of √45.

By solving √45 = √(5×9) = √5×√9 = 3√5 = 3×2.24 = 6.72

6.72 can be represented as point C on the given number line.

The question involves solving a basic algebra problem to determine the ages of three children. By setting up an equation based on the given information, we find that each twin sister is 12 years old and Kevin is 18 years old.

The question revolves around finding the ages of three children, Kevin and his twin sisters, given that Kevin is six years older than his twin sisters and the sum of their ages equals their father's age, who is 42 years old. First, let's denote the age of each twin sister as x. Since Kevin is six years older, his age will be x + 6. The sum of their ages equals their father's age, which is given as 42 years. Therefore, the equation to find their ages will be:

[tex]x + x + (x + 6) = 42[/tex]

This simplifies to:

3x + 6 = 42

Subtracting 6 from both sides gives:

3x = 36

Dividing by 3:

x = 12

So, the age of each twin sister is 12 years, and Kevin's age is 12 + 6 = 18 years.

The answer is a.

12x