A = b x h, donde la b = (20 - 2x) y h = (16 +10x)

•Si x = 3 metros, ¿cuál es el área del terreno?


P = 2 (b + h), donde la

b = (20 - 2x) y h = (16 +10x)

•Si x = 2 metros, ¿cuál es el perímetro del terreno?

The change that happened from the first half of the equation to the second half was you moved the 9 and the 4c around.

Commutative property of addition allows you to do that. It's what says that 2+3 is the same thing as 3+2

Hope this helps you

The interval of convergence of the series ∑a_n x^n is given by |x|∞} |a_{n+1} nx^n| / |a_n x^(n-1)|.We can write L as L = lim_{n->∞} |a_{n+1}| / |a_n| x, where x is the same in the numerator and denominator. Since the series ∑a_n x^n converges for |x|<2, we have lim_{n->∞} |a_{n+1}| / |a_n| = L' < 2. Thus, L = L' x.

For the series to converge, we need L < 1, which gives |x| < 1 / L'. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L'.Since the radius of convergence is the same as that of the series ∑a_n x^n, we get L' = 2. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L' = 1/2. Thus, the interval of convergence of the series ∑a_n nx^(n-1) is |x| < 1/2. However, since the interval of convergence of the series ∑a_n x^n is |x| < 2, we have |nx^(n-1)| = n|x^(n-1)| <= 2n for |x|<=1. Thus, we have |a_n nx^(n-1)| <= |a_n| 2n for |x|<=1, which shows that the series converges for x=-1, and thus for -1<=x<=1. Also, we have |a_n nx^(n-1)| <= |a_n| 2^n for |x|<=2, which shows that the series converges for x=2, and thus for -2<=x<=2. Thus, the possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

The possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

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An algebraic expression equivalent to tan(arcsin(x)) is simply x.

To find an algebraic expression equivalent to tan(arcsin(x)), we can start by considering a right triangle. Let's assume one of the acute angles of the triangle is θ, and the opposite side is x, the adjacent side is 1, and the hypotenuse is h.

Since sin(θ) is defined as the ratio of the length of the opposite side to the hypotenuse, we have sin(θ) = x/h.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h^2 = x^2 + 1^2

h^2 = x^2 + 1

h = √(x^2 + 1)

Now, we can find tan(θ) using the definition of the tangent function:

tan(θ) = sin(θ) / cos(θ)

cos(θ) is defined as the ratio of the length of the adjacent side to the hypotenuse. In our case, cos(θ) = 1/h.

Substituting the values we found earlier, we have:

tan(θ) = (x/h) / (1/h)

tan(θ) = x

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Answer:

x =  -14

Step-by-step explanation:

Based on the above, the graph of the resultant vector is shown in the image attached  (x-axis).

In the  graph construction, We need to carry out a sum of vectors and then draw the resultant vector.

Note that the resultant vector need to be <4, 0>

Hence when we view the graph attached, we can say that the vectors areas:

w = <3, 3>

u = <-3, -4>

v = <-4, -1>

So, the sum = u - v + w

Note also that in the sum of the vectors we need to add and subtract the correspondent parts and it will be:

u - v + w

= <-3, -4> - <-4, -1> + <3, 3>

= <-3 + 4 + 3, -4 + 1 + 3>

= <4, 0>

Therefore, Based on the above, the graph of the resultant vector is shown in the image attached  (x-axis).

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Polygons are closed two-dimensional shapes with straight sides. They have various characteristics, including the number of sides, angles, and the presence of parallel sides. These properties help classify and identify different polygon shapes

The number of sides in a polygon determines its shape. For example, a triangle has three sides, a quadrilateral has four sides, and a pentagon has five sides. The number of sides can vary, and polygons with more sides are called n-gons, where "n" represents the number of sides.

The number of angles in a polygon is equal to the number of sides. Each vertex, or corner, of a polygon corresponds to an angle. For instance, a triangle has three angles, a quadrilateral has four angles, and so on. The sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180 degrees, where "n" is the number of sides.

Parallel sides are a characteristic of specific types of polygons called parallelograms. Parallelograms have opposite sides that are parallel and congruent. This means they never intersect and are of equal length.

Understanding these properties of polygons allows for the identification and classification of different shapes based on their number of sides, angles, and the presence of parallel sides. These properties play a fundamental role in geometry and shape analysis.

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Area = 8,100 square feet

area of a square = a²

8,100 square feet = a²

√8,100 square feet = √a²

90 feet = a

total length each row of bookshelf is 4/5 of the length of the storage space.

90 feet * 4/5 = (90*4)/5 = 360/5 = 72 feet.

Area = (72 ft)²

Area = 5,184 square feet.

Answer:

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements. “Or” indicates that, as long as either statement is true, the entire compound sentence is true. It is the combination or union of the solution sets for the individual statements. A compound inequality that uses the word “and” is known as a conjunction. Although “and” and “or” are parts of speech known as conjunctions, the mathematical conjunction has a different meaning from the grammatical one. To prove the point, the conjunction (part of speech) “or”—when used in a compound inequality—forms what is known as a disjunction. Just remember “con” means “with another,” and “dis” means “one OR the other.”

Answer:

\(\huge\boxed{\sf x = -100}\)

Step-by-step explanation:

\(\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}\)

Answer:

sandwich and drink only (no dessert)

so 4 x 6 = 24

you have 24 different combinations you can do

hope this helps

Step-by-step explanation:

a.)The probability of getting a sum which is a multiple of 3 = 1/3

b.)The probability of getting a sum which is a multiple of 4 = 1/4

To calculate the probability of the given event, the formula that should be used is given as follows;

Probability = possible event/sample space.

For a.)

sample space = 36

possible event = 12

probability = 12/36 = 1/3

For b.)

sample space = 36

possible event = 9

probability = 9/36 = 1/4

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Answer:

9

Step-by-step explanation: 3x4= 12  -3=9

Answer:

what's nelly's age

Step-by-step explanation:

4x divided by 3?

We are given the Bernoulli's equation x^(-) + y = (x^2 ln(x))y^2, where x > 0, and we need to solve this differential equation for y as a function of x.

To solve the Bernoulli's equation, we can use a substitution technique. Let's make the substitution v = y^(1 - 2), which transforms the equation into a linear form. We can rewrite the equation as follows:

v' = (1 - 2) * (x^2 ln(x)) * v

Simplifying this equation gives us:

v' = -2x^2 ln(x) v

This is now a separable first-order linear differential equation. We can separate the variables and integrate both sides:

1/v * dv = -2x^2 ln(x) dx

Integrating both sides, we get:

ln|v| = -2 * (x^3/3) ln(x) + C

where C is the constant of integration.

Now, we can substitute back v = y^(1 - 2) to find y in terms of x:

ln|y^(1 - 2)| = -2 * (x^3/3) ln(x) + C

Simplifying further:

ln|y^(-1)| = -2 * (x^3/3) ln(x) + C

Using the property of logarithms, we can rewrite this as:

y^(-1) = e^(-2 * (x^3/3) ln(x) + C)

y^(-1) = e^(-2 * (x^3/3) ln(x)) * e^C

y = (e^C) / (e^(-2 * (x^3/3) ln(x)))

Simplifying the expression, we get:

y = e^(C + (2 * (x^3/3) ln(x)))

So, the solution to the Bernoulli's equation is y = e^(C + (2 * (x^3/3) ln(x))), where C is the constant of integration.

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Given

To find:

Explanation:

It is given that,

That implies,

Therefore, for x=-4,

Hence, the value of (g-f)(-4)=-13.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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The volume of a sphere is V = 4/3 x pi x r^3 .

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

V' equals (4 pi x r' x r'2) (4 pi x (.9 3) x r2 x r')

This equation expresses how quickly the rind volume changes over time.

As stated in the issue, r' = 2.

Additionally, the radius will be r = 2 * 5 = 10 after 5 weeks.

V' equals (4 pi x 102 x 2) (Pi x (.93) x 10 x 2) = -

V' is equal to (800 pi) - (800 pi x (.729)).

V' = (800 x pi) (1 - .729) (1 - .729)

V' = (800 x pi)(.271) (.271)

681.09 cubic centimeters make up V'.

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The Law of detachment states that if m then n and m is true then q is true.

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

The Law of detachment states that if m then n and m is true then q is true.

We have,

If two angles are complementary, then the sum of their measures is 90°.

This is in the form of,

If M then N and if M is true then N must be true.

So,

If two angles are complementary, then the two angles' sum is 90 degrees.

If the two angles are m∠E and m∠F.

m∠E + m∠F = 90

Thus,

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

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2(x + 7) = x + 19

Use distributive property on left side;

2x + 14 = x + 19

Subtract 14 from both sides:

2x = x + 5

Subtract 1 x from both sides:

X = 5

Answer:

  (a)  3.8

Step-by-step explanation:

The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.

__

The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.

Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.

  EF > DE

  EF > 3

Only one answer choice satisfies this inequality.

  EF = 3.8

__

Additional comment

If you want to do the actual computation, we have ...

  EF/sin(D) = DE/sin(F)

  EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828

  EF ≈ 3.8

In finance, interest is the cost of borrowing money or the compensation paid to an individual or organization for lending money. It is usually expressed as a percentage of the amount borrowed and is calculated over a specific period of time.

1. To calculate the total interest payment for the first year, follow these steps in Excel:

Step 1: Enter the given values in separate cells.
Loan amount: $250 million in A1
Monthly installment: $5 million in A2
Number of installments: 60 in A3

Step 2: Calculate the monthly interest rate (i) using the RATE function.
In cell A4, type the formula: =RATE(A3, -A2, A1)

Step 3: Calculate the annual interest rate (I) by multiplying the monthly interest rate by 12.
In cell A5, type the formula: =A4*12

Step 4: Calculate the total interest for the first year by multiplying the annual interest rate by the loan amount.
In cell A6, type the formula: =A1*A5
The total interest payment for the first year is approximately $17 million.

2. To calculate the effective interest rate (j12) of the loan, use the following formula in Excel:

In cell A7, type the formula: =(1+A4)^12-1
The effective interest rate (j12) is approximately 7.4% p.a.

3. To calculate the principal repayment during the first year, follow these steps:

Step 1: Calculate the total amount paid in the first year by multiplying the monthly installment by 12.
In cell A8, type the formula: =A2*12

Step 2: Subtract the total interest payment for the first year (calculated in Step 1) from the total amount paid in the first year.
In cell A9, type the formula: =A8-A6
The principal repayment during the first year is approximately $43 million.

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Answer:

-√-3

Step-by-step explanation:

Answer:The

Step-by-step explanation \(-\sqrt{-3}\)

The value of the middle side length is 21 inches.

Let's denote the three consecutive odd integers as x, x+2, and x+4, representing the lengths of the sides of the triangle.

The perimeter of a triangle is the sum of its three sides. In this case, the perimeter is given as 63 inches:

x + (x+2) + (x+4) = 63

Simplifying the equation, we have:

3x + 6 = 63

Subtracting 6 from both sides:

3x = 57

Dividing both sides by 3:x = 19

So, the first odd integer is 19. The consecutive odd integers would then be 19, 21, and 23.

The middle side length is x+2, which is 19 + 2 = 21 inches.

Therefore, the value of the middle side length is 21 inches.

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0.29 km is equal to 290,000 mm when rounded to two significant figures.

Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).

Step 1: Multiply 0.29 km by the conversion factor:

0.29 km x 1,000,000 = 290,000,000 mm

Step 2: Round the result to two significant figures:

Since the original value, 0.29 km, has two significant figures, we round the result to match.

290,000,000 mm becomes 290,000 mm.

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Answer:

hello

Step-by-step explanation:

hope it helps

have a great day

a)  Ideal assignment, each power shovel should be assigned one truck at all times. b) Minimum Five trucks are required to avoid idle time for the power shovel. c) The cost of operating each truck can be minimized to $0.62 per minute. d) Five trucks should be assigned to the power shovel to minimize the cost per truck load hauled.

The ideal assignment of trucks to the power shovel is to have one truck assigned to the power shovel at all times, so that as soon as one truck is loaded, it can immediately be replaced by another truck, and there is no waiting time for the power shovel. so, three trucks should be assigned to each power shovel.

To prevent idle time for the power shovel, we need to have a truck arrive as soon as the previous truck has been loaded and left. Therefore, the minimum number of trucks required is equal to the cycle time divided by the time to load a truck:

Cycle time = time to load + travel time + dumping time + return time = 4 + 8 + 4 + 3 = 19 minutes

Minimum number of trucks = cycle time / time to load a truck = 19 / 4 = 4.75

Since we cannot have a fractional number of trucks, we need to round up to the nearest integer. Therefore, the minimum number of trucks required is 5.

The cost of operating the power shovel is $25 per hour, which is equivalent to $0.42 per minute (since there are 60 minutes in an hour). The cost of operating each truck is $37 per hour, which is equivalent to $0.62 per minute.

To minimize the cost per truck load hauled, we need to find the optimal number of trucks to assign to the power shovel. Let's assume that x trucks are assigned to the power shovel. Then, the total cost per truck load hauled is given by:

Total cost = (cost per power shovel minute) * (cycle time) + (cost per truck minute) * (time to load + travel time + return time) / x

Substituting the values we calculated earlier:

Total cost = (0.42) * (19) + (0.62) * (4 + 8 + 3) / x

Total cost = 8.88 + 1.56 / x

To minimize the total cost, we need to find the value of x that minimizes this expression. Taking the derivative of the expression with respect to x and setting it equal to zero, we get:

d(Total cost) / dx = -1.56 / x^2 = 0

x^2 = 1.56 / 0

x = ∞

Since we cannot assign an infinite number of trucks to the power shovel, this means that the total cost is minimized when we assign as many trucks as possible to the power shovel, which is equal to the minimum number of trucks we calculated earlier. Therefore, the optimal number of trucks to assign to the power shovel is 5.

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Answer:

Slope (m) = 2
y = 2x

Step-by-step explanation:

Change in y / Change in x
-1 becomes 1 (positive)

1 + 1 = 2
1 - 5 = 4
4/2 = 2

y = 2x

Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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Work Shown:

(real height)/(scale height) = (real length)/(scale length)

(10 feet)/(8 inches) = (14 feet)/(x inches)

10/8 = 14/x

10x = 8*14

10x = 112

x = 112/10

x = 11.2 inches

Answer:

5x + 10y + 5z

Step-by-step explanation:

1/2 (10x+20y+10z)

Distribute

1/2 (10x)+1/2(20y)+1/2(10z)

5x + 10y + 5z

Answer: Your correct would be  5x+ 10y+5z

Step-by-step explanation:

Hope this helps you!!!