Which function is the inverse of f(x)=-x³-9?​

Answer:

175m²

Step-by-step explanation:

Total area (of pool):

50 × 21 = 1050

Area of each lane:

1050 ÷ 6 = 175

The weight of each bag is 23.25 pounds.

For given question,

Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.

If all the bags were identical, we need to find the weight of each bag.

Let 'm' be the weight of each bag.

As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.

8 × m = 187.6

now we solve above expression to find the value of m i.e., to find the weight of each bag.

⇒ 8 × m = 187.6

⇒ m = 187.6 / 8

⇒ m = 23.25 pounds

Therefore, the weight of each bag is 23.25 pounds.

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The width of the box is approximately 3 inches.

A shape is a geometric figure that can be described by its size, orientation, and position in space. Shapes can be two-dimensional, such as squares, circles, and triangles, or three-dimensional, such as cubes, spheres, and pyramids.

A rectangular prism is a three-dimensional shape that has six rectangular faces. It is also known as a rectangular parallelepiped or a cuboid. The opposite faces of a rectangular prism have the same size and shape, and the edges where the faces meet are all perpendicular to each other. The volume of a rectangular prism is calculated by multiplying its length, width, and height, while its surface area is calculated by adding up the areas of all six faces.

volume of a rectangular prism:

volume = length * width * height

We know the volume is 219.375 in³, the height is 6.5 in, and the length is 11.25 in. Let's substitute these values into the formula and solve for the width:

219.375 = 11.25 * width * 6.5

Dividing both sides by (11.25 * 6.5), we get:

width = 219.375 / (11.25 * 6.5) ≈ 3

Therefore, the width of the box is approximately 3 inches.

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Answer:

no

Step-by-step explanation:

because when lines are perpendicular, the angles are 90 degree angles.

Hi there!

\(\large\boxed{ \lim_{x \to 0} x^{2} - 2= -2}\)

In direct substitution, simply plug in the x-value given to solve for the limit as x approaches zero:

\(\lim_{x \to 0} x^{2} - 2 \\\\ \lim_{x \to 0} (0)^{2} - 2\\\\ \lim_{x \to 0} x^{2} - 2= -2\)

Answer:

trigonometry

Step-by-step explanation:

hope this helps lovely

Answer:

trigonometry

Step-by-step explanation:

Have a great day!

Answer:

y = - 3x + 15

Answer:

C. 5 1/5

Step-by-step explanation:

A, B, and D are all 5.5 and C alone is 5.2

Answer:

Step-by-step explanation:

Let's verify each option.

Option A

Option B

Option C

Option D

Looking at the options, we can see that the result of Option A, B, and D are same.

This means that the odd one is Option C.

Answer:

You have to convert 4 and 1/4 to 17/4. Then, the LCM of 3 and 4 is 12, so multiply 17/4 by 3/3 and 2/3 by 4/4 to get 51/12 and 8/12. Now, subtract.

51/12 - 8/12 = 43/12. That is the final answer.

Answer:

B

Step-by-step explanation:

M is a factor of N and \((1+r)^t\), which is not influenced by N. This is because N is just the initial amount of people, and does not change no matter the rate of new members. Hope this helps!

Answer:

30 and 9

Step-by-step explanation:

x+y=39 , x-y=21

Solve for x:

x+y=39 , x-y=21

x= 30

Substitute x with 30:

(30)+y=39 , (30)-y=21

Solve for y:

y=9

Answer:

30 and 9

Eeexplination;

Answer:

Step-by-step explanation:

There are four methods of sampling namely Random sampling,Stratified sampling, Cluster sampling and Multistage sampling. Let’s look at them one by one.

Random sampling - When each subject of the population is equally likely to be included in the sample, the sampling method is called random sampling.

Stratified sampling- Under this, the data are first divided into stratas. Each stratum consists of homogeneous subjects and strata are heterogeneous among themselves. Samples are randomly taken from each strata. Example- In an investigation of mortality rate of the insured, we can first subdivide the data into males and females and then take sample from each group. Here, male and female groups represent stratas.

Cluster sampling- Under this we first divide the data into clusters that are homogeneous among themselves and then select few of them and sample all observations from the randomly selected clusters. For example- suppose we want to take a sample of people's weight in a specific city. We observed that the areas in that city are similar to each other , so instead of travelling to each area and collecting data we can select few areas and then take observations from all people of those areas.

Multistage sampling - This adds one more stage to cluster sampling. Unlike cluster sampling where we sample all observations from the selected clusters, In multistage sampling we randomly sample observations from each selected cluster.

I hope this helped.

Answer:

a) 12:12 simplified version is 1:1

b) 5:12:12 cannot be simplified

c) 12:5:12 cannot be simplified

d) 0.50:3.00:0.60

Step-by-step explanation:

The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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I. The bacteria culture doubles in size every. day

Answer:

3x - 4y = 11

For (3, -8): 3(3) - 4(-8) = 9 + 32 = 41 ≠ 11.

For (4, 4): 3(4) - 4(4) = 12 - 16 = -4 ≠ 11

Neither ordered pair is a solution.

Step-by-step explanation:

Answer:

\(P(A\ and\ B) = 44\%\)

Step-by-step explanation:

Given

Represents the event as follows:

A = \(Elon\ Musk\) will offer you a \(free\ trip\) into space in the next month\

B = Scientists from \(Area\ 51\) will \(start\ selling\) pet aliens next month

So, we have:

\(P(A) = 41\%\)

\(P(B) = 27\%\)

\(P(A\ or\ B) = 24\%\)

Required

Determine \(P(A\ and\ B)\)

This is calculated as:

\(P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)\)

So, we have:

\(P(A\ and\ B) = 41\% + 27\% - 24\%\)

\(P(A\ and\ B) = 44\%\)

The statement "Any u linearly independent vectors from Py will definitely form a basis for the vector space P4" is false.

To understand why this statement is false, we need to first understand what a basis is. A basis for a vector space is a set of vectors that are linearly independent and span the entire vector space. In other words, any vector in the vector space can be expressed as a linear combination of the basis vectors, and no basis vector can be expressed as a linear combination of the other basis vectors.

Now let's consider the vector space P4, which consists of all polynomials of degree 4 or less. Suppose we have a set of u linearly independent vectors from Py, where Py is a subset of P4. It is possible that these vectors do not span the entire vector space P4. In other words, there may be some polynomials in P4 that cannot be expressed as a linear combination of the u vectors. If this is the case, then the u vectors do not form a basis for P4.

To illustrate this, consider the following example. Let Py = {1, x, x^2} be a subset of P4. We can see that these three vectors are linearly independent, since there is no non-zero linear combination of them that equals the zero polynomial. However, they do not span the entire vector space P4, since there are polynomials of degree 3 or less that cannot be expressed as a linear combination of 1, x, and x^2. For example, the polynomial p(x) = x^3 cannot be expressed as a linear combination of 1, x, and x^2. Therefore, 1, x, and x^2 do not form a basis for P4.

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The maximum height reached by the projectile is 12 feet, and it hits the ground approximately 1.228 seconds and 3.772 seconds after being launched.

To find the maximum height reached by the projectile and the time it takes to hit the ground, we can analyze the given quadratic function H(t) = -16t^2 + 72t + 12.

The function H(t) represents the height of the projectile at time t seconds after its launch. The coefficient of t^2, which is -16, indicates that the path of the projectile is a downward-facing parabola due to the negative sign.

To determine the maximum height, we look for the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of t^2 and t, respectively. In this case, a = -16 and b = 72. Substituting these values, we get x = -72 / (2 * -16) = 9/2.

To find the corresponding y-coordinate (the maximum height), we substitute the x-coordinate into the function: H(9/2) = -16(9/2)^2 + 72(9/2) + 12. Simplifying this expression gives H(9/2) = -324 + 324 + 12 = 12 feet.

Hence, the maximum height reached by the projectile is 12 feet.

Next, to determine the time it takes for the projectile to hit the ground, we set H(t) equal to zero and solve for t. The equation -16t^2 + 72t + 12 = 0 can be simplified by dividing all terms by -4, resulting in 4t^2 - 18t - 3 = 0.

This quadratic equation can be solved using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a), where a = 4, b = -18, and c = -3. Substituting these values, we get t = (18 ± √(18^2 - 4 * 4 * -3)) / (2 * 4).

Simplifying further, we have t = (18 ± √(324 + 48)) / 8 = (18 ± √372) / 8.

Using a calculator, we find that the solutions are t ≈ 1.228 seconds and t ≈ 3.772 seconds.

Therefore, the projectile hits the ground approximately 1.228 seconds and 3.772 seconds after its launch.

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Hello !

Answer:

4x² + 3x + 4

Step-by-step explanation:

 (3x² + 2x + 3) + (x² + x + 1)

= 3x² + 2x + 3 + x² + x + 1

= 3x² + x² + 2x + x + 3 + 1

= 4x² + 3x + 4

To prove the equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x), we can start by expressing the trigonometric functions csc(x) and cot(x) in terms of sine and cosine:

csc(x) = 1/sin(x)

cot(x) = cos(x)/sin(x)

Substituting these expressions into the equation, we get:

(1/sin(x))^4 - (cos(x)/sin(x))^4 = (1/sin(x))^2 + (cos(x)/sin(x))^2

Next, we simplify each term separately:

(1/sin(x))^4 = 1/sin^4(x)

(cos(x)/sin(x))^4 = cos^4(x)/sin^4(x)

Expanding the powers, we have:

1/sin^4(x) - cos^4(x)/sin^4(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)

Combining the fractions on the left side:

(1 - cos^4(x))/sin^4(x) = (1 + cos^2(x))/sin^2(x)

Now, let's simplify the left side:

1 - cos^4(x) = sin^4(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

sin^4(x) = sin^4(x)

The equation simplifies to an identity, showing that the original equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x) is true for all values of x.

Therefore, we have proved the given equation.

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Answer:

101º

Step-by-step explanation:

supplementary angles mean they equal 180

so 180 - 79=101

Answer:

1080°

Step-by-step explanation:

Sum of interior angles = 180°(n-2)

Where n is the number of sides of the polygon

Therefore,

Sum of interior angles of an octagon =180°(8-2)

=1080°

A polygon is a geometrical shape that has between 1 to an infinite number of sides. A polygon can come in two forms:

The sum of the interior angles of the irregular octagon is 1080°

The formula to solve for the sum of the interior angles of an irregular polygon is given as:

(n - 2) x 180°

Where n =  number of sides.

An octagon is a polygon that has 8 sides. Hence, n = 8

So: (8 - 2) x 180°

= 6 x 180°

= 1080°

Therefore, the sum of the interior angles of the irregular octagon is 1080°

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To disprove Micah's claim that the base of the prism must be a square, we can draw a rectangular base for the prism with dimensions that satisfy the volume and height requirements.

Micah's claim states that the base of the prism must be a square. However, to show that this claim is incorrect, we need to provide a counterexample by drawing a base that is not a square but still satisfies the given conditions.

Given that the volume of the prism is 360 cubic units and the height is 10 units, we can find the dimensions of the base by dividing the volume by the height: 360/10 = 36.

Now, we can draw a rectangle as the base of the prism with dimensions that multiply to give a product of 36. For example, we can draw a base with dimensions of 4 units by 9 units. This rectangle is not a square since its sides have different lengths.

By constructing a rectangular base with dimensions of 4 units by 9 units, we demonstrate that Micah's claim is incorrect. This shows that the base of the prism does not have to be a square, as there are other valid configurations that satisfy the given volume and height requirements.

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Answer:

28%

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Percent of catalogues received = 100% - percent of magazines received

100 - 22 = 78%

Percent of clothing catalogues = 0.78 x 36 = 28%

Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, you can calculated in this case:

Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:

m= (-4 - (-8))÷ (4 - (-1))

m= (-4 + 8)÷ (4 + 1)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-8= 4/5× (-1) + b

-8= -4/5 +b

-8 + 4/5= b

-36/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.

Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:

m= (-5 - (-9))÷ (7 - 2)

m= (-5 + 9)÷ (5)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-9= 4/5× (-2) + b

-9= -8/5 +b

-9 + 8/5= b

-37/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.

You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.

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