A pilot of an airplane flying at 12,000 feet sights a water tower. The angle of depression to the base of the tower is 25°. What is the length of the line of sight from the plane to the tower?

Answer:

One method for solving quadratic equations is factoring. Factoring involves finding the two factors of a quadratic equation and setting each factor equal to zero. For example, the quadratic equation x^2 + 5x + 6 = 0 can be factored into (x + 2)(x + 3) = 0. Setting each factor equal to zero, we get x + 2 = 0 and x + 3 = 0, which gives us the solutions x = -2 and x = -3.

Another method for solving quadratic equations is completing the square. This method involves manipulating the equation to transform it into a perfect square trinomial, which can then be easily solved. For example, the quadratic equation x^2 + 6x - 7 = 0 can be completed by adding (6/2)^2 = 9 to both sides of the equation, resulting in x^2 + 6x - 7 + 9 = 9, or (x + 3)^2 = 16. Taking the square root of both sides and solving for x, we get x = -3 + 4 or x = -3 - 4, giving us the solutions x = 1 and x = -7.

A third method for solving quadratic equations is using the quadratic formula. The quadratic formula is derived from completing the square and gives us the solutions to any quadratic equation. For the quadratic equation ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a. For example, the quadratic equation 2x^2 + 3x - 2 = 0 can be solved using the quadratic formula, giving us x = (-3 ± √(3^2 - 4(2)(-2))) / 2(2), or x = (-3 ± √25) / 4. This gives us the solutions x = -1/2 and x = -2.

In responding to my classmates, I would choose the method based on the specific quadratic equation given. For example, if the quadratic equation is easily factorable, I would use the factoring method. If it is not factorable, I would use either completing the square or the quadratic formula. Completing the square may be preferable if the coefficient of x^2 is 1, while the quadratic formula can be used for any quadratic equation.

Answer:

☆ -10 ☆ is your correct answer!

The pairs of lines are classified as: perpendicular, parallel, neither, neither.

The slopes of the first pair of lines differ, making them neither parallel nor perpendicular. The slopes of the first and second lines are 1/2 and -2, respectively.

The second set of lines is perpendicular because the slopes of the first line, which is -3, and the second line, which is 1/3, are the opposites of each other.

The third set of lines have varying slopes and are neither equal nor perpendicular. The slopes of the two lines are -2/3 for the first line and 6/4 for the second, which reduces to 3/2.

To classify each pair of lines as parallel, perpendicular, or neither, we need to compare their slopes.

2y = x and y = -2x + 6

The first equation can be written in slope-intercept form as y = (1/2)x, which means its slope is 1/2. The second equation can be written in slope-intercept form as y = -2x + 6, which means its slope is -2. Since the slopes are negative reciprocals of each other, these lines are perpendicular.

y + 3x = 1 and 2y = -6(x - 1)

The first equation can be written in slope-intercept form as y = -3x + 1, which means its slope is -3. The second equation can be written in slope-intercept form as y = -3x + 3, which means its slope is also -3. Since the slopes are the same, these lines are parallel.

3y + 2x = -3 and 4y = 6x + 12

The first equation can be written in slope-intercept form as y = (-2/3)x - 1, which means its slope is -2/3. The second equation can be written in slope-intercept form as y = (3/2)x + 3, which means its slope is 3/2. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

y + 2 = 5x and 5y - x = -2

The first equation can be written in slope-intercept form as y = 5x - 2, which means its slope is 5. The second equation can be written in slope-intercept form as y = (1/5)x - 2/5, which means its slope is 1/5. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

Therefore, the pairs of lines are classified as follows:

perpendicular

parallel

neither

neither

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Answer:

Width = 10

Step-by-step explanation:

let length = X

width = 3X - 2

Area = length x width

40 = X x (3X - 2)

40 = 3X^2 - 2X

therefore 3X^2 - 2x - 40 = 0

3x^2 + 10x - 12x - 40 = 0

x(3x + 10) - 4(3x + 10) = 0

(x - 4) (3x + 10) = 0

(x - 4) = 0

x = 4

(3x + 10) = 0

3x = - 10

x = -10/3

Since the lenght can't be negative, we'll work with x = 4

Therefore the width = 3x - 2

Width = 3(4) -2

Width = 12 - 2

Width = 10

Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5).

A translation in mathematics is a transformation of such a curve or a this double object that entails moving the curve or item from point to point along its graph. We have different terms to express this kind of alteration according to the nature of translation.

Initial coordinates of Retention Pond 1:

(-8,8) , (-8, 3), (-4, 3) and (-4, 8)

After the translation of 8 units to the right. Add 8 to each x-coordinates.

After the translation of  13 units down. subtract 13 to each y-coordinates.

(-8,8)  = (-8 + 8,8 - 13)  = (0, -5)

(-8, 3) =  (-8 + 8, 3 - 13) = (0, -10)

(-4, 3) = (-4 + 8, 3 - 13) = (4, -10)

(-4, 8) = (-4 + 8, 8 - 13)  = (4, -5)

Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5). There will be no change in the area.

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The rate that Danielle drank water is 8/3 liters per hour.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13. Here, 2x – 5 and 13 are expressions The sign that connects these two expressions is “=”.

To find the rate that Danielle drank water in liters per hour, we need to divide the amount of water she drank by the time taken to drink it and then convert to hours.

The equation that shows how to find the rate is:

Rate = (Amount of water drank ÷ Time taken to drink) x (Time in 1 hour ÷ Time in the given period)

Substituting the given values, we get:

Rate = (2/3 ÷ 1/4) x (1 ÷ 1/4)

Simplifying the fractions, we get:

Rate = (2/3 x 4/1) x (4/1)

Rate = 8/3 liters per hour

Therefore, the rate that Danielle drank water is 8/3 liters per hour.

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Let "e" be the elevation of the submarine and "t" be the time taken to descend.

Then, the equation representing the relationship between the submarine elevation and time is:

e = -105t + 2100

where the coefficient of "t" (-105) represents the rate of descent of the submarine, and the constant term (2100) represents the initial elevation of the submarine.

Answer:

Solution for What is 0.56 percent of 72:

0.56 percent *72 =

(0.56*72):100 =

40.32:100 = 0.4032

Now we have: 0.56 percent of 72 = 0.4032

Question: What is 0.56 percent of 72?

Percentage solution with steps:

Step 1: Our output value is 72.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 72=100\%

Step 4: Similarly, x=0.56%.

Step 5: This results in a pair of simple equations

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%)

Step 7: Again, the reciprocal of both sides gives

I hope this helped! A brainilist is appreciated and helpful! <333

Answer:

Rectangular prism: A prism with bases rectangle in shape. Pentagonal Prism: A prism with bases pentagon in shape. Hexagonal Prisms: A prism with bases hexagon in shape. Octagonal Prism: A prism with bases octagon in shape.

Step-by-step explanation:

Rectangular prism: A prism with bases rectangle in shape. Pentagonal Prism: A prism with bases pentagon in shape. Hexagonal Prisms: A prism with bases hexagon in shape. Octagonal Prism: A prism with bases octagon in shape.

This should work

Step-by-step explanation:

2. name: rectangular parallelepiped

bases: rectangles

lateral faces: rectangles

3. name: right triangular prism

bases: right triangles

lateral faces: rectangles

4. name: right hexagonal prism

bases: hexagons

lateral faces: rectangles

Answer: length is 33ft

Step-by-step explanation:

Perimeter = length x2 + width x2 (add all sides of a rectangle)

width = 15ft

15 x 2 = 30 ft

86ft - 30 ft = 66 ft

66/2 = length of 1 side = 33 ft

If 7 people each got a train ticket instead of buying one train ticket, they would pay a total of £28.70, which is £24.60 more than the cost of one train ticket.

If one train ticket costs £4.10, then the cost of 7 train tickets would be:

7 x £4.10 = £28.70

Therefore, if 7 people each got a train ticket instead of one train, they would pay a total of £28.70.

To find out how much more money they would pay in total, we need to subtract the cost of one train ticket from the total cost of 7 train tickets:

£28.70 - £4.10 = £24.60

Therefore, 7 people would pay £24.60 more in total if each of them got a train ticket instead of buying one train ticket.

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Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

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The value of k is 2.

Instead of producing approximations at random, it is better to use moving numeral variables, which may be rising, declining, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, parts, and mathematical comments for equation techniques like additional disapproval, production.

To simplify the expression, we need to first convert the mixed numbers [tex]3 8/2[/tex] and [tex]3 8/4[/tex] to improper fractions:

[tex]3 8/2 = 3 (24 + 8)/2 = 312/2 = 18[/tex]

[tex]3 8/4 = 3 (4 + 8/4) = 3*(4+2) = 18[/tex]

Now, we can rewrite the expression as:

[tex](3 8/2) (3 8/4) = 18 * 18 = 18^2[/tex]

Therefore, [tex]k = 2[/tex], and the expression ([tex]3 8/2) (3 8/4[/tex]) can be written as [tex]3^2 = 9.[/tex]

So the final answer is: The expression [tex](3 8/2) (3 8/4)[/tex] simplifies to 9, which can be written in the form [tex]3^2.[/tex] Therefore, the value of k is 2.

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The probability that Precious has a job or is a university student is 1/12.

What is probability ?

Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
Probability can be used in a wide variety of applications, such as in gambling, statistics, and science. In these fields, probability is used to make predictions, analyze data, and test hypotheses.

According to the question:
To find the probability that Precious has a job or is a university student, we can use the formula:

P(job or university student) = P(job) + P(university student) - P(job and university student)

We are given that the probability that Precious has a job is 3/8, and the probability that she is a university student is 1/4. We are also given that the probability that she works and is a university student is 13/24.

So, we can substitute these probabilities into the formula:

P(job or university student) = 3/8 + 1/4 - 13/24

We can simplify by finding a common denominator:

P(job or university student) = 9/24 + 6/24 - 13/24

P(job or university student) = 2/24

Finally, we can simplify by dividing both the numerator and denominator by 2:

P(job or university student) = 1/12

Therefore, the probability that Precious has a job or is a university student is 1/12.

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Answer:7/10

Step-by-step explanation:

Answer:

[tex] \frac{7}{9} [/tex]

Explanation:

First, you have to write a number in the numerator, that is after the comma (in this case it's 7)

And then, in the denominator, you have to write a number that is made of nines only (the number of nines you have to write is the number of decimal numbers, in this case it's 1 nine)

Sample selection bias occurs when a selection process influences the availability of data and that process is related to the dependent variable.

The correct answer is an option (c)

We know that in statistics the sample selection bias is nothing but the bias that results from the failure to ensure the proper randomization of a sample.

It is caused by choosing non-random data for statistical analysis.

Here a subset of the data is excluded from the study, due to the flaws in the sample selection process.

There types of sample selection bias are: pre-screening bias, self-selection bias, exclusion bias, and observer bias.

therefore, this bias occurs when a selection process influences the availability of data and that process is related to the dependent variable.

The correct answer is an option (c)

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Answer:

the total area under the normal distribution is 0.0684.

Step-by-step explanation:

We can use a standard normal distribution table or a calculator to find the areas S₁ and S₂.

Using a standard normal distribution table or calculator, we find:

S₁ = 0.0158

S₂ = 0.0526

To find the total area S₁ + S₂, we simply add these two values:

S₁ + S₂ = 0.0158 + 0.0526 = 0.0684

Therefore, the total area under the normal distribution is 0.0684.

Answer:

64 in^2.

Step-by-step explanation:

The surface consists of 4 congruent triangles and a square base.

Area of 1 triangle = 1/2 * 4*6  = 12.

Area of the base = 4*4 = 16.

So the required surface area

= 4*12 + 16

= 64 in^2.

192 ways that Fred can dress for the week

Outfit Choices: 7 Days

Angel

Fred is looking to pick out his clothes for the next 7 days. He has two different pairs of pants and

two different shirts. Each day he needs to wear a different outfit than what he wore the day before.

However, he has already chosen his outfit for Friday due to a formal occasion. How many ways can he

dress for the week?

Since Fred has already chosen his outfit for Friday, he only needs to choose 6 outfits for the remaining days of the week (Saturday through Thursday).

For each day, he has 2 choices for pants and 2 choices for shirts. So there are 2 × 2 = 4 possible outfits for each day.

To make sure he wears a different outfit each day, Fred needs to choose a different outfit from the previous day's outfit. For Saturday, he has 4 choices. For Sunday, he has 3 choices (since he cannot wear Saturday's outfit), and so on, until Thursday, for which he has only 1 choice.

The measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

The upper base angles m∠DAB and m∠ADC are equal, and angles m∠ADC and m∠DCB are supplementary, so we shall calculate for the angle m∠DAB by first evaluating for angle m∠ADC as follows:

m∠ADC + m∠DCB = 180° {opposite angles are supplementary}

m∠ADC + 105° = 180°

m∠ADC = 180° - 105° {subtract 105° from both sides}

m∠ADC = 75°

m∠ADC = m∠DAB = 75°

Therefore, the measures of the angle m∠DAB for the isosceles trapezoid is equal to 75°.

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If sinA = 3/8, the value of cosec A - sec A is (72√55 - 440)/495

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

If sin A = 3/8

and SinA = opp/ hyp

opp = 3 and hyp = 8

using Pythagoras theorem

8² = 3²+adj²

adj = √ 8²-3²

adj = √64-9

adj = √55

cos A = √55/8

sec A = 1/CosA = 8/√55

cosec A = 1/sinA = 8/3

cosec A-sec A = 8/ √55 - 8/3

= (24-8√55)/3√55

= (72√55 - 440)/495

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The answer is x = 12.

The probability of one microbial spore surviving in 10x containers processed is given by the formula:1/10x. The question below asks for a process that reduces cell numbers by 12 decimal reductions (a 12d process) applied to a raw material that contains 1,000,000 spores per container would reduce microbial numbers to 10-x per container. x is then found by solving the equation `10-x = 1/10¹²`.Here's how to solve the equation:First, the fraction 1/10¹² is simplified.10¹²=10x10x=10¹²log(10x)=log(10¹²)x=log(10¹²)/log(10)x=12

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Answer:

7 - 3

And if you want the difference it is 4

Step-by-step explanation:

because difference means subtract

We can conclude by answering the provided question that Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

In mathematics, a function appears to be a connection between two groups of numbers in which each member of the first set (known as the domain) correlates to a specific member of the second set (called the range). In other terms, a function takes input from one set and generates output from another. The variable x has frequently been used to represent inputs, and the variable y has been used to represent outcomes. A formula or a grid can be used to describe a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x gives a unique value of y.

We can deduce from the provided function:

g(x) = 0 when x = 0.

For 0 x 1, g(x) = x2.

g(x) = 2 - x for 1 x 2.

g(x) = 0 when x > 2.

So, to draw the graph of g(x), we can join the points (x, g(x)) for various values of x within the specified intervals.

Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

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(a) The number of distinguishable arrangements of the word "acbens" is 180.

(b) The number of distinguishable arrangements of the word "baaben" is 60.

(c) The number of distinguishable arrangements of the word "aabbba" is 15.

(a) The word "acbens" has 6 letters, but two of them ("a" and "b") are repeated. We can use the formula for the number of permutations of n objects with k1, k2, ..., km indistinguishable objects of types 1, 2, ..., m, respectively:

P(n; k1, k2, ..., km) = n! / (k1! k2! ... km!)

For this word, we have k1 = 2 (for the two "a"s) and k2 = 1 (for the "b"). Plugging these values into the formula, we get

P(6; 2, 1) = 6! / (2! 1!) = 360 / 2 = 180

Therefore, there are 180 distinguishable arrangements of the word "acbens."

(b) The word "baaben" also has 6 letters, but this time there are three "a"s and two "b"s. Using the same formula as before, we have k1 = 3 and k2 = 2, so

P(6; 3, 2) = 6! / (3! 2!) = 720 / 12 = 60

Therefore, there are 60 distinguishable arrangements of the word "baaben."

(c) The word "aabbba" has 6 letters, but this time there are four "a"s and two "b"s. Using the same formula as before, we have k1 = 4 and k2 = 2, so

P(6; 4, 2) = 6! / (4! 2!) = 720 / 48 = 15

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Answer:170

Step-by-step explanation: Since you know that to find a circumference you need a 2pi diameter so what you do is divide the circumference by 2 to find the radius

The length οf οne side οf the cube is 4 cm.

In geοmetry, a cube is a three-dimensiοnal sοlid shape that has six square faces οf equal size, and all its angles are right angles (90 degrees). A cube is a regular pοlyhedrοn, which means that all its faces are cοngruent (i.e., identical) regular pοlygοns and its edges have the same length.

The surface area οf a cube with edge length "s" is given by the fοrmula:

[tex]SA = 6s^{2}[/tex]

We are given that the surface area οf the cube is [tex]96 cm^2[/tex]. Therefοre, we can set up the equatiοn:

[tex]96 = 6s^{2}[/tex]

Dividing bοth sides by 6, we get:

[tex]16 = s^{2}[/tex]

Taking the square rοοt οf bοth sides, we get:

s = 4

Therefοre, the length οf οne side οf the cube is 4 cm.

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The quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:

[tex]$x^2 + 12x - 17 = 0$[/tex].

What is quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means it involves an unknown variable (usually denoted as x) that is raised to the power of 2. The general form of a quadratic equation is given by:

a[tex]x^{2}[/tex] + bx + c = 0

where a, b, and c are constants, and a is not equal to 0.

The quadratic equation that could be solved to find any solutions to the system of equations

[tex]$y = -5x + 6$[/tex]

[tex]$y = x^2 + 7x - 11$[/tex]

is given by:

[tex]$x^2 + 12x - 17 = 0$[/tex]

Therefore, the quadratic equation that could be solved to find any solutions to the system of equations [tex]$y = -5x + 6$[/tex] and [tex]$y = x^2 + 7x - 11$[/tex] is:

[tex]$x^2 + 12x - 17 = 0$[/tex]

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The angle x to the nearest degree is 47°.

To find the value of the angle to the nearest degree, we can use the inverse tangent function, which relates the opposite and adjacent sides of a right triangle to the angle opposite the opposite side. Specifically, we can use the formula:

tan(A) = opposite/adjacent where A is the value of angle.

Here, "opposite" is the height of the triangle (11) and "adjacent" is the base of the triangle (10).

We can solve for x by taking the inverse tangent (or arctangent) of both sides of the equation:

[tex]$ \rm x = tan^{-1} \left( \frac{opposite }{adjacent}\right)[/tex]

[tex]$ \rm x = tan^{-1} \left( \frac{11}{10}\right)[/tex]

Using a calculator, we can evaluate this expression to find

x ≈ 47.34 °

To round this to the nearest degree, we can look at the decimal part of the answer (0.34) and see that it is closer to 0.5 than 0. Therefore, we can round up to the nearest degree x ≈ 47 degrees

So, the angle x to the nearest degree is 47 degrees.

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Complete question: