Find a parametrization of the circle with center (1, 3, 5) and radius 3 in a plane parallel to the xy-plane.

Step-by-step explanation:

a) 2y = 3x + 4

b) given the perpendicular

3x + 5y = 1

5y = 1 - 3x

y = 1/5 - 3x/5

m¹ = -3/5

perpendicular

m¹m² = -1

-3m²/5 = -1

m² = 5/3

so (1,8)

x¹ = 1 y¹ = 8

m² = (y - y¹)/(x - x¹)

5/3 = (y - 8)/(x - 1)

5x - 5 = 3y - 24

3y - 5x + 5 - 24 = 0

3y = 19 + 5x

Answer:

----------------------

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

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We have a group of 169 students that needs to be seated in a square formation. Then, the number of rows has to be the square root of 169 :-

\(r = \sqrt{169} = 13\)

Then, a square of 13 rows and 13 columns will fit the 169 students.

If the number of students is 1024, then the number of rows N can be calculated as :-

\( {N}^{2} = 1024\)

\(N = \sqrt{1024} \)

\(N = 32\)

169 students will seat in a 13×13 formation.

1024 students will seat in a 32×32 formation (N=32)

-------------------★-------------------

The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

Given that,

The system of inequality

y < x² + 2

y > x² - 6

We have to find the common point of the system of inequality.

We know that,

The graph is shown in the image.

Using the graphing technology,

A will be the first equation's vertex (0,2)

The parabola's outer region will be shaded and its boundary will be a dotted line because y is less than the value required by the quadratic equation.

In a similar way, the second equation's vertex, (0,-6), will be a dotted parabola with shaded inner portions.

The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

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The given statement " If two sounds can form a minimal pair, they are allophones of two distinct phonemes." is true. because when two sounds can form a minimal pair, it demonstrates that the difference between the sounds is crucial for distinguishing the meaning of the words in the language as a result these sounds cannot be considered as allophones of the same phoneme, as they do not share the same underlying representation.

A minimal pair refers to two words that differ in only one sound but have different meanings. For example, "bat" and "pat" differ only in their initial consonants, /b/ and /p/, but have distinct meanings. This difference in meaning indicates that the two sounds are part of separate phonemes.

Phonemes are the basic, abstract units of sound in a language that can change the meaning of a word when substituted for one another. Allophones, on the other hand, are the various concrete realizations of a phoneme that do not change the meaning of a word. They are considered to be different surface forms of the same underlying phoneme.

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The statement ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)) is false.

Let's start by understanding what "p" is. "p" is a function that takes in two arguments, x and y. It tells us whether the relationship between x and y is true or false.

Now, let's look at the statement

=>∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

This statement says that for every x, there exists a y and a z such that y is not equal to z and both p(x, y) and p(x, z) are true.

This statement is actually false.

Why? Imagine if p(x, y) only returned true when y was equal to x. Then, there would be no y and z such that y is not equal to z and both p(x, y) and p(x, z) are true.

Therefore, it is possible for the function "p" to return false for the statement

=> ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).

It depends on the definition of the function. To determine if the statement is true or false, we need to know what the function "p" is.

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The area principle is a fundamental concept in data visualization that states that the size of a graphical element (such as a bar, a pie slice, or a bubble) should be proportional to the quantity it represents.

In other words, the area of the graphical element should accurately reflect the magnitude of the data it is displaying. This principle is particularly important when comparing quantities, as it allows the viewer to quickly and accurately perceive the relative differences between them. For example, if two bars in a bar chart have the same width but different heights, the viewer may be misled into thinking that the two quantities are closer in magnitude than they actually are.

The area principle is often applied in conjunction with other principles of good data visualization, such as using clear and simple designs, avoiding clutter, and choosing appropriate scales and units. The goal is to create visualizations that are not only aesthetically pleasing but also informative and effective in communicating the underlying data.

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The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function. m represents the line's slope, or how steep it is. The coordinate for x is x.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function.

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Answer:

2

Step-by-step explanation:

Given

f(x) = | x - 4 | - 9, then

f(- 7) = | - 7 - 4 | - 9

        = | - 11 | - 9 ( absolute value returns a positive value )

        = 11 - 9

        = 2

Answer:

M= -3

Step-by-step explanation:

The two points on the graph are (0,4) and(1,1), using the slope formula you get a slope of - 3

Answer:

x=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

9+11= 20

4x=20

20/4x= 5

Answer:

7x the answer i think

Step-by-step explanation:

Answer:

\(\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}\)

Step-by-step explanation:

We are asked to check is -2 is the solution of the following equation.

\(2-x= 4x+3\)

We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.

\(2- (-2) = 4(-2)+3\)

Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Let's start with the left side.

\(2+2= 4(-2)+3 \\\)

\(4= 4(-2)+3\)

Now solve the right side. Remember to multiply first.

\(4= -8+3\)

\(4= -5\)

\(4\neq -5\)

4 is not equal to -5, so -2 is not the solution for this equation.

Answer:

B, C, D, and F are all possible.

Answer:

B, C, D

Step-by-step explanation:

1. A is not possible because right and obtuse both define triangle angles. An angle cannot be obtuse and right at the same time.

2. B is possible because a right triangle can have all sides of different length.

3. C is possible because a scalene triangle can have an obtuse angle.

4. D is possible because an isosceles triangle can have all acute angles.

5. E is not possible because of how equilateral triangles work. When a triangle is equilateral, it is also equiangular, meaning all of its angles are the same. The angles on every type of triangle always add up to 180 degrees. If a triangle is equiangular, the 180 degrees are divided evenly, with every angle being 60 degrees, which is acute. Therefore, an equilateral triangle cannot have a right angle.

6. F is not possible because isosceles and scalene both refer to the side lengths of triangles. A triangle cannot be isosceles and scalene at the same time.

7. G is not possible because equilateral triangles cannot have angles other than 60 degrees and therefore cannot be obtuse.

There are a total of 9 possible sums. Suppose, the cards in the first set are 4, 5, and 6.

Similarly, the cards in the second set are 5, 6, and 7. A total of nine cards are there. If we choose one card from the first set and one card from the second set, then we get a total of nine possible pairs.

Hence, the sum of these pairs can be 4 + 5, 4 + 6, 4 + 7, 5 + 5, 5 + 6, 5 + 7, 6 + 5, 6 + 6, and 6 + 7. Therefore, there are nine possible sums possible.

Additionally, there are three possibilities in the first set (4, 5, and 6) and three possibilities in the second set (5, 6, and 7).

This means that there are 3 × 3 = 9 possible pairs of cards that we can choose, so there are 9 possible sums.We can list all of these sums as follows:4 + 5 = 96 + 5 = 116 + 5 = 116 + 6 = 127 + 5 = 127 + 6 = 137 + 7 = 14. Therefore, there are a total of 9 possible sums.

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The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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Answer:

32:24

Step-by-step explanation:

So ratios are like fractions

You can write 32:24 like \(\frac{32}{24}\)

and 30:22 like \(\frac{30}{22}\)

Like fractions you can simplify them, you want to get the denominator or the bottom numbers the same so you can compare the top number.

\(\frac{32}{24}\)     \(\frac{30}{22}\)     One way to make the denominator the same is to do 24x22=528

then do 32x22=704          then 30x24=720

Then that gives you \(\frac{704}{528} \frac{720}{528}\)    Here you can see that 704 is smaller then 720

and since 704 is the same as 32:24

32:24 is the smaller ratio

Answer:

You will need 7 vans and 4 buses

Step-by-step explanation:

7 vans would take care of 35

4 buses would take care of 140 kids

and it uses a total of 11 vehicles

Hope this helps  

Answer:

Vans = 7

Buses = 4

Step-by-step explanation:

x = vans

y = buses

x + y = 11                           (1)

5x + 35y = 175                 Divide this equation by 5

x + 7y = 35                       (2)  

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

                                        Subtract (1) from (2)

x + 7y = 35

x +  y =   11

     6y = 24                      Divide by 6

     6y/6 =24/6

       y = 4

===========

x + y = 11

x + 4 = 11

x = 11 - 4

x = 7

Now Let's check it

x is the number of vans which holds 5 students each

7 * 5 = 35

y is the number of buses which holds 35 students each

4 * 35 =140

Total number of students = 35 + 140 = 175

So it checks.

Answer:

Step-by-step explanation:

Just simplify 144/864 to its simplest version.

144/864, divide numerator and denominator by 144 and you get 1/6, it's simplest form.

line segment DE is also 10 inches long, matching the length of line segment AB.

If line segment AB is congruent to line segment DE, it means that they have the same length.

In this case, it is stated that line segment AB is 10 inches long.

Therefore, we can conclude that line segment DE is also 10 inches long.

Congruent segments have identical lengths, so if AB and DE are congruent, they must both measure 10 inches.

Thus, line segment DE is also 10 inches long, matching the length of line segment AB.

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Answer:

its y+-2+7

Step-by-step explanation:

According to the given work and time, if Julio works for only 2 minutes, it would take approximately 3.33 minutes for both Julio and Jaden working together to change one tire.

Julio can change a tire in 5 minutes, while his twin brother Jaden takes 10 minutes. We need to determine how much time it would take for both brothers, working simultaneously, to change one tire if Julio only works for 2 minutes.

Let's assume that the time it takes for both brothers working together to change one tire is represented by "t" minutes. We can set up a proportion based on the work rates of Julio and Jaden:

Julio's work rate: 1 tire / 5 minutes

Jaden's work rate: 1 tire / 10 minutes

Combined work rate: 1 tire / t minutes

According to the work rate principle, the combined work rate is the sum of the individual work rates. Therefore, we have the equation:

1/5 + 1/10 = 1/t

To find the value of "t", we need to solve this equation. Multiplying through by the least common denominator (LCD) of 10t, we get:

2t + t = 10

Combining like terms, we have:

3t = 10

Dividing both sides by 3, we find:

t = 10/3

So, it would take both Julio and Jaden working simultaneously approximately 3.33 minutes (or 3 minutes and 20 seconds) to change one tire if Julio only works for 2 minutes.

Therefore, if Julio works for only 2 minutes, it would take approximately 3.33 minutes for both Julio and Jaden working together to change one tire.

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Step-by-step explanation:

here ! I used the formula area = length × width

and just some algrbric expressions solving

You arrange 5 letters in 7893600 ways

From the question, we have the following parameters that can be used in our computation:

Letters to use = 5

Total available letters = 26

The letters are distinct

This means that the letters cannot be repeated

So, we have

First = 26, Second = 25 ....... Fifth = 22

Using the above as a guide, we have the following:

Ways = 26 * 25 * 24 * 23 * 22

Evaluate

Ways = 7893600

Hence, the arrangement is 7893600

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nub 5777977777777777777777777777777777777777777

Answer:

2101=64...............

Answer:

slope = for every +3x there is a gain of +6y. so slope is 2.

Step-by-step explanation:

There are 2 tablespoons in an ounce. So for 2 ounces, you will need 4 tablespoons, for 4 ounces 8 tablespoons, and so on.

A tablespoon is a unit of volume measurement in United States, and some other countries. It is equal to approximately 15 milliliters (0.51 fluid ounces). One tablespoon can be further divided into three teaspoons, meaning that one tablespoon is equal to three teaspoons.

In the United States, one tablespoon is equal to 0.5 ounce, which is equal to 14.3 grams. This is slightly different in the UK, where one tablespoon is equal to 0.6 ounces (which is equal to 17.7 grams). To convert tablespoons to ounces, you can use the following formula is 1 tablespoon = 0.5 ounces.

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The function f(x) = 1/2(3)ˣ + 7 depicts exponential decay.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Euler’s Number ‘e’ is a numerical constant used in mathematical calculations and is an irrational number. Jacob Bernoulli discovered the mathematical constant e.

e =  \(\lim_{n \to \infty} (1 + 1/n)^{n}\)

We have the following function -

f(x) = 1/2(3)ˣ + 7

It can be seen that the graph decreases and becomes constant in the first quadrant. Therefore, the function depicts exponential decay.

Therefore, the function f(x) = 1/2(3)ˣ + 7 depicts exponential decay.

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By taking the difference between the two times, we will see that he has 28 minutes to get ready.

To find this, we need to take the difference between the hour at which he needs to leave (first value that we need to write in the number line) and the hour at which he wakes up (second value in the number line)

The time that he has to get ready is just the distance between these two points on the number line, or we can get it by taking the difference.

He wakes up at 7:47 am = 7 hours and 47 minutes.

He needsto leave at 8:15 am = 8 hours and 15 minutes.

The differnece is:

(8h and 15m) - (7h and 47m)

(8h - 7h) + (15m - 47m)

1h + ( -32m)

And we know that 1 hour = 60 min, then:

1h + ( -32m) = 60 min - 32 min = 28min

He has 28 minutes to get ready.

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