find and sketch the domain of the function. f(x, y) = ln(25 − x2 − 25y2)

On solving the provided question we can say that - the value of the equation x = y^2 -5 from the graph will be 59.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here, the equation from the graphs is

[tex]y^2 = x^8 -7.8x-9,=.43y[/tex]

and y = 8

x = 59

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The value of the trigonometric functions cos 2θ and cos 0.5θ for the given angle are - 7 / 25 and - 2√5 / 5, respectively.

In this problem we must determine the cosine of the double angle and half angle based on the exact values of the cosine of an angle and the quadrant location of the angle.

Cosine is a function between - 1 and 1 and whose period is 2π (360°), positive when angle is either on first quadrant (0 < θ < 0.5π) or on fourth quadrant (1.5π < θ < 2π). In addition, sine function is positive on first quadrant and negative on fourth quadrant.

The required trigonometric formulas in terms of trigonometric function cos θ are described below:

sin θ = √(1 - cos² θ)

cos 2θ = cos² θ - sin² θ

cos 0.5θ = ± √ [(1 + cos θ) / 2]

First, determine the exact value of sine:

sin θ = - √[1 - (3 / 5)²]

sin θ = 4 / 5

Second, determine the exact value of cosine of the double angle:

cos 2θ = (3 /  5)² - (4 / 5)²

cos 2θ = - 7 / 25

Third, determine the exact value of cosine of the half angle:

cos 0.5θ = - √[(1 + 3 / 5) / 2]

cos 0.5θ = - 2√5 / 5

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The surface whose equation is given. [tex]rho2(sin2(φ) sin2(θ) + cos2(φ)) = 4[/tex] is a cylinder with radius 2.

The cylinder has two key characteristics, namely surface area and volume, because it is a three-dimensional form. The combined curved surface area of the cylinder and the areas of the two circular bases make up its whole surface area. A cylinder's volume is the term used to describe the three-dimensional space it takes up.

A surface is a representation of a surface in mathematics. Similar to how a curve generalizes a straight line, it is a generalization of a plane but unlike a plane, it may be curved.

A thing or body's top or outer limit. on the water's surface. the surface of the earth. a two-dimensional locus of points that can be flat or curvy (such as the boundary of a three-dimensional region).

The equation of the surface is

[tex]$$\rho^2\left(\sin ^2 \phi+\sin ^2 \theta+\cos ^2 \phi\right)=4[/tex]

equation of a cylindrical surface is [tex]$y^2+z^2=r^2$$$[/tex]

[tex]\begin{aligned}& y^2=\rho^2 \sin ^2 \phi \sin ^2 \theta \\& \mathrm{y}=\rho \sin \phi \sin \theta\end{aligned}$$[/tex]

and, [tex]$\mathrm{z}=\rho \cos \phi$[/tex]

and, Radius of the cylinder is

[tex]$$r=2 \text {. }$$[/tex]

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[tex](\stackrel{x_1}{x}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{x}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{4}}\implies \cfrac{3}{9-x}=\cfrac{1}{4}\implies 12=9-x \\\\\\ 12+x=9\implies \boxed{x=-3}[/tex]

Answer:

7 5/12 hope this helps:)

Step-by-step explanation:

(you can use ph0t0math for these types of questions)

Answer:

y = - x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 6 ) and (x₂, y₂ ) = (4, 0 )

m = [tex]\frac{0-6}{4-(-2)}[/tex] = [tex]\frac{-6}{4+2}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation.

using (4, 0 ) , that is x = 4, y = 0

0 = - 4 + c ⇒ c = 0 + 4 = 4

y = - x + 4 ← equation of line

The linear equation from the equation given in the picture, would be  y = - 0. 2x + 2

A linear equation is used to determine the direction and values of a line in a chart or graph. It takes the form shown below of :

y = mx + b

y is the dependent variable

m is the slope of the line

x is the independent variable

b is the y - intercept

When given the formula, x + 5y = 10, the linear equation can be found in the steps of :

x + 5y = 10

5y = 10 - x

Divide all sides by 5 to get rid of the 5 next to y:
5y / 5 = 10 / 5 - x / 5

y = 2 - 1 / 5 x

y = - 0. 2x + 2

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The five number summary of the given data is the minimum value = 20, maximum value = 100, median = 69.5, Q1 = 48, and Q3 = 89.

A number summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median. In order to find the five number summary,

1. Arrange the given data in ascending order. In the given case, the data is already in ascending order.

2. Determine the minimum and maximum value for the data set. In the given case, the minimum value is 20 and maximum value is 100.

3. Determine the median of the data set. The median refers to the middle number of the data set. If the data is an even set of numbers, the middle two terms are averaged. In the given case, there are 14 numbers, hence the median is an average of 7th and 8th term.

Median = (69 + 70)/2 = 69.5

4. Determine the lower quartile (Q1) and upper quartile (Q3). The Q1 and Q3 are the middle term of the lower and upper range respectively.

For the lower range, 20, 33, 43, 48, 64, 68, 69, the middle term is 48. Hence Q1 = 48.

For the upper range, 70, 72, 83, 89, 96, 99, 100, the middle term is 89. Hence Q3 = 89.

Note: The question is incomplete. The complete question probably is: Find the 5 number summary for the data shown. 20, 33, 43, 48, 64, 68, 69, 70, 72, 83, 89, 96, 99, 100

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The quadratic function answer for 2(x^2-3x+6) is 4x^2 - 6x + 12.

I believe that is correct

The statement that is false is: " lf p q is true, then p is a necessary condition in order that q holds."

In a logical statement "p implies q" (p->q), if p is true, then q must be true as well. However, this doesn't mean that p is necessary for q to hold. A necessary condition means that p is required for q to be true, but it's not sufficient, it may be other conditions that are also needed. In this statement, p is a sufficient condition for q to hold, but it's not necessary. This statement is a logical converse of the second statement "If p q is true, then p is a sufficient condition in order that q holds."

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a. The percent of Benny's mom's age to his age is 400%.

b.  Benny's mom's age is 400% of his age.

What is a percent of numbers?

The percent of a number is its fraction that is expressed as percentage. Thus the percentage of a number or part of a number can be determined.

Considering the given question, the years of Benny and that of his mom were given as;

Benny's age = 12 years

His mom's age = 48 years

Thus we can deduce that;

a. The percent of his mom's age to that of Benny's = 48/ 12 * 100%

                                            = 400%

b. Benny's mom's age is 400% of his age.

Therefore, the correct option to be selected is D.

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The rational expressions include the following two (x²+6)/x²-4,  6/x²-7

You should understand that a rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.

Rational fractions can be reduced to their lowest terms

Examples rations expressions include

(7n-9)(p+5)

Radical expression which is used to indicate a root is called a radical and is therefore read "x radical n," or "the nth root of x." In the radical symbol, the horizontal line is called the vinculum, the quantity under the vinculum is called the radicand, and the quantity n written to the left is called the index.

Example 1) (6p+9)/5p = √(6p+9)/√(5p)  (2) (7n-9)(p+5) = √(7n-9)(p+5)

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The area of the path as a function is A(x) = (4x²+80x) square meters.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A pool measuring 28 meters by 12 meters is surrounded by a path of uniform width, as shown in the figure.

To express the area of the path, A, in square meters, as a function of its width, x, in meters:

The area of the path

A(x) = (12+2x)(28+2x) - (28 × 12)

A(x) = 4x²+56x+24x+336 - 336

A(x) = (4x²+80x) square meters.

This is a quadratic function.

Therefore, (4x²+80x) square meters are the area of the path.

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statistics is the calculation or manipulation of data or any other things where the operation of addition division multiplication substraction will be held but not any other logic related to non tangible

non statistical sampling is where calculation or any other means of addition substraction is not done but the judgement is done on the basis of examiners mind but not on the basis of any calculation .

we can use statistic in every day life also in every field because if we do any calculation then it is a part of mathematical statistic

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Answer:

[tex]f(g(x)) = g(f(x)) =x[/tex]

So [tex]f(x)[/tex] and [tex]g(x)[/tex] are inverses of one other

Step-by-step explanation:

If two functions [tex]f(x)[/tex] and [tex]g(x)[/tex] are inverses of each other, their compositions will equal [tex]x[/tex]

Thus proved

The difference between the two probabilities is about 4.06 percentage points, so the answer is (c).

To compare the theoretical probability and the experimental probability of drawing a blue tile, we need to calculate both probabilities.

First, let's calculate the theoretical probability. There are a total of 36 tiles in the bag, and 10 of them are blue, so the theoretical probability of drawing a blue tile is 10/36, or about 27.78%.

Now let's calculate the experimental probability. In the five trials, you drew a total of 236 tiles, and a total of 75 blue tiles. So the experimental probability of drawing a blue tile is 75/236, or about 31.86%.

Comparing the theoretical probability and the experimental probability, we can see that the experimental probability is greater than the theoretical probability. The difference between the two probabilities is about 4.06 percentage points, so the answer is (c).

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By using the substitution approach and resolving the variable x, the equations Y=4x - 11 and Y= -3x + 10 are each solved as x,y = 2,3.

Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.

given

Solve equation [2] for the variable  y

 y = 6x - 9

variable  y  ...... equation [1]

  4x + (6x-9) = 11

  10x = 20

Solve equation [1] for the variable  x

10x = 20

  x = 2

   y = 6x-9

y = 6(2)-9 = 3

By using the substitution approach and resolving the variable x, the equations Y=4x - 11 and Y= -3x + 10 are each solved as x,y = 2,3.

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[tex]\it \begin{cases}\it y=4x-11\\ \\ \it y=-3x+10\end{cases}\ \Rightarrow 4x-11=-3x+10 \Rightarrow 4x+3x=10+11 \Rightarrow 7x=21\Rightarrow \\ \\ \\ \Rightarrow x=3;\ \ \ y=4\cdot3-11=12-11=1\\ \\ S=\{(2,\ \ 1)\}[/tex]

Answer:

  1064

Step-by-step explanation:

You want the product g(3)·g(4), given that g(x) = x³ -8.

For each function value, put the number where the variable is and do the arithmetic.

  g(3)·g(4) = (3³ -8)(4³ -8) = (27 -8)(64 -8) = 19·56

  g(3)·g(4) = 1064

The value of the sales tax will be 1.21. Sales tax is a fee that is charged in addition to the cost of products and services. We have to use basic percentage mathematics concepts.

Let's first try to understand what is sales tax.

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government. A company is liable for sales taxes in a particular jurisdiction if it has a nexus there, which, depending on the local rules, can be a physical location, an employee, an affiliate, or some other presence.

Sales taxes typically take a portion of the cost of the items sold. For instance, a city's residents might pay a total of 7.5% in sales taxes if the state levies a 4% rate, the county 2%, and the city 1.5%. However, frequently certain things—like food—are exempt or are exempt if they fall below a specific amount, such as apparel purchases under $200. Additionally, many products are subject to additional taxes known as excise taxes. A type of excise tax known as a "sin tax" is the $1.50 municipal excise tax that New York City imposes per pack of 20 cigarettes in addition to the $4.35 state excise tax.

In this Question, The bill before tax and tip was $17.35.

Sales tax of 7% added.

7% of  $17.35 = 7 * 17.35/100 = 1.2145

The nearest cent value will be 1.21.

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The sales tax was $1.22 and the total amount of the bill including the tip was $18.57.

The total cost of the meal before tax and tip was $17.35. The sales tax rate for the area was 7%. To calculate the sales tax, we must first determine the pre-tax cost of the meal multiplied by the tax rate.

Formula:

Sales Tax = Pre-tax cost × Tax Rate

Calculation:

Sales Tax = $17.35 × 0.07

Sales Tax = $1.22

This means that the sales tax amount was $1.22. Vani tipped 18% on the amount after the sales tax was added. To calculate the total amount of the bill after tip, we must first add the sales tax to the pre-tax cost of the meal.

Formula:

Total Cost = Pre-tax cost + Sales Tax

Calculation:

Total Cost = $17.35 + $1.22

Total Cost = $18.57

We can then calculate the tip amount by multiplying the total cost of the meal by the tip rate.

Formula:

Tip = Total Cost × Tip Rate

Calculation:

Tip = $18.57 × 0.18

Tip = $3.35

Therefore, the sales tax was $1.22 and the total amount of the bill including the tip was $18.57.

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The equations that show the properties of the exponenets are a, c and d

We know that there are certain properties that are common to the numbers that appear in the exponential form. We shall look at some of those properties.

1) when we have;

(ab)^x, it is the same as a^x b^x

2) When we have b^2 * b^x, it is the same as b^2 + x

3) When we have; x^-2, it is the same as 1/x^2

These are the basics of the properties of the exponents as we can see in the question and these obey the properties of the exponents.

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It will take to complete the entire order of sneakers in 8 days.

To find out how long it will take to complete the entire order of sneakers, you need to multiply the time it takes to complete 1/10 of the order by the total number of orders. Since there are 10 orders in the entire order of sneakers, it will take 10 times as long to complete the entire order as it does to complete 1/10 of the order.

Since it takes 4/5 of a day to complete 1/10 of the order, it will take 4/5 * 10 = 8 days to complete the entire order. Therefore, the answer is 8 days.

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At given rate, it will take 8 days to complete the entire order of sneakers

In this questiion we have been given at Sami's Shoe Warehouse, it takes 4/5 day to complete 1/10 of an order of sneakers.

We need to find the number of days it will take to complete the entire order of sneakers, at this rate.

It takes 4/5 day to complete 1/10 of an order of sneakers.

If we multiply a fraction by 10 then it would be 10/10

This means, 10/10 represents the complete order of sneakers.

4/5 days are required to complete 1 of 10 order of sneakers.

For 10 of 10 order of sneakers:

By unitary method,

10 × 4/5

= 2 × 4

= 8 days

So, it will take 8 days to complete the order.

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The unit that is most appropriate for the time at which the number of weeks is 120 is given as follows:

Week.

The general format for an exponential function is given as follows:

[tex]y = a(b)^{\frac{x}{n}}[/tex]

The parameters for the exponential function are defined as follows:

The number of weeds in my yard doubles every 3 weeks, and the initial number of weeks is of 80, hence the values of the parameters are given as follows:

a = 80, b = 2, n = 3.

As n = 3, we have that the unit of the output variable is of weeks, hence weeks is the appropriate measure in this problem.

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Answer:

Step-by-step explanation:

I can calculate the volume of a prism with a complicated base by decomposing the Which of these solids are prisms

Their monthly income of George is 57,600.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given spends of George from monthly income,

let monthly income be x

spends on food = 5/8 of salary

spends on food = 5x/8

amount left = x - 5x/8 = 3x/8

spends on fees = 1/6 of remainder

spends on fees = 1/6 × 3x/8 = x/16

amount left = 3x/8 - x/16 = 5x/16

spend on contingencies = 2/3 of remainder

spend on contingencies = 2/3 × 5x/16

spend on contingencies = 5x/24

amount left = 5x/16 - 5x/24 = 5x/48

amount left = 6000 = 5x/48

x = (6000×48)/5

x = 57,600.

Hence monthly income is 57,600.

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George's monthly salary is 57600

A fraction represents a numerical value, which defines the parts of a whole. the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction. The top number represents the number of selected or shaded parts of a whole whereas the bottom number represents the total number of parts.

Let monthly salary of George be x.

Given, Money spend on food = 5/8th of salary = 5/8x

Remaining salary = x - 5x/8 = 3x/8

Amount on school fees = 3x/8 × 1/6 = x/16

Remaining amount = 3x/8 - x/16 = 5x/16

Amount on contingencies = 5x/16 × 2/3 = 5x/24

According to the question

5x/8 + x/16 + 5x/24 + 6000 = x

(30x + 3x + 10x) /48 +6000 = x

43x /48 + 6000 = x

x-43x/48 = 6000

48x - 43x = 6000 × 48

5x = 288000

x = 57600

George monthly salary = 57600

Hence, George get a monthly salary of 57600

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Answer:

y = 4/5x + 3

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope slopes.

The first line is y = 4/5x + 2. Its slope is 4/5. A line parallel to this one will also have a slope of 4/5.

Plug this value (4/5) into your standard point-slope equation of y = mx + b.

y = 4/5x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (5, 7). Plug in the x and y values into the x and y of the standard equation.

7 = 4/5(5) + b

To find b, multiply the slope and the input of x (5)

7 = 4 + b

Now, subtract 4 from both sides to isolate b.

3 = b

Plug this into your standard equation.

y = 4/5x + 3

This equation is parallel to your given equation (y = 4/5x + 2) and contains point (5, 7).

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The amount of Indian rupees that I would be able to receive when $13 is exchanged would be = 601.2 Indian rupees.

Local currency exchange is defined as the exchange of a money currency from its local form to another form which depends of its current exchange rate.

From the expression given;

62.4d -210

Where d = $13

= (62.4× 13 )-210

= 811.2- 210

= 601.2

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Yes, the set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of [tex]$\mathbb{R}^n$.[/tex]

A subspace is a set of vectors that is closed under linear combinations. This means that if two vectors in the set are added together, the result is also in the set. A system of m homogeneous equations in n unknowns can be represented as a system of linear equations. The solution set of the system is the set of all vectors that satisfy the linear equations. Since the solution set is closed under addition, it is a subspace of [tex]$\mathbb{R}^n$[/tex]Furthermore, any linear combination of two solutions of the system is also a solution of the system, which further confirms that the solution set is a subspace of [tex]$\mathbb{R}^n$[/tex]

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Answer:

a)6.4x 10^-4 (b)1.40068493150 x10^3

Step-by-step explanation:

multiply 0.0064 by 10000 and as it is going from a smaller number to a bigger number it is 10 to the negative power of 4

b)place into a calculator and devide the number untill u get a number between 1 and 9

Answer:

After investing for 3 years at 7% interest, your $600 investment will have grown to $735.03

Step-by-step explanation: