the total cost of 4 pens and 7 mechanical pencils is $13.25 the cost of each pencil is $0.75 write an equation that could be used to find the cost of a pen

The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].

To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.

In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).

In interval notation, we can express this as:

[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]

This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.

For more such questions on domain

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The greatest number of identical bracelets that can be made using all the beads is 4. This is found by determining the greatest common divisor (GCD) of 16, 20, and 24, which is 4. Each bracelet will consist of 4 yellow beads, 5 red beads, and 6 orange beads.

The subject of this question is the mathematical concept of the greatest common divisor (GCD). In the given problem, you are tasked with finding the maximum number of identical bracelets you can make with a given number of beads. The concept of GCD is used here.

First, we need to determine the GCD of the quantities of the three different colored beads:

The GCD of 16, 20, and 24 is 4. This means the largest number of identical bracelets you can make, using all of the beads, is 4. Each bracelet will have 4 yellow beads, 5 red beads, and 6 orange beads.

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The expression 2x-3 represent's: The number of songs downloaded by Nicholas.

The variable x represents: The number of songs downloaded by Sabrina.

Answer:

△PQR and △RST are not similar.

Step-by-step explanation:

In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is

[tex]180-34-80=66[/tex]

In triangle △RST, two known interior angles are 24° and 90°.

[tex]180-24-90=66[/tex]

Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.

Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.

Answer:.1

Step-by-step explanation:

The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.

The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.

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Answer:

Step-fbccbbby-CBC step explanation:

A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log 100 = 2

because

102 = 100

This is an example of a base-ten logarithm. We call it a base ten logarithm because ten is the number that is raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. If you wanted, you could use two as a base unit. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight: 

log2 8 = 3

because

23 = 8

In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written 

log

and a base ten logarithmic equation is usually written in the form:

log a = r 

A natural logarithm is written

ln

and a natural logarithmic equation is usually written in the form:

ln a = r

So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.

Final answer:

Logarithms are used in Mathematics to solve exponential equations by converting them into linear equations. They involve finding the exponent to which a base must be raised to equal a given number. Properties of logarithms, such as the product and quotient rules, help manipulate and solve logarithmic equations.

Explanation:

Logarithms are mathematical tools used to solve exponential equations and simplify complex calculations. They are the inverse function of exponential functions and help us solve for the unknown exponent in an equation.

Logarithms work by converting exponential equations into linear equations. When we take the logarithm of a number, we are finding the exponent to which a base must be raised to equal that number. For example, the logarithm (base 10) of 100 is 2, because 10 raised to the power of 2 equals 100.

The properties of logarithms allow us to manipulate them to solve equations. Some key properties include:

Each student will receive approximately 0.1667 parts of a whole cantaloupe when Mr. Chu evenly divides 4 cantaloupes among 24 students.

The subject of this problem is how to divide a quantity fairly between multiple recipients, also known as division. If Mr. Chu is slicing 4 cantaloupes and wants to divide them equally among 24 students, we need to find how much each student would receive.

This is solved by simply dividing the total quantity of cantaloupes by the number of students. So, 4 (whole cantaloupes) divided by 24 (students) equals 0.1667.

Therefore, each student will get approximately 0.1667 of a whole cantaloupe.

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The probability that exactly 13 students will take up arts in the coming year is; 76.47%

We are given;

Number of students that study art each year = 17

Now, we want to find the probability that 13 students will take up arts in the following year. This is;

P(13 will take art the next year) = 13/17 * 100%

P(13 will take art the next year) = 76.47%

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The measure of angle APC equals 69°

What is the measure of angle APC?

∠1 = 42°

∠2 = 27°

Angle APC is equal to the sum of angle 1 and angle 2.

∠APC = ∠1 + ∠2

= 42° + 27°

= 69°

Hence, m ∠ APC = 69°

Complete question:

if m ∠ 1 = 42 and m ∠ 2 = 27, then m ∠ APC = ?

That is the correct graph that represents

{3y≥x−9 3x+y>−3

hope i helped =D

we have

[tex]3y\geq x-9[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the solid red line

See the attached figure N [tex]1[/tex]

[tex]3x+y> -3[/tex] ----> inequality B              

The solution of the inequality B is the shaded area above the dotted blue line

See the attached figure N [tex]2[/tex]

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

See the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure