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Final answer:

Numbers or variables are placed outside of the radical sign when multiplied by a radical. This representation indicates that the entire radical, not just the number inside, is to be multiplied by that number or variable.

Explanation:

If a radical is multiplied by a number or variable, you should put the number or variable outside the radical sign. In mathematics, multiplication or division by the same number on both sides of an equation does not change the equality. When you multiply a radical by a number or variable, you are essentially multiplying the contents inside the square root by that number or variable, but outside of the radical sign to maintain proper order of operations.

When writing an expression involving radicals mathematically, numbers or variables outside the radical do not directly interact with the values inside until simplification or further operations are performed. For example, if you're multiplying 3 by √2, you would write it as 3√2, not √(3×2). The multiplication of the coefficient (the number in front of the radical) applies to the entire radical, not just the number inside it.

Answer:

D. The geodesics connecting the North and South Poles intersect at both of the Poles

Step-by-step explanation:

Answer:

D) The geodesics connecting the North and South Poles intersect at both of the Poles.

Step-by-step explanation:

got it right on edge 2021 :)

Answer: 54

Step-by-step explanation:

Average = Total/ total number

Average= 36 +72/2

             = 108/2

             = 54

54 is the  average of the two numbers 36 and 72.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the average of the two numbers 36 and 72.

The average (A) of two number, M and N, is given by the formula A=m+n/2

Let m = 36

n=72

Now to find the average of two numbers we have to plug in these values in the formula

A=36+72/2

=108/2

=54

Hence, 54 is the  average of the two numbers 36 and 72.

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Answer:

Both the equation and its inverse are functions.

Step-by-step explanation:

A function is relation in which one input gives one and only one output.

Here, the given function,

[tex]f(x)=5x+1[/tex]

Which is a polynomial,

A polynomial is a function because for each input value it gives only one output value.

⇒ f(x) is a function.

Now, For finding the inverse of f(x),

Replace f(x) by y,

y = 5x + 1

Switch x and y,

x = 5y + 1

Isolate y on the left side,

-5y = 1 - x

[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]

Replace y by [tex]f^{-1}(x)[/tex],

[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]

Which is also a polynomial,

Hence, the inverse of f(x) is also a function,

Last option is correct.

Final answer:

To calculate the sum of the squares of the roots of a quadratic equation, apply Vieta's formulas to find the sum and product of the roots and use them in the identity (α + β)² - 2αβ to avoid directly solving for the roots.

Explanation:

To find the sum of the squares of the roots of an equation, especially for a quadratic equation of the form ax²+bx+c=0, we use the relationship between the coefficients and the roots provided by Vieta's formulas.

The sum of the roots, denoted as α and β, is given by -b/a, and the product of the roots is c/a. To find the sum of the squares of the roots (α² + β²), you can use the identity (α + β)² = α² + 2αβ + β², or α² + β² = (α + β)² - 2αβ.

By substituting the sum and product of the roots from Vieta's formulas, you can calculate the sum of the squares without actually solving for the roots. This approach is especially useful in equilibrium problems or other situations where you might encounter square roots or higher powers and wish to simplify calculations.

Answer:

c is the answer

Step-by-step explan ation:

Answer:27

Step-by-step explanation:

For the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the given expression is 2(v-h)/k=r

We have to solve the expression in the term v as,

2(v-h)/k=r

Open the brackets and multiply 2 in the bracket as

(2v-2h)/k=r

Apply the cross-multiplication operation as

2v-2h=r·k

Rearrange the equation as

2v=r·k+2h

The equation for v in terms of all other variables involved is obtained as,

v=(r·k)/2+h

Thus, for the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.

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Set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function because it has an 'x' value (4) that corresponds to more than one 'y' value (2,-2), which contradicts the definition of a function.

The given set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function. In mathematical terms, for a set of ordered pairs to be considered a function, each input (or 'x' value) must have exactly one output (or 'y' value). However, in B, the input 4 corresponds to two different outputs: 2 and -2. This violates the definition of a function, proving that B is not a function.

It's useful to remember this as a rule: in functions, a particular x-value can only be paired with a single y-value. In contrast, in non-functions, a single x-value can be linked to multiple y-values, as demonstrated by set B.

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The interval on which f(x) is integrable is:

                             [-2, ∞)

We are given a function f(x) as:

               [tex]f(x)=\sqrt{x+2}[/tex]

We know that a function is integrable over a given interval if it is continuous over a given interval.

Now, we know that the square root function is well defined if the function under the square root sign is positive.

This means here the function is well defined if:

[tex]x+2\geq 0[/tex]

i.e.

[tex]x\geq -2[/tex]

Also, the square root function is continuous over it's domain.

and hence it is integrable over it's domain.

This means that the function is integrable over:

                       [-2,∞)

Answer:c(x)=2.00 +0.05x

Step-by-step explanation: