A circle is centered at K(0,0)K(0,0)K, left parenthesis, 0, comma, 0, right parenthesis. The point U(6,-4)U(6,−4)U, left parenthesis, 6, comma, minus, 4, right parenthesis is on the circle.Where does the point V(\sqrt{2},-7)V(
2
​
,−7)V, left parenthesis, square root of, 2, end square root, comma, minus, 7, right parenthesis lie?

The all other 3 factors of the equation  x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3).

What are the roots of an equation?

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.

Given the equation,

x⁴ + 2x³ − 7x² − 8x + 12

If (x - 2) is a factor of the equation then it should be divisible by it.

So,

(x⁴ + 2x³ − 7x² − 8x + 12) / (x - 2) = (x³ + 4x² + x - 6)

Now divide by (x - 1) of  (x³ + 4x² + x - 6)

(x³ + 4x² + x - 6) / (x - 1) = x² + 5x + 6

So,

⇒ (x - 2)(x - 1)(x² + 5x + 6)

⇒  (x - 2)(x - 1)( x² + 2x + 3x + 6)

⇒   (x - 2)(x - 1)[ x(x + 2) + 3(x + 2) ]

⇒  (x - 2)(x - 1)(x + 2)(x + 3)

Hence "The all other 3 factors of the equation  x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3)".

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Answer:

Step-by-step explanation:

The given equation is:

Now, (x-2) is a factor of the given equation, therefore

Therefore, the other factors are (x-1), (x+2) and (x+3).

Answer:

Step-by-step explanation:

I am assuming that you are referring to the diameter and area of a circle. If this is false, then please note that my answer is wrong.

Ok, we know that the area formula for a circle is A = , where r is the radius.

We also know that the diameter, a, is two times the radius. Thus, , which also means that  . This means that we can substitute the radius (r) with half the diameter () in the area formula equation:

Your question asks us to find the diameter, which means we must solve for, or isolate, the diameter (a):

Using the function concept, it is found that:

A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.

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

• A function has the following format:

• In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

• The input is x and the output is y.
• Then, the word independent completes the sentence.

A similar problem is given at brainly.com/question/21084589

Answer:

A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.

Step-by-step explanation:

We have been an incomplete statement. We are asked to complete the given statement.

We know that a function is a relation between two sets. A relation is known as function when each input in the domain has exactly one specific corresponding output.

We also know that independent variable is known as input of function and dependent variable is known as output of function.

Therefore, the correct word for given statement would be independent variable.

The pair of equations best models the relationship between c and a is option D :  c = a + 5,  c = a - 3

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given conditions are;

c is 5 more than variable a.

( c = a + 5)

c is also three less than variable a.

(c = a - 3)

Now, lets look at the answer choices,

c = a − 5

c = a + 3

Here, c is 5 less than "a". so it will be automatically disqualified.

a = c + 5

a = 3c − 3

So,

Simplified version :

c = a - 5

Here, c is 5 less than "a"..so it will be automatically disqualified.

a = c − 5

a = 3c + 3

Here also, we have to get "c" by itself in both top and bottom equation.

So,

Simplified version:

c = a + 5

Here, c is 5 more than "a"

c = (a - 3) / 3

thus, c is 3 less than "a" divided by 3 . So, this is not correct.

c = a + 5

c = a − 3

Here, c is 5 more than "A"

Also, c is 3 less than "a"

So, Which satisfies the given.

So, our answer is going to be the option D :

c = a + 5

c = a - 3

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