Write a verbal description for each algebraic expression 100-5n

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

Alla [95]

Considering the given equation of the circle, the true statements are given as follows:

The radius of the circle is of 3 units.

The center of the circle lies on the x-axis.

The circle has the same radius as the circle with equation x² + y² = 9.

<h3>What is the equation of a circle?</h3>

The equation of a circle of center $(x_0, y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The equation given is:

x2 + y² - 2x - 8 = 0.

Completing the squares, the equation is given as follows:

(x - 1)² + y² = 8 + 1

(x - 1)² + y² = 9.

Researching the problem on the internet, the true statements are:

The radius of the circle is of 3 units.

The center of the circle lies on the x-axis( $y_0 = 0$ ).

The circle has the same radius as the circle with equation x² + y² = 9.

More can be learned about the equation of a circle at brainly.com/question/24307696

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8 0

1 year ago

The triangle shown is a right triangle. Create the equation to be used to find the missing lengths.

telo118 [61]

The equation used to find the missing lengths:
9 = __SR (5^2 + x^2)__
As long as it is a right triangle, this is called the Pythagorean Theorem
${9}^{2} = {x}^{2} + {5}^{2} \\ \sqrt{ {9}^{2} } = \sqrt{( {x}^{2} + {5}^{2} )} \\ 9= \sqrt{( {x}^{2} + {5}^{2} )}$

** FYI- if you wanted to SOLVE FOR THE MISSING SIDE X, then just switch around the original equation solving in terms of x:
${9}^{2} = {x}^{2} + {5}^{2} \\ {x}^{2} = {9}^{2} - {5}^{2} \\ x= \sqrt{( {9}^{2} - {5}^{2})} = \sqrt{(81 - 25)} \\$
$x = \sqrt{56} = \sqrt{(8 \times 7)} \\ x= \sqrt{(4 \times 14)} = \sqrt{4}\times \sqrt{14} \\ x = 2 \sqrt{14}$

6 0

3 years ago

Someone remind me of what the Pythagorean theorem is (Geometry)

Ugo [173]

Answer:b

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Describe the graph of the function.<br> y =Square root of<br> x-1 + 4

Ulleksa [173]

Answer: Square root of x+3

Step-by-step explanation:

Insert the denominator to 3

5 0

3 years ago

Read 2 more answers

Write the equatoin of a graph that has Roots of x={-2,0,4} and has a point of (-1,10)

zheka24 [161]

Step-by-step explanation:

to have "roots" means that the function delivers 0 as function result for these values of x.

so,

f(x) = 0 for x = -2, x = 0 and x = 4

we can build this function as a product of factors.

each factor is an expression of x that turns 0 for the given value of x.

what is the simplest expression of x that turns 0, when x = -2 ?

well : x + 2

as you can easily see, this is 0, when x = -2.

and the easiest existing of x that is 0, when x = 0 ?

totally simple : just x.

and then x - 4 for x = 4

so, our function is

f(x) = x(x + 2)(x - 4)

but : this is one of infinite possibilities.

let's see what happens, if we use the x coordinate (-1) of the given point (-1, 10).

we know, the result must be 10.

-1×(-1 + 2)(-1 - 4) = -1×1×-5 = 5

aha ! so, in order to get 10 instead of just 5 we must multiply the whole thing by 2.

as n×0 is always still 0, this does not change our 0 points (or roots).

so, our full function is :

f(x) = 2x(x + 2)(x - 4)

or, if you need the function as a polynomial, we need to do the multiplications :

f(x) = 2x(x² - 4x + 2x - 8) = 2x(x² - 2x - 8) = 2x³ - 4x² - 16x

3 0

1 year ago