A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.

The given equation is

$|\frac{1}{4}x+2 | -3=5$

Solving the equation:

$or,|\frac{1}{4}x+2 | =5+3\\or,|\frac{1}{4}x+2 |=8\\or,\frac{1}{4}x+2=\pm8\\or,x+8=\pm32\\or,x=-8\pm32$

Now we take the two separate values of x:

either x=-8+32 or x=-8-32

or,x=24 or x=-40

The value of x is 24 and - 40.

To learn more about number line:

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7 0

1 year ago

The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) a

Anuta_ua [19.1K]

Remember that

If the given coordinates of the vertices and foci have the form (0,10) and (0,14)

then

the transverse axis is the y-axis

the equation is of the form

(y-k)^2/a^2-(x-h)^2/b^2=1

In this problem

center (h,k) is equal to (0,4)

(0,a-k)) is equal to (0,10)

a=10-4=6

(0,c-k) is equal to (0,14)

c=14-4=10

Find out the value of b

b^2=c^2-a^2

b^2=10^2-6^2

b^2=64

therefore

the equation is equal to

<h2>(y-4)^2/36-x^2/64=1</h2><h2>the answer is option A</h2>

6 0

1 year ago