Rewrite the equation y=2|x−3|+5 as two linear functions f and g with restricted domains.

The absolute value transforms a negative number into a positive number.

For example

Let z be a real number, then:

| z | It will always be a positive number.

This means that:

If z is a negative number, then:

| z | = -z

If z is a positive number, then:

| z | = z

This means that for the expression the expression y = 2 | x-3 | +5

When x-3 > 0 then:

| x-3 | = x-3

When x-3 < 0 then:

| x-3 | = - (x-3)

Then we can divide the expression into two functions f (x) and g (x).

f (x) = 2 (x-3) +5

f (x) = 2x-6 + 5

f (x) = 2x-1

For

g (x) = 2 (-x + 3) +5

g (x) = -2x + 6 + 5

g (x) -2x +11

For

(x-3) < 0

x < 3

The two functions are

Step-by-step explanation:

Given: the equation .

From the question,

If , then

If , then

Now, divide the given expression into two different functions and solve it further

Here, then

And, then

Hence, two functions are

Learn more about Inequality here:

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a

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.