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3 years ago

Evaluate using the definition of absolute value |x-2|=6

Mathematics

1 answer:

lesantik [10]3 years ago

7 0

Well, the definition of absolute value is distance from zero, so we're making a graph.

Make a number line where 0 is in the center. You know that the distance from 0 is 6, so put x-2 at the -6 and the 6 points. Now add two to both of those, and now graph on the -4 point "x₁", and on the 8 point "x₂". Put down x₁ = -4 and x₂ = 8 (the normal way, not on the graph) next to it, and you'll be done.

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Elena-2011 [213]

Answer:

$g(x)=-(x+1)^2-4$ .

Step-by-step explanation:

The parent function is

$f(x)=x^2$

Step 1: Start with the equation $f(x)=x^2$ . Write the equation for the graph of g(x) that has been

reflected, or flipped, over the x-axis.

$f_1(x)=-f(x)$

$f_1(x)=-x^2$

Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has

also been shifted down 4 units.

$f_2(x)=f_1(x)-4$

$f_2(x)=-x^2-4$

Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has

also been shifted left 1 unit.

$g(x)=f_2(x+1)$

$g(x)=-(x+1)^2-4$

Therefore, the required equation is $g(x)=-(x+1)^2-4$ .

4 0

3 years ago

The volume of a cube is 36 cm3. What is the surface area of the cube, rounded to the nearest tenth of a cm2

alekssr [168]

Answer:

65.4 cm²

Step-by-step explanation:

The volume of a cuboid is calculated by multiplying the length, base, and height together. Since a cube has equal sides, the formula for the volume of a cuboid can be simplified as shown below.

Volume of cube

= side ×side ×side

= side³

Given that the volume is 36 cm³, let's find the length of each side.

side³= 36

Cube root both sides:

side= $\sqrt[3]{36}$

Total surface area of a cube is the sum of the surface areas of its 6 identical square faces.

Area of a square

= side ×side

= side²

Surface area of 1 face= $(\sqrt[3]{36})^2$

Total surface area

= $6(\sqrt[3]{36} )^2$

= 65.416 (5 s.f.)

= 65.4 cm² (nearest tenth)

Additional:

To learn more about surface area of cube, do check out the following!

brainly.com/question/21600799

3 0

2 years ago

The picture is up there thank you:))

MA_775_DIABLO [31]

Search up the question and you will find your answer

6 0

3 years ago

2 – 2n = 3n -+- 17<br>pls help

gayaneshka [121]

Answer:

n=-3

Step-by-step explanation:

3 0

4 years ago

Question 1

lesya [120]

It would be 12h :))((:

7 0

3 years ago

Evaluate using the definition of absolute value |x-2|=6​

Evaluate using the definition of absolute value |x-2|=6