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UkoKoshka [18]
3 years ago
6

Rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if x>5

Mathematics
2 answers:
Wittaler [7]3 years ago
5 0

Answer:

  y = x + 4

Step-by-step explanation:

Since x > 5, x-3 > 0, x + 2 > 0 and x - 5 > 0

So Ix - 3I = x - 3,   Ix + 2I = x + 2   and x - 5 = x - 5

Therefore, y = x - 3 + x + 2 - x + 5

                  y = x + 4

Svetlanka [38]3 years ago
5 0

Answer:

Step-by-step explanation:

It might interest you to know what this question means without the restriction. See graph 36b. This shows exactly what happens to the absolute value. There are all sorts of turns and twists in it. Notice all the changes in direction and the minimum at -2,-2. The y intercept is at 0,0.

0,0 is also one of the x intercepts as well. The other is -4,0. The whole point of showing you this is to make you aware of what the restriction does.

The graph is reduced to a line starting at (5,9)

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3 years ago
A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1). Write a function in standard form that can repres
VLD [36.1K]

Answer:

(x^4) - 64x

Step-by-step explanation:

zeros at 4 and 0 are the roots so can be factor as x*(x-4) and the multiplicity tels to what power you have to raise those factors

x^{1} *(x-4)^{3} becuase multiplicity of 1 for root at 0, and multiplicity of 3 at root 4

now to write this in standard form

x*(x-4)^{3} = \\x*(x-4)(x^{2} +4x+16)= \\(x^{2} -4x)(x^{2} +4x+16) = \\x^{4} +4x^{3} +16x^{2} -4x^{3} -16x^{2} -64x = \\x^{4} -64x

8 0
3 years ago
Do the equations x + y = -2 and 3x + 3y = −6 define the same line? Explain.
tino4ka555 [31]

Answer:

Yes, they do.

Step-by-step explanation:

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6 0
3 years ago
A 24-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 6 feet
andrezito [222]

Answer:

23.24 feet

Step-by-step explanation:

Use the pythagorean theorem: a² + b² = c², where a and b are legs of the right triangle and c is the hypotenuse.

In this situation, the ladder is the hypotenuse of the triangle, and the distance from the base of the building is the long leg.

Plug in the ladder length as c and plug in the distance from the base of the building as a:

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(6²) + b² = (24)²

36 + b² = 576

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So, the ladder reaches approximately 23.24 feet up the wall

5 0
3 years ago
Read 2 more answers
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