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Vitek1552 [10]
3 years ago
5

Consider M, N, and P. collinear points on MP.

Mathematics
1 answer:
Kobotan [32]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

There are three possible cases:

1. Point N lies between M and P, then MN + NP = MP. Consider needed difference:

\dfrac{MN}{NP}-\dfrac{MN}{MP}=\dfrac{MN}{NP}-\dfrac{MN}{MN+NP}=\dfrac{MN(MN+NP)-MN\cdot NP}{NP(MN+NP)}=\\ \\=\dfrac{MN^2+MN\cdot NP-MN\cdot NP}{NP(MN+NP)}=\dfrac{MN^2}{NP(MN+NP)}

2. Point N lies to the right from point P, then MP + PN = MN.  Consider needed difference:

\dfrac{MN}{NP}-\dfrac{MN}{MP}=\dfrac{MP+PN}{NP}-\dfrac{MP+PN}{MP}=\dfrac{MP}{NP}+1-1-\dfrac{NP}{MP}=\dfrac{MP^2-NP^2}{NP\cdot MP}

3. Point N lies to the left from point M, then NM + MP = NP. Consider needed difference:

\dfrac{MN}{NP}-\dfrac{MN}{MP}=\dfrac{MN}{MN+MP}-\dfrac{MN}{MP}=\dfrac{MN\cdot MP-MN(MN+MP)}{MP(MN+MP)}=\\ \\=\dfrac{MN\cdot MP-MN^2-MN\cdot MP}{MP(MN+MP)}=\dfrac{-MN^2}{MP(MN+MP)}

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Step-by-step explanation:

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(3x-2)(4x-7)=(3x)(4x)+(3x)(-7)+(-2)(4x)+(-2)(-7)\\\\=12x^2-21x-8x+14\qquad\qquad\text{combine like terms}\\\\=12x^2+(-21x-8x)+14=12x^2-29x+14

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Find the amount of tax and the tax rate. Round to two decimal places
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Answer:

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Step-by-step explanation:

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Type the correct answer in the box. Rewrite the quadratic equation in the form y = a(x − h)2 + k. y=5x^2-30x+95
S_A_V [24]

Answer:

y = 5(x - 3)^2 + 50

Step-by-step explanation:

The problem wants you to rewrite the quadratic equation in the vertex form y = a(x - h)^2 + k

You are given a quadratic equation in standard form (ax^2 + bx = c).

To convert from standard form to vertex form, there are two ways but I will show you the easier(?) way.

Use the formula x = -b/2a to find the x-value (h) of the vertex. Note that the vertex in "vertex form" is (h, k) which is virtually the same as (x, y).

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Substitute the values for h and k into the vertex form.

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Answer:

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Step-by-step explanation:

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