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3 years ago

What is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4

Mathematics

1 answer:

aev [14]3 years ago

7 0

Answer:

$\large\boxed{y=3x-11}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=3x-4\to m_1=3\\\\\text{Therefore}\ m_2=3.\\\\\text{We have the equation:}\ y=3x+b.\\\\\text{Put the coorsdinates of the point (2, -5) to the equation of the line}\\\\-5=3(2)+b\\-5=6+b\qquad\text{subtract 6 from both sides}\\-11=b\to b=-11$

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Correct Answer:
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vfiekz [6]

Answer:

<h3>Toni can type words in 3 minutes is 270 words</h3>

Step-by-step explanation:

Given that the double number line shows that Toni can type 180 words in 2 minutes.

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Read 2 more answers

Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y = 1 into two regions with equ

Dennis_Churaev [7]

Answer:

y=1/∛4 divides the area in half

Step-by-step explanation:

since the minimum value of x² is 0 (for x=0 ) and for y=1

1 = 25*x² → x= ±√(1/25) = ±1/5

then the total area between y=1 and y = 25*x² is bounded to x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus

Area below x=C = Area above x=C

Area below x=C = Total area - Area below x=C

2*Area below x=C = Total area

Area below x=C = Total area /2

∫ 25*x² dx from x=c to x=-c = 1/2 ∫ 25*x² dx from x=1/5 to x=-1/5

25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]

2*c³/3 = (1/5)³/3

c = 1/(5*∛2)

thus

y=25* x² = 25*[1/(5*∛2)]² = 1/∛4

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