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lys-0071 [83]
3 years ago
5

A motorboat travels 105 kilometers in 3 hours going upstream. It travels 165 kilometers going downstream in the same amount of t

ime. What is the rate of the
boat in still water and what is the rate of the current?
Mathematics
1 answer:
Novay_Z [31]3 years ago
8 0

Answer:

Rate in still water = 45 km/h

Rate of the current = 10 km/h.

Step-by-step explanation:

Let the rate of the current be x and rate in still water be y.

So the rate of the boat upstream is y - x and the rate downstream = x + y.

Rate upstream = distance / time

y - x = 105/3 = 35 ...... (1)

Rate downstream:

y + x = 165/3 = 55 .......(2)

Adding (1) + (2):

2y = 90

y = 45 km/h.

Using equation (1):

45 - x = 35

x = 45-35 = 10 km/h.

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Most staircases in use today have 9−inch treads and 8 12 −inch risers. What is the slope of a staircase with these measurements?
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Answer:

The value is  m  = 0.9022

Step-by-step explanation:

From the question we are told that

    The length of the treads is  a =  9 \  inch

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Generally the slope of the staircase is

         m  =  \frac{b}{a}

=>       m  =  \frac{8.12}{9}

=>       m  = 0.9022

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2 years ago
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Answer:

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Step-by-step explanation:

5 0
3 years ago
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lubasha [3.4K]

Answer:

Therefore the equation of the line through ( -2 , -7 ) and ( 5 , 7 ) is

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Step-by-step explanation:

Given:

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Let,

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point B( x₂ , y₂) ≡ ( 5 , 7 )

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Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula,

(y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\

Or

Equation of a line passing through a points A( x₁ , y₁) and i having slope m is given by the formula,

(y - y_{1} )=m\times(x-x_{1}) \\

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(y-(-7))=2\times (x-(-2))\\ \\(y+7)=2(x+2)\\\\(y+7)=2x+4\\2x-y=3\\2x-y=3...............\textrm{which is the required equation of the line AB}

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2x - y = 3

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A dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre-image. How do you know that
Marat540 [252]

A dilation can elongate or diminish a figure. It can create an image the same as the original by using a scale factor. The scale factor of a dilation is the ratio of corresponding side lengths.  To dilate a polygon, multiply the coordinates of each vertex by the scale factor k and connect the vertices.

4 0
2 years ago
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There are about 45000 farms in Nebraska using approximately 45 million acres of land. This farmland covers about 9/10 of the sta
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9/10 : 1/10 = 45,000,000 : x

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