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Mnenie [13.5K]
3 years ago
9

What is the equation of a line that passing through points (-2, 5) and (3, 25)

Mathematics
1 answer:
Llana [10]3 years ago
5 0
\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad 
(\stackrel{x_2}{3}~,~\stackrel{y_2}{25})
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{25-5}{3-(-2)}\implies \cfrac{25-5}{3+2}
\\\\\\
\cfrac{20}{5}\implies 4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=4[x-(-2)]
\\\\\\
y-5=4(x+2)\implies y-5=4x+8\implies y=4x+13
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A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 65 miles north of the t
mart [117]

Answer:

29% of the drive

Step-by-step explanation:

The plot of the problem is:

Transmitter at origin (0,0)  

City to the north at (0,70)

City to the east at (74,0)

The path from city to city is a line with slope:

m = (-70)/74 = -35/37

and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.

The transmitter reach the area enclosed by the next circle:

x^2 + y^2 = 53^2

See the picture attached

The intersection is gotten from the picture or solving:

x^2 + [(-35/37)*x + 70]^2 = 53^2

the points approximately are: (24.1, 47.2) and (45.8, 26.7)

From Pythagorean theorem the total distance of the trip is:

d1 = √(70^2 + 74^2) ≈ 101.9 miles

And the distance when the signal is picked up is:

d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles

You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.

7 0
2 years ago
In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.
Hitman42 [59]

\longmapstoThe value of "x" is 5.

\large\underline{\sf{Solution-}}

Given that,

A trapezium ABCD in which AB || CD such that

  • AO = x - 1

  • CO = BO = x + 1

  • OD = x + 4

Now,

\rm In \: \triangle  \: AOB  \: and \: \triangle \:  COD

\rm  \: \angle  \: AOB  \: and \: \angle \:  COD \:  \:  \{vertically \: opposite \: angles \}

\rm  \: \angle  \:ABO  \: and \: \angle \:  CDO \:  \:  \{alternate \: interior \: angles \}

\bf \: \triangle  \: AOB \:  \sim \:  \triangle  \: COD \:  \:  \:  \{AA \: similarity \}

\bf\longmapsto\:\dfrac{AO}{CO}  = \dfrac{BO}{DO}

\rm \longmapsto\:\dfrac{x - 1}{x + 1}  = \dfrac{x + 1}{x + 4}

\rm \longmapsto\:(x - 1)(x + 4) =  {(x + 1)}^{2}

\rm \longmapsto\: {x}^{2} - x + 4x - 4 =  {x}^{2} + 1 + 2x

\rm \longmapsto\: 3x - 4 =  1 + 2x

\rm \longmapsto\: 3x  -  2x=  1 +4

\bf\longmapsto \:x = 5

7 0
3 years ago
Shaded areas <br>please help guys ❤❤❤​
pentagon [3]

Answer:

77cm

Step-by-step explanation:

Area of a rectangle=L×B

So

7×11=77cm

3 0
3 years ago
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PLEASE HELP QUESTION: What is the midpoint of the line containing the points X(4,-1) and Y(-4,1)?
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Answer:

( D ) , ( 0 , 0 )

6 0
3 years ago
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Inessa [10]

Answer:

y=-1

Step-by-step explanation:

it is a straight line graph with no gradient therefore no X value. It crosses the y axis at -1

8 0
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