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Alika [10]
3 years ago
13

consider the line y= 2/3x-0. Find the equation of the line that is parallel to this line and passes through the point (8, 4).

Mathematics
1 answer:
tresset_1 [31]3 years ago
3 0
Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)

slope intercept form :
y=m+b

m=slope

If the line is parallel to y=2/3 x-0, the line will have the same slope, therefore the slope will be: 2/3.

Data:
(8,4)
m=2/3

y-y₀=m(x-x₀)
y-4=2/3(x-8)
y-4=2/3 x-16/3
y=2/3 x-16/3+4
y=2/3 x-4/3  (slope intercept form)

Answer: The equation of the line would be: y=2/3 x-4/3.


if we have the next slope "m",then the perendicular slope will be:
m´=-1/m

We have this equation: y=2/3 x+0; the slope is: m=2/3.

The perpendicular slope will be: m`=-1/(2/3)=-3/2

And the equation of the perpendicular line to : y=2/3 x+0, given the point (8,4) will be:

y-y₀=m(x-x₀)
y-4=-3/2 (x-8)
y-4=-3/2 x+12
y=-3/2x + 12+4
y=-3/2x+16

answer: the perpendicular line to y=2/3 x+0 , given the point (8,4) will be:
y=-3/2 x+16
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N is an integer s=1/2 n(n+1) prove that 8s + 1 is an odd square number
pychu [463]
s=\frac{1}{2}n(n+1) \\ \\
8s+1=8 \times \frac{1}{2}n(n+1)+1=4n(n+1)+1=4n^2+4n+1=(2n+1)^2

n is an integer, so 2n+1 is also an integer. 8s+1 is equal to the square of 2n+1, so it's a square number.

2n+1 is an odd integer for any value of n. The square of an odd integer is always an odd integer. Therefore 8s+1=(2n+1)² is odd.

8s+1 is an odd square number.
7 0
3 years ago
(Picture) INFINITE SEQUENCES AND SERIES PLEASE HELP!!
mojhsa [17]

Answer:

C) x=\frac{17}{33}

Step-by-step explanation:

0.51 repeating decimal

x= 0.51515151

multiply by 100 on both sides

100x = 51.515151.........

     x=    0.515151...............

--------------------------------------------(subtract)

   99x = 51

divide by 99 on both sides

x=\frac{51}{99}

divide both sides by 3

x=\frac{17}{33}


5 0
2 years ago
A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $18 p
Alona [7]

Answer:

250 minutes of calling will cost same using both plans.

$53

Step-by-step explanation:

Please consider the complete question.

A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $18 plus an additional $0.14 of each minute of calls.  For what amount of calling do the two plans cost the same?  What is the cost when the two plans cost the same?

Let x represent the number of call minutes.

The total cost of calling for x minutes using plan A would be cost of x minutes plus fixed charge that is 0.12x+23.

The total cost of calling for x minutes using plan B would be cost of x minutes plus fixed charge that is 0.14x+18.

To find the number of minutes for which both plans will have same cost, we will equate total cost of x minutes for both plans and solve for x.

0.14x+18=0.12x+23

0.14x-0.12x+18=0.12x-0.12x+23

0.02x+18=23

0.02x+18-18=23-18

0.02x=5

\frac{0.02x}{0.02}=\frac{5}{0.02}

x=250

Therefore, calling for 250 minutes will cost same using both plans.

Upon substituting x=250 in expression 0.14x+18, we will get:

0.14(250)+18=35+18=53

Therefore, the cost will be $53, when the two plans cost the same.

5 0
2 years ago
Megan starts eating breakfast at 9:54 AM. Tell what time she is done with breakfast if she takes the given number of minutes to
Studentka2010 [4]

The time she will be done with her breakfast is by = 10:48 am

<h3>Conversation of time</h3>

The time Megan started her breakfast = 9:54 AM.

In terms of hours = 9

In terms of minutes = 54

If she takes the given number of minutes to eat which is = 54 mins .

Therefore, the time she will be done with her breakfast is = 9:54 + 54

= 10: 48 am

Learn more about time here:

brainly.com/question/10428039

8 0
2 years ago
If C(x) is the total cost incurred in producing x units of a certain commodity, then the average cost of producing x units of th
nataly862011 [7]

Answer:

x  =  2000 cameras

Step-by-step explanation:

C(x)     Total cost in producing  x units

C- = C(x) /x   Average cost of producing x units    x > 0

Cannon Precision Instrument

C (x)   Total monthly cost for producing x units of M1 cameras

is    C(x)  =  0.0025x²  + 80x  +  10000

Then average cost of producing x cameras M1 is

C-(x)  =  ( 0.0025x²  + 80x  +  10000)  /x

C-(x)  =   0.0025x  + 80  + 10000/x

Taking derivatives on both sides of the equation

C-´(x)   =  0.0025   -  10000/x²

Then

C-´(x)   = 0

( 0.0025x² - 10000 ) / x²   =  0

0.0025x² - 10000 =  0

x²  =  10000 /0.0025         x²  = 4000000

x  =  2000 cameras

8 0
3 years ago
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