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3 years ago

Which is an equation of a direct proportion? a.y=1/6x+6 b.y=6/x c.y=6x-6 d.y=6x

Mathematics

1 answer:

Amanda [17]3 years ago

6 0

Answer:

Option D. y=6x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case a) y=(1/6)x+6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case b) y=6/x

The equation represent an inverse variation

case c) y=6x-6

Is a linear equation, but is not a direct variation. The line not passes through the origin

case d) y=6x

The equation represent a direct variation

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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be

sweet-ann [11.9K]

The distance between David's home and the airport is 210 miles.

<h3>Distance traveled after 1 hour</h3>

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

Learn more about distance here: brainly.com/question/2854969

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7 0

2 years ago

Solve the system of equations

Solnce55 [7]

Hey, there!!

Given that:

y = 3x.........(i)

$y = {x}^{2} + 3x - 16.......(ii)$

Putting the value of y in equation (ii)

${3x}^{} = {x}^{2} + 3x - 16$

${x }^{2} - 16$ =0

$( {x)}^{2} - {4}^{2} = 0$

$(x + 4)(x - 4) = 0$

Therefore,

Either Or

(x+4)=0 (x-4)=0

x= -4 x= 4

so, x= (+ -)4

And if you wanna get value of y, just keep value of x in equation (i).

y= 3x

y= (3×4) or (3×-4)

y= 12 or -12

{As it is the quadratic equation it has two values. }

Hope it helps....

5 0

3 years ago

Diana looks up at an angle of 57 and sees a hot air balloon 150 meters away. To the nearest meter, what is the value of x,

LekaFEV [45]

Answer:

230.98 meters

Step-by-step explanation:

8 0

3 years ago

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Susan wants to have 30% of her gumballs be green If there are

Inga [223]

Answer:

15 gumballs

Step-by-step explanation:

There would have to be...

30%*50 green gumballs

We can start by converting 30% to a fraction. Any percentage is just that number over one hundred so...

30/100*50

We can simplify 30/100 by dividing the numerator and the denominator by 10...

3/10*50

Cancel out 10 and 50 (50/10=5)

3*5

15 gumballs would have to be green

6 0

2 years ago

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A sample of 5 strings of thread is randomly selected and the following thicknesses are measured in millimeters. Give a point est

liq [111]

Answer:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

Step-by-step explanation:

For this case we have the following data:

1.48,1.45,1.54,1.52,1.52

The first step for this cae is find the sample mean with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_}{n}$

And replacing we got:

$\bar X= \frac{1.48+1.45+1.54+1.52+1.52}{5} = 1.502$

And now we can calculate the sample variance with the following formula:

$s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And replacing we got:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

4 0

3 years ago

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