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3 years ago

Which situation represents a proportional relationship?

Mathematics

1 answer:

murzikaleks [220]3 years ago

6 0

Answer:

option B) The cost of purchasing oranges for $1.50 per pound plus a shipping fee of $0.25 per pound.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ 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) The cost of purchasing a basket of oranges for $1.80 per pound plus $5.00 for the basket

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

$y=1.80x+5$

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship

case B) The cost of purchasing oranges for $1.50 per pound plus a shipping fee of $0.25 per pound

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

$y=(1.50-0.25)x$

$y=(1.25)x$

The line passes through the origin

therefore

This situation represent a proportional relationship

case C) The cost of purchasing oranges for $1.90 per box with a delivery charge of $3.50

Let

x ----> the number of box

y ---> the total cost

The linear equation is equal to

$y=1.90x+3.50$

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship

case D) The cost of purchasing oranges for $1.75 per pound with a coupon for $1.00 off the total cost

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

$y=1.75x-1.00$

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship

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Answer:

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The last time he checked, Matthew was 40 inches tall. Matthew just measured himself again and found out that he is 10% taller no

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4 years ago

When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elap

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Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

<h3>Methods used to calculate speed and distance traveled</h3>

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, t = 10 s - 5 s = 5 s

$Speed = \mathbf{\dfrac{Distance}{Time}}$

Therefore;

$Bill's \ maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}$

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance, s = Speed, v × Time, t

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = 69 meters

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = 57 meters

Learn more about distance, speed, time, relationship here:

https://brainly.in/question/49075584

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