Question

read the instructions first and answer the questions that follow​

Answer 1

Step-by-step explanation:

Given:-

Suppose you want to call your friend on a pay phone The charge is Php. 5 for the first 3 minutes and an additional charge of Php. 2 for every additional minute or a fraction of it.

To find:-

How much will you pay if you have called your friend

i) for 3 minutes

ii) for 4 minutes

iii) for 5 minutes

iv)for 6 minutes

v) for 10 minutes

vi) How are time and charge related to each other?

Solution:-

Charge for first 3 minutes =Php.5

Charge for the next additional minute or a fraction of it =Php. 2

i) Charge for 3 minutes =Php. 5

ii) Charge for 4 minutes (3+1 minutes)=5+2=Php.7

iii)Charge for 5 minutes(3+2 minutes)

=>5+2×2

=>5+4

=>Php. 9

iv) Charge for 6 minutes(3+3 minutes)

=>5+3×2

=>5+6

=>Php. 11

v) Charge for 10 minutes(3+7 minutes)

=>5+7×2

=>5+14

=>Php. 19

from above we conclude that

2)Let the total amount be Php. Y then the charge for every additional minute after 3 minutes be Php. 2 then Y=3+2X

=>Y=2X+3

Here,n is the number of additional minutes after first three minutes

If the time increases then the charge will be increased so, The time and the charge are in the direct Proportional.

3)

If we convert the above relation into a linear equation in two variables it becomes Y=2X+3

If X=0 then Y=2(0)+3=3

If X =1 then Y=2(1)+3=2+3=5

If X=2 then Y=2(2)+3=4+3=7

If X=3 then Y=2(3)+3=6+3=9

If X=4 then Y=2(4)+3=8+3=11

If X=5 then Y=2(5)+3=10+3=13

The coordinates are

(0,3)

(1,5)

(2,7)

(3,9)

(4,11)

(5,13)

(6,15)

(7,17)

(8,19)

(9,21)

and so on

There is no representation in the coordinates

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

According to statement, it is given that

• The charge is Php 5 for first three minutes
• The additional charge of Php 2 for additional minute or a part of it.

$\bf \:\large \red{AηsωeR : 1}$

★The amount paid in 3 minutes = Php 5

★The amount paid for 4 minutes = Php 7

(This is evaluated as

5 Php for 3 minutes

2 Php for additional minute)

★The amount paid for 5 minutes = Php 9

(This is evaluated as

5 Php for 3 minutes

4 Php for additional 2 minutes)

★The amount paid for 6 minutes = Php 11

(This is evaluated as

5 Php for 3 minutes

6 Php for additional minute)

★The amount paid for 10 minutes = 19 Php

(This is evaluated as

5 Php for 3 minutes

14 Php for additional 7 minute)

$\bf \:\large \red{AηsωeR : 2}$

From above we concluded that

$\begin{gathered}\boxed{\begin{array}{c|c} \bf time & \bf charge \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 5 \\ \\ \sf 4 & \sf 7 \\ \\ \sf 5 & \sf 9\\ \\ \sf 6 & \sf 11\\ \\ \sf 10 & \sf 19 \end{array}} \\ \end{gathered}$

★This implies that as time increases, charges also increases.

So, it implies

$\boxed {\red{ \bf \: charge \: \: \alpha \: \: time}}$

⇛Its a direct variation between charge and time.

$\bf \:\large \red{AηsωeR : a}$

If we plot the above points (3, 5), (4, 7), (5, 9), (6, 11), we get a line.

$\boxed{ \blue{ \bold{ \rm \: (Please \: check \: the \: attachment.)}}}$

⇛There is a linear relationship between charge and time.

Now, to define linear relationship, use two point form of a line.

$\boxed{ \blue{\bf \:y - y_1 = \dfrac{y_2-y_1}{x_2-x_1} (x-x_1)}}$

where,

$\red{ \tt \: x_1 =3 , \: y_1 =5, \: x_2=4 , \: y_2=7 \: }$

$:  \implies \tt \: y - 5 = \dfrac{7 - 5}{4 - 3} (x - 3)$

$:  \implies \tt \: y - 5 = 2(x - 3)$

$:  \implies \boxed{ \pink { \tt \: y = 2x - 1}}$

$\bf \:\large \red{AηsωeR : b}$

$\begin{gathered}\boxed{\begin{array}{c|c} \bf time & \bf charge \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 5 \\ \\ \sf 4 & \sf 7 \\ \\ \sf 5 & \sf 9\\ \\ \sf 6 & \sf 11\\ \\ \sf 10 & \sf 19 \end{array}} \\ \end{gathered}$

From above table, we concluded that there is no repetition in first coordinate and no repetition in second coordinate.

$\bf \:\large \red{AηsωeR : c}$

$\begin{gathered}\boxed{\begin{array}{c|c} \bf time & \bf charge \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 5 \\ \\ \sf 4 & \sf 7 \\ \\ \sf 5 & \sf 9\\ \\ \sf 6 & \sf 11\\ \\ \sf 10 & \sf 19 \end{array}} \\ \end{gathered}$

From this table, we conclude that there is one one Correspondence, so this relation is a function.