Step-by-step explanation:
FORMATION OF TABLE FOR THE FUNCTION ![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
As t represents the temperature in degrees Fahrenheit and c represents the number of cricket chirps per minute.
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
when
then ![c = 4(40) - 150 = 160 - 150 = 10](https://tex.z-dn.net/?f=c%20%3D%204%2840%29%20-%20150%20%3D%20160%20-%20150%20%3D%2010)
when ![t = 50](https://tex.z-dn.net/?f=t%20%3D%2050)
then ![c = 4(50) - 150 = 200 - 150 = 50](https://tex.z-dn.net/?f=c%20%3D%204%2850%29%20-%20150%20%3D%20200%20-%20150%20%3D%2050)
when
then ![c = 4(60) - 150 = 240 - 150 = 90](https://tex.z-dn.net/?f=c%20%3D%204%2860%29%20-%20150%20%3D%20240%20-%20150%20%3D%2090)
when
then ![c = 4(70) - 150 = 280 - 150 = 130](https://tex.z-dn.net/?f=c%20%3D%204%2870%29%20-%20150%20%3D%20280%20-%20150%20%3D%20130)
when ![t = 80](https://tex.z-dn.net/?f=t%20%3D%2080)
then ![c = 4(80) - 150 = 320 - 150 = 170](https://tex.z-dn.net/?f=c%20%3D%204%2880%29%20-%20150%20%3D%20320%20-%20150%20%3D%20170)
when
then ![c = 4(90) - 150 = 360 - 150 = 210](https://tex.z-dn.net/?f=c%20%3D%204%2890%29%20-%20150%20%3D%20360%20-%20150%20%3D%20210)
when ![t = 100](https://tex.z-dn.net/?f=t%20%3D%20100)
then ![c = 4(100) - 150 = 400 - 150 = 250](https://tex.z-dn.net/?f=c%20%3D%204%28100%29%20-%20150%20%3D%20400%20-%20150%20%3D%20250)
So
Lets form the data table for this function based on the determined values
![t\:\:\:\:\:\:\:40\:\:\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:60\:\:\:\:\:\:\:\:\:\:70\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:\:\:100](https://tex.z-dn.net/?f=t%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A40%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A60%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A70%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A80%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A100)
![c\:\:\:\:\:\:\:\:10\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:130\:\:\:\:\:\:\:\:\:170\:\:\:\:\:\:\:\:\:210\:\:\:\:\:\:\:\:\:\:250](https://tex.z-dn.net/?f=c%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A10%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A130%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A170%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A210%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A250)
PART 1)
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
As we know that
when
then ![c = 4(60) - 150 = 240 - 150 = 90](https://tex.z-dn.net/?f=c%20%3D%204%2860%29%20-%20150%20%3D%20240%20-%20150%20%3D%2090)
- Meaning the number of chirps per minute would increase to
, when the temperature t in degrees Fahrenheit increase to 60.
The appropriate logic is that the speed at which cricket chirps is based on the temperature. The table table also indicates that as the temperature t increases, the number of cricket chirps also increases.
PART 2)
- A rate of change is a rate that determines how one quantity changes in relation to another quantity.
Considering the two points
![\mathrm{Slope\:between\:two\:points}:\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(40,\:10\right),\:\left(x_2,\:y_2\right)=\left(50,\:50\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%2840%2C%5C%3A10%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%2850%2C%5C%3A50%5Cright%29)
![m=\frac{50-10}{50-40}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B50-10%7D%7B50-40%7D)
![m=4](https://tex.z-dn.net/?f=m%3D4)
It logically means for every increase of
units in
(temperature in degrees Fahrenheit), the value of
(number of chirps) is increasing to
units.
Thus, the rate of change will be
.
Part 3)
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
The data table for this function
![t\:\:\:\:\:\:\:40\:\:\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:60\:\:\:\:\:\:\:\:\:\:70\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:\:\:100](https://tex.z-dn.net/?f=t%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A40%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A60%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A70%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A80%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A100)
![c\:\:\:\:\:\:\:\:10\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:130\:\:\:\:\:\:\:\:\:170\:\:\:\:\:\:\:\:\:210\:\:\:\:\:\:\:\:\:\:250](https://tex.z-dn.net/?f=c%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A10%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A130%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A170%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A210%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A250)
Putting
in the function brings the value of
as
.
i.e.
![c\:=\:4\left(40\right)\:-\:150=160=10](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4%5Cleft%2840%5Cright%29%5C%3A-%5C%3A150%3D160%3D10)
Yes, it does make sense.
Its logical meaning is that at the start, when the value of
was
temperature in degrees Fahrenheit, then the value of
(number of chirps per minute) was
.
Answer:
N = 18
Step-by-step explanation:
The triangles are similar, thus the ratios of corresponding sides are equal, that is
=
( cross- multiply )
5N = 90 ( divide both sides by 5 )
N = 18
Answer:
Step-by-step explanation:
step a system of two equations c = child ticket a = adult ticket
eq 1) 2c + 1a = 8.2 multiply by 2
eq 2) 3c + 2a = 14.1
I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)
eq 1a) 4c + 2a = 16.4
eq 2) 3c + 2a = 14.1
subtract (4c - 3c) + (2a -2a) = 16.4 - 14.1
c + 0 = 2.3 euros for one child ticket
Now find the adult ticket price, plug 2.3 for c into eq 1)
eq 1) 2c + 1a = 8.2
eq 1) 2(2.3) + 1a = 8.2 solve for a
4.6 + a = 8.2 substract 4.6 from both sides
a = 8.2 - 4.6
= 3.6 euros for one adult ticket
double check using eq 2) we know c and a values
eq 2) 3c + 2a = 14.1
eq 2) 3(2.3) + 2(3.6) = 14.1
6.9 + 7.2 = 14.1
14.1 = 14.1
Answer:
Simplifying
4x + 9 = 12x + -3
Reorder the terms:
9 + 4x = 12x + -3
Reorder the terms:
9 + 4x = -3 + 12x
Solving
9 + 4x = -3 + 12x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12x' to each side of the equation.
9 + 4x + -12x = -3 + 12x + -12x
Combine like terms: 4x + -12x = -8x
9 + -8x = -3 + 12x + -12x
Combine like terms: 12x + -12x = 0
9 + -8x = -3 + 0
9 + -8x = -3
Add '-9' to each side of the equation.
9 + -9 + -8x = -3 + -9
Combine like terms: 9 + -9 = 0
0 + -8x = -3 + -9
-8x = -3 + -9
Combine like terms: -3 + -9 = -12
-8x = -12
Divide each side by '-8'.
x = 1.5
Simplifying
x = 1.5
Step-by-step explanation: