Answer: 8.01
Step-by-step explanation:
Speed = distance/time = 280/4.5 = 62.44mph
Time = distance/speed = 500/62.44 = 8.0071 hrs
Hello!
Here we have $21.28 total spent and paid for with $30. So 30-21.28= $8.72 so our change must equal this amount. The only choice then would be A.
Hope this helps. Any questions please ask. Thank you kindly.
Answer:
880 bonus miles
Step-by-step explanation:
220 times 4 equals 880
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 <u>(assuming it can be in slope-intercept form)</u>:
Step-by-step explanation:
1) First, find the slope of the line using the slope formula,
. Substitute the x and y values of (0,0) and (5,2) into the formula and simplify like so:
![m = \frac{2-0}{5-0} \\m = \frac{2}{5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2-0%7D%7B5-0%7D%20%5C%5Cm%20%3D%20%5Cfrac%7B2%7D%7B5%7D)
So, the slope is
.
2) Now, use the point-slope formula to write the equation of the line. Using the point-slope formula
, substitute values for
,
, and
.
Since
represents the slope, substitute
in its place. Since
and
represent the x and y values of a point the line intersects, we can substitute the x and y values of one of the given points (I chose (0,0)) into the formula as well. Then, isolate y to put in slope-intercept form:
![y-0=\frac{2}{5} (x-0)\\y = \frac{2}{5} x](https://tex.z-dn.net/?f=y-0%3D%5Cfrac%7B2%7D%7B5%7D%20%28x-0%29%5C%5Cy%20%3D%20%5Cfrac%7B2%7D%7B5%7D%20x)