Step-by-step explanation:
Part A: Linear Equation.
- One of the points is (0,15). This means 0,15 is the y intercept so b=15.
We can find the slope
![\frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%20-%2015%7D%7B1%20%20-%200%20%7D%20%20%3D%20%20%5Cfrac%7B%20-%2010%7D%7B1%7D%20%20%3D%20%20-%2010)
So our equation is
![y = - 10x + 15](https://tex.z-dn.net/?f=y%20%3D%20%20-%2010x%20%2B%2015)
Part B: Exponential Equation
We know that
![15 = a \times b {}^{0}](https://tex.z-dn.net/?f=15%20%3D%20a%20%5Ctimes%20b%20%7B%7D%5E%7B0%7D%20)
B to the zero power is 1 so
![15 = a](https://tex.z-dn.net/?f=15%20%3D%20a)
This means a =15. Now let find b.
![5 = 15 \times b {}^{1}](https://tex.z-dn.net/?f=5%20%3D%2015%20%5Ctimes%20b%20%7B%7D%5E%7B1%7D%20)
![\frac{1}{3} = b](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20b)
So the equation is
![y = 15( \frac{1}{3} ) {}^{x}](https://tex.z-dn.net/?f=y%20%3D%2015%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%7B%7D%5E%7Bx%7D%20)
1st car = 3x
2nd car = 3(x-12)
3x + 3(x-12) = 570
3x + 3x-36 = 570
6x = 570 +36
6x = 606
x = 606/6 = 101
101-12 = 89
fast car = 101 km per hour
slower car = 89 km per hour
6 half dollar coins would= $3.00 so you would add $3.00+$3.00=$6.00
You can read 100 pages in 5 hours.
40 pages in 2 hours. We need to get the unit rate. In this case, we need to get the number of pages read in 1 hour.
40 pages ÷ 2 hours = 20 pages per hour.
20 pages per hours * 5 hours = 100 pages.
$50.40 since 12% of 45 is $5.40
5.4+45=50.4