Answer:
![d < \frac{3}{2}x](https://tex.z-dn.net/?f=d%20%3C%20%5Cfrac%7B3%7D%7B2%7Dx)
Step-by-step explanation:
Represent a cup with x; the cat with c and the dog with d
From the first statement, we have:
![c < x](https://tex.z-dn.net/?f=c%20%3C%20x)
From the second, we have:
![c = \frac{1}{3}d + \frac{1}{2}x](https://tex.z-dn.net/?f=c%20%3D%20%20%5Cfrac%7B1%7D%7B3%7Dd%20%2B%20%5Cfrac%7B1%7D%7B2%7Dx)
Required
Express d in terms of x
We have:
and ![c < x](https://tex.z-dn.net/?f=c%20%3C%20x)
Merge both expressions to give:
![\frac{1}{3}d + \frac{1}{2}x < x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%2B%20%5Cfrac%7B1%7D%7B2%7Dx%20%3C%20x)
Collect Like Terms
![\frac{1}{3}d < x - \frac{1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20x%20-%20%5Cfrac%7B1%7D%7B2%7Dx)
![\frac{1}{3}d < \frac{1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20%5Cfrac%7B1%7D%7B2%7Dx)
Multiply both sides by 3
![3 * \frac{1}{3}d < \frac{1}{2}x * 3](https://tex.z-dn.net/?f=3%20%2A%20%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20%5Cfrac%7B1%7D%7B2%7Dx%20%2A%203)
![d < \frac{3}{2}x](https://tex.z-dn.net/?f=d%20%3C%20%5Cfrac%7B3%7D%7B2%7Dx)
Answer:
y = -3000 + 25,635
m = -3000
b = 25,635
Step-by-step explanation:
well if the inital value of the car is $25,635 this means that when
x = 0 y = 25,635
(0 , 25635)
this will be our first point
Now if you tell us that in 1 year depreciate in value $3,000
this means thaw when
x = 1 y = 25,635 - 3,000
x = 1 y = 22,635
(1, 22635)
Now that we have 2 points we can have the equation
First we take the slope as follows
y = mx + b
m = (y2 - y1) / (x2 - x1)
m = (22,635 - 25,635) / (1 - 0)
m = -3000 / 1
m = -3000
after calculating the slope we have to replace it in the following formula
(y - y1) = m (x - x1)
y - 25,635 = -3000 ( x - 0)
y - 25,635 = -3000x
y = -3000x + 25,635
b = 25,635
Finally we replace the value of y by 10000
10,000 = -3000x + 25,635
10,000 - 25,635 = -3000x
-15,635 = -3000x
-15,635/-3000 = x
5.21167 = x years
These are the years it would take for the value to be 10,000
Answer:
Wait time=6hrs25min-3hrs55 min
=<em><u>2 hrs 30min</u></em>
We are given with two dimaters of piston 8 cm and 40 cm while the load is equivalent to 15000N. We are asked to determine the force applied to the small piston. Pressure is equal to force per unit area. In a, 15,000 N / 40^2 cm2 = F2 / 8^2cm2; F2 is equal to 600 N. In b, pressure is equal to 9.375 Pa
If Mary brought five bags for $11,000, Her friend gave her $4,400.