Her salary 4 years ago would have been $30,000.
If 45,000 is 15,000 less than double her previous salary, we must first add 15,000 to 45,000 to find what double her salary was.
45,000+15,000=60,000.
Since this is twice her salary, we divide this by 2.
60,000/2= 30,000.
So, her salary 4 years ago would have been $30,000.
I hope this helps!
Answer:
n ≥ 1/5
Step-by-step explanation:
Let the number be n. Then 5n + 2 ≥ 3.
If you want to solve this for n, then subtract 2 from both sides, obtaining:
5n ≥ 1. Isolate n by dividing both sides by 5. Then we have n ≥ 1/5
A=automobile S=SUV
0.4A+A=98 (to change a percent to a decimal you move the decimal point two places to the right)
1.4A=98 (I combined like terms)
A=70 (divided each side by 1.4)
Answer:
We'll solve that in parts.
The upper part is a right triangle that is 4 by (2 + 2 +6)
Area = (4 * 10) /2 = 20
The bottom of that figure is made of 3 parts.
A) a 2 by 2 right triangle. area equals (2*2)/2 = 2
B) a 2 by 2 square whose area equals 2*2 = 4
C) a 6 by 2 right triangle whose area equals (6*2) / 2 = 6
Total Area = 20 + 2 + 4 + 6 = 32
Step-by-step explanation:
Step-by-step explanation:
<h3>Appropriate Question :-</h3>
Find the limit
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)

Given expression is
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
On substituting directly x = 1, we get,


which is indeterminant form.
Consider again,
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
can be rewritten as
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%203x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%202x%20-%20x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20x%28x%20-%202%29%20-%201%28x%20-%202%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%7B%28x%20-%202%29%7D%5E%7B2%7D%20-%201%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%202%20-%201%29%28x%20-%202%20%2B%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%28x%20-%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%7D%7Bx%28x%20-%202%29%7D%5Cright%5D)



Hence,
![\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}](https://tex.z-dn.net/?f=%5Crm%5Cimplies%20%5C%3A%5Cboxed%7B%20%5Crm%7B%20%5C%3A%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D%20%3D%202%20%5C%3A%20%7D%7D)
