Given:
The inequalities are:
![2x-3](https://tex.z-dn.net/?f=2x-3%3C7)
![2x+1>-3x-4](https://tex.z-dn.net/?f=2x%2B1%3E-3x-4)
To find:
The range of values of
for the given inequalities.
Solution:
We have,
![2x-3](https://tex.z-dn.net/?f=2x-3%3C7)
Adding 3 on both sides, we get
![2x-3+3](https://tex.z-dn.net/?f=2x-3%2B3%3C7%2B3)
![2x](https://tex.z-dn.net/?f=2x%3C10)
Divide both sides by 2.
![\dfrac{2x}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B2%7D%3C%5Cdfrac%7B10%7D%7B2%7D)
...(i)
The second inequality is:
![2x+1>-3x-4](https://tex.z-dn.net/?f=2x%2B1%3E-3x-4)
Subtracting 1 from both sides, we get
![2x+1-1>-3x-4-1](https://tex.z-dn.net/?f=2x%2B1-1%3E-3x-4-1)
![2x>-3x-5](https://tex.z-dn.net/?f=2x%3E-3x-5)
Adding
on both sides, we get
![2x+3x>-3x-5+3x](https://tex.z-dn.net/?f=2x%2B3x%3E-3x-5%2B3x)
![5x>-5](https://tex.z-dn.net/?f=5x%3E-5)
Divide both sides by 5.
![\dfrac{5x}{5}>\dfrac{-5}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B5x%7D%7B5%7D%3E%5Cdfrac%7B-5%7D%7B5%7D)
...(ii)
Using (i) and (ii), we get
![-1](https://tex.z-dn.net/?f=-1%3Cx%3C5)
Therefore, the required range is
.
Answer:
Step-by-step explanation:
= (x^2 + h^2 - 2xh) + (y^2 + k^2 - 2yk) As, (a-b)^2 = a^2 + b^2 - 2ab
= x^2 + h^2 - 2xh + y^2 + k^2 - 2yk
Answer:
The price of the shirt at the store is $16
Step-by-step explanation:
12 x .25 = 4
4 + 12 = 16
Answer:
√7 units, √98 units
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2. So 9+b^2=16. So b^2=7. So b=√7
a^2+b^2=c^2. SO 49+49=c^2. So 98=c^2. So c=√98.
Answer:
1.47 years
Step-by-step explanation:
Given that,
The height of male elephant is given by the formula,
![h=62.5\sqrt[3]{t} +75.8](https://tex.z-dn.net/?f=h%3D62.5%5Csqrt%5B3%5D%7Bt%7D%20%2B75.8)
If h = 275 cm, we need to find the age of the elephant.
Put h = 275 cm in the above formula,
![275=62.5\sqrt[3]{t} +75.8\\\\275-75.8=62.5\sqrt[3]{t}\\\\199.2=62.5\sqrt[3]{t}\\\\t=1.47\ years](https://tex.z-dn.net/?f=275%3D62.5%5Csqrt%5B3%5D%7Bt%7D%20%2B75.8%5C%5C%5C%5C275-75.8%3D62.5%5Csqrt%5B3%5D%7Bt%7D%5C%5C%5C%5C199.2%3D62.5%5Csqrt%5B3%5D%7Bt%7D%5C%5C%5C%5Ct%3D1.47%5C%20years)
So, the required time be 1.47 years.