We have been given the expression
![72 \times \frac{3}{4}](https://tex.z-dn.net/?f=72%20%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D)
We can rewrite the expression as ![\frac{72\times 3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B72%5Ctimes%203%7D%7B4%7D)
In order to simplify the given expression, we can check if we have any common terms in the numerator and denominator.
We can write the term 72 which is in the numerator as ![18\times 4](https://tex.z-dn.net/?f=18%5Ctimes%204)
Thus, the expression becomes
![\frac{18\times 4\times 3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B18%5Ctimes%204%5Ctimes%203%7D%7B4%7D)
We can see that 4 is common in both numerator and denominator. Hence, we can cancel 4. Thus, we are left with
![18 \times 3\\ =54](https://tex.z-dn.net/?f=18%20%5Ctimes%203%5C%5C%0A%3D54)
Therefore, we can rewrite the given expression as 54.
Answer:
f(-4) = -12
Step-by-step explanation:
![f(x)=2x-4](https://tex.z-dn.net/?f=f%28x%29%3D2x-4)
To calculate f(-4), we need to substitute x in our equation above with -4:
![f(x)=2x-4\\f(-4) = 2*(-4) - 4\\f(-4) = -8-4 = -12](https://tex.z-dn.net/?f=f%28x%29%3D2x-4%5C%5Cf%28-4%29%20%3D%202%2A%28-4%29%20-%204%5C%5Cf%28-4%29%20%3D%20-8-4%20%3D%20-12)
Note that 2*(-4) = -8
Answer: f(-4) = -12
Two or more independent functions (say f(x) and g(x)) can be combined to generate a new function (say g(x)) using any of the following approach.
![h(x) = f(x) - g(x)](https://tex.z-dn.net/?f=h%28x%29%20%3D%20f%28x%29%20-%20g%28x%29)
![h(x) = f(g(x))](https://tex.z-dn.net/?f=h%28x%29%20%3D%20f%28g%28x%29%29)
And many more.
The approach or formula to use depends on the question.
In this case, the combined function is:
![f(x) = 75+ 10x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2075%2B%2010x)
The savings function is given as
![s(x) = 85](https://tex.z-dn.net/?f=s%28x%29%20%3D%2085)
The allowance function is given as:
![a(x) = 10(x - 1)](https://tex.z-dn.net/?f=a%28x%29%20%3D%2010%28x%20-%201%29)
The new function that combined his savings and his allowances is calculated as:
![f(x) = s(x) + a(x)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20s%28x%29%20%2B%20a%28x%29)
Substitute values for s(x) and a(x)
![f(x) = 85 + 10(x - 1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%2085%20%2B%2010%28x%20-%201%29)
Open bracket
![f(x) = 85 + 10x - 10](https://tex.z-dn.net/?f=f%28x%29%20%3D%2085%20%2B%2010x%20-%2010)
Collect like terms
![f(x) = 85 - 10+ 10x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2085%20%20-%2010%2B%2010x)
![f(x) = 75+ 10x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2075%2B%2010x)
Read more about functions at:
brainly.com/question/15458447
Answer:
It is 80
Step-by-step explanation:
Percentage Calculator: 240 is what percent of 300? = 80.
Answer:
Yes, it is a quadratic equation.
Step-by-step explanation:
<em>Let's solve it to make it a quadratic equation:</em>
=> ![\frac{x^2+1}{x^2} =5](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%2B1%7D%7Bx%5E2%7D%20%3D5)
=> x²+1 = 5x²
=> 5x²-x²-1 = 0
=> 4x²-1 = 0
<em>Comparing it with the standard form of quadratic equation i.e. </em>
![ax^2+bx+c = 0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%20%3D%200)
So, we get
a = 4 , b = 0 and c = -1
<u><em>So, yes. It is a quadratic equation and it is a pure quadratic equation since b is equal to 0.</em></u>