Answer:
1) D: all real/(-inf, +inf) R: all real/(-inf, +inf)
2) x
5 or (-inf, 5)U(5,+inf)
Step-by-step explanation:
1) This is a linear equation, meaning that it has all real numbers all throughout.
This implies that you can plug in any x value and it will have a definite y value.
Domain is all reals or (-inf, +inf)
Range is all reals or (-inf, +inf)
2) We can see that if you plug in the number 5 for x, you would get 5-5 = 0 for the denominator. We can not divide a number by 0, therefore the domain is
x can not equal to 5 or (-inf, 5)U(5,+inf)
![g(x)+-2x^5-4](https://tex.z-dn.net/?f=g%28x%29%2B-2x%5E5-4)
Substitute the value of x = 2 to the equation:
![g(2)=-2\cdot2^5-4=-2\cdot32-4=-64-4=-68](https://tex.z-dn.net/?f=g%282%29%3D-2%5Ccdot2%5E5-4%3D-2%5Ccdot32-4%3D-64-4%3D-68)
Answer:
(x + 2)² + (y − 9)² = 36
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
Here, the center is (-2, 9) and the radius is 12/2 = 6.
(x + 2)² + (y − 9)² = 36
Answer:
$12000 should be invested in a fund with a 4% return.
Step-by-step explanation:
Consider the provided information.
An amount of $15,000 is invested in a fund that has a return of 6%.
We need to calculate how much money is invested in a fund with a 4% return if the total return on both investments is $1380.
Let $x should be invested in a fund with a 4% return.
The above information can be written as:
![1380=15000\times 6\%+x\times 4\%](https://tex.z-dn.net/?f=1380%3D15000%5Ctimes%206%5C%25%2Bx%5Ctimes%204%5C%25)
![1380=15000\times \frac{6}{100}+x\times \frac{4}{100}](https://tex.z-dn.net/?f=1380%3D15000%5Ctimes%20%5Cfrac%7B6%7D%7B100%7D%2Bx%5Ctimes%20%5Cfrac%7B4%7D%7B100%7D)
![1380=150\times6+x\times 0.04](https://tex.z-dn.net/?f=1380%3D150%5Ctimes6%2Bx%5Ctimes%200.04)
![1380-900=0.04x\\480=0.04x\\x=12000](https://tex.z-dn.net/?f=1380-900%3D0.04x%5C%5C480%3D0.04x%5C%5Cx%3D12000)
Hence, $12000 should be invested in a fund with a 4% return.