Answer:
The system has two distinct solutions.
Step-by-step explanation:
The given system of equations are:
![y=-2x+1--(1)](https://tex.z-dn.net/?f=y%3D-2x%2B1--%281%29)
and
![y=-2x^2+1---(2)](https://tex.z-dn.net/?f=y%3D-2x%5E2%2B1---%282%29)
In order to determine the number of solutions the two equations have, we need to equate the two equations to obtain,
![-2x^2+1=-2x+1](https://tex.z-dn.net/?f=-2x%5E2%2B1%3D-2x%2B1)
We now group all terms on the left hand side and equate everything to zero.
![-2x^2+2x=0](https://tex.z-dn.net/?f=-2x%5E2%2B2x%3D0)
![x^2-x=0](https://tex.z-dn.net/?f=x%5E2-x%3D0)
This is now a quadratic equation in
with
.
At this stage we check the number of solutions using the discriminant.
![D=b^2-4ac](https://tex.z-dn.net/?f=D%3Db%5E2-4ac)
![\Rightarrow D=(-1)^2-4(1)(0)=1](https://tex.z-dn.net/?f=%5CRightarrow%20D%3D%28-1%29%5E2-4%281%29%280%29%3D1)
Since the discriminant is greater than zero, the equation will have two distinct roots.
Therefore the system of equations has exactly two distinct solutions.
If you wish to see these solutions, you can continue as follows;
We factor
to obtain,
![x(x-1)=0](https://tex.z-dn.net/?f=x%28x-1%29%3D0)
![\Rightarrow x=0,x-1=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D0%2Cx-1%3D0)
![\Rightarrow x=0,x=1](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D0%2Cx%3D1)
When ![x=0,y=-2(0)+1](https://tex.z-dn.net/?f=x%3D0%2Cy%3D-2%280%29%2B1)
Then we have,
![x=0,y=1](https://tex.z-dn.net/?f=x%3D0%2Cy%3D1)
When ![x=1,y=-2(1)+1](https://tex.z-dn.net/?f=x%3D1%2Cy%3D-2%281%29%2B1)
Then we have,
![x=0,y=-1](https://tex.z-dn.net/?f=x%3D0%2Cy%3D-1)
See graph
The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901
The amount of money gained after an investment is compounded is given by:
![A=P(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
Where P is principal, A is the final amount, r is the rate, n is the number of times compounded per period and t is the time
Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:
![A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%5C%5C%5C%5CA%3D1689%281%2B%5Cfrac%7B0.03%7D%7B1%7D%20%29%5E%7B4%2A1%7D%5C%5C%5C%5CA%3D%5C%241901)
The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901
Find out more at: brainly.com/question/14295570
Answer:
<h2>(90Degree)(0.3Degree/1min) = 300min</h2><h2>since 60min = 1hr</h2><h2>(300min)(1hr/60min) = 5hrs</h2>
4: (3/4 - 1/2) X 3/5.
You need them all to have the same denominator (bottom number)
The lowest common denominator (LCM) of 2,4 and 5 is 20
4 X 5 = 20
2 X 10 = 20
5 X 4 = 20
Then multiply the top number by the amount you need to multiply the bottom number by to get 20
3 X 5 = 15
1 X 10 = 10
3 X 4 = 12
(3/4 - 1/2) X 3/5. Turns to (15/20 - 10/20) X 12/20.
15 - 10 = 5
5 X 12 = 60
Answer: 60/20
Simplified: Either 3 or 3/1.
If you use the steps above then you should be able to do the rest :D
If you need anymore help, please ask
Answer:
Point C
Step-by-step explanation:
If you retrieve 90 backwards, then you will get the point C.