Answer:
-4,2
Step-by-step explanation:
![let \: two \: consecutive \: even \: numbers \: be \: x \: and \: x + 2 \\ so \: by \: the \: question \\ {x}^{2} + {(x + 2)}^{2} = 20 \\ or \: {x}^{2} + {x}^{2} + 4x + 4 = 20 \\ or \: 2 {x}^{2} + 4x = 20 - 4 \\ or \: 2( {x}^{2} + 2x) = 16 \\ or {x}^{2} + 2x = 8 \\ or \: {x}^{2} + 2x - 8 = 0 \\ or \: {x}^{2} + (4 - 2)x - 8 = 0 \\ or \: {x}^{2} + 4x - 2x - 8 = 0 \\ or \: x(x + 4) - 2(x + 4) = 0 \\ or \: (x + 4)(x - 2) = 0 \\ either \: x + 4 = 0 \\ or \: x = - 4 \\ or \: x - 2 = 0 \\ orx = 2](https://tex.z-dn.net/?f=let%20%5C%3A%20two%20%5C%3A%20consecutive%20%5C%3A%20even%20%5C%3A%20numbers%20%5C%3A%20be%20%5C%3A%20x%20%5C%3A%20and%20%5C%3A%20x%20%2B%202%20%5C%5C%20so%20%5C%3A%20by%20%5C%3A%20the%20%5C%3A%20question%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7B%28x%20%2B%202%29%7D%5E%7B2%7D%20%20%3D%2020%20%5C%5C%20or%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20%2B%204%20%3D%2020%20%5C%5C%20or%20%5C%3A%202%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20%3D%2020%20-%204%20%5C%5C%20or%20%5C%3A%202%28%20%7Bx%7D%5E%7B2%7D%20%20%20%2B%202x%29%20%3D%2016%20%5C%5C%20or%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%3D%208%20%5C%5C%20or%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20-%208%20%3D%200%20%5C%5C%20or%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%20%2B%20%284%20-%202%29x%20-%208%20%3D%200%20%5C%5C%20or%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%20%2B%204x%20%20-%20%202x%20-%208%20%3D%200%20%5C%5C%20or%20%5C%3A%20x%28x%20%2B%204%29%20-%202%28x%20%2B%204%29%20%3D%200%20%5C%5C%20or%20%5C%3A%20%28x%20%2B%204%29%28x%20-%202%29%20%3D%200%20%5C%5C%20either%20%5C%3A%20x%20%2B%204%20%3D%200%20%5C%5C%20or%20%5C%3A%20x%20%3D%20%20-%204%20%5C%5C%20or%20%5C%3A%20x%20-%202%20%3D%200%20%5C%5C%20orx%20%3D%202)
therefore, x= -4 and 2
Answer:
a) Amount saved if the interest is compounded annually is $5832
b) Amount saved if the interest is compounded semi-annually is $5849.5
Step-by-step explanation:
Principal Amount P = 5000
Time t = 10 years
Annual interest i = 8% = 0.08
We need to find amount saved if interest is compounded a) annually b) semi-annually
a) Amount saved if the interest is compounded annually
If interest compounded annually, n= 1
Using Formula: ![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Putting values:
![A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{1})^{1*2}\\A=5000(1+0.08)^2\\A=5000(1.08)^2\\A=5000(1.1664)\\A=5832](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20%5C%5CA%3D5000%281%2B%5Cfrac%7B0.08%7D%7B1%7D%29%5E%7B1%2A2%7D%5C%5CA%3D5000%281%2B0.08%29%5E2%5C%5CA%3D5000%281.08%29%5E2%5C%5CA%3D5000%281.1664%29%5C%5CA%3D5832)
So, Amount saved if the interest is compounded annually is $5832
b) Amount saved if the interest is compounded semi-annually
If interest compounded semi-annually, n= 2
Using Formula: ![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Putting values:
![A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{2})^{2*2}\\A=5000(1+0.04)^4\\A=5000(1.04)^4\\A=5000(1.1699)\\A=5849.5](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20%5C%5CA%3D5000%281%2B%5Cfrac%7B0.08%7D%7B2%7D%29%5E%7B2%2A2%7D%5C%5CA%3D5000%281%2B0.04%29%5E4%5C%5CA%3D5000%281.04%29%5E4%5C%5CA%3D5000%281.1699%29%5C%5CA%3D5849.5)
So, Amount saved if the interest is compounded semi-annually is $5849.5
Answer:
if you are solving for then it is x = 4/3
Step-by-step explanation:
Answer:
y=3x-1
Step-by-step explanation:
![(x - 2) \div (2 - 1) = (y - 5) \div (5 - 2)](https://tex.z-dn.net/?f=%28x%20-%202%29%20%20%5Cdiv%20%20%282%20-%201%29%20%3D%20%28y%20-%205%29%20%5Cdiv%20%285%20-%202%29)
![x - 2 = (y - 5) \div 3](https://tex.z-dn.net/?f=x%20-%202%20%3D%20%28y%20-%205%29%20%5Cdiv%203)
3x - 6= y-5
y=3x-1
Answer:
Quadrant II
Step-by-step explanation:
This is because the top right is I, the top left
is II, the bottom left is III, and the bottom right is IV.