Answer:
Lins house is 315 metres from school
Step-by-step explanation:
It's simple, just do 450-135.
Answer:
(x, y) = (4, 9)
Step-by-step explanation:
You can use the second equation to write an expression for y.
y = 10 - 1/4x . . . . subtract 1/4x from the given 2nd equation
Now, substitute that for y in the first equation:
1/2x + 1/3(10 -1/4x) = 5
1/2x + 10/3 -1/12x = 5 . . . . eliminate parentheses
You can work this a couple of ways from here. One is to multiply by 12 to eliminate fractions. Another is to work with the numbers as they are. We'll do that, because we don't get enough practice doing arithmetic with fractions.
5/12x = 5/3 . . . . . subtract 10/3
x = (5/3)/(5/12) = 12/3 = 4
From above, we can use our expression for y:
y = 10 - 1/4·4 = 9
The solution is (x, y) = (4, 9).
Answer: the cost per unit of gas is $0.38
Step-by-step explanation:
Let x represent the cost per unit of electricity.
Let y represent the cost per unit of gas.
During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of $344. It means that
600x + 100y = 344- - - - - - - - - -1
The next month, 400 units of electricity and 250 units of gas were used for a total cost of $299.
It means that
400x + 250y = 299- - - - - - - - - -1
Multiplying equation 1 by 400 and equation 2 by 600, it becomes
240000x + 40000y = 137600
240000x + 150000y = 179400
Subtracting, it becomes
- 110000y = - 41800
y = - 41800/- 110000
y = 0.38
Substituting y = 0.38 into equation 1, it becomes
600x + 100 × 0.38 = 344
600x + 38 = 344
600x = 344 - 38 = 306
x = 306/600
x = 0.51
Answer:
n times 5
Step-by-step explanation:
A matrix Anxn of this way is called an upper triangular matrix. It can be proved that the determinant of this kind of matrix is
In this case, it would be 5+5+...+5 (n times) = n times 5
We are going to develop each determinant by the first column taking as pivot points the elements of the diagonal
![det\left[\begin{array}{cccc}5&a_{12}&a_{13}...&a_{1n}\\0&5&a_{23}...&a_{2n}\\...&...&...&...\\0&0&0&5\end{array}\right] =5+det\left[\begin{array}{ccc}5&a_{23}...&a_{2n}\\0&5&a_{3n}\\...&...&...\\0&0&5\end{array}\right]=5+5+...+det\left[\begin{array}{cc}5&a_{n-1,n}\\0&5\end{array}\right]=5+5+...+5+5\;(n\;times)](https://tex.z-dn.net/?f=det%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%26a_%7B12%7D%26a_%7B13%7D...%26a_%7B1n%7D%5C%5C0%265%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C...%26...%26...%26...%5C%5C0%260%260%265%5Cend%7Barray%7D%5Cright%5D%20%3D5%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C0%265%26a_%7B3n%7D%5C%5C...%26...%26...%5C%5C0%260%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26a_%7Bn-1%2Cn%7D%5C%5C0%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2B5%2B5%5C%3B%28n%5C%3Btimes%29)
Answer:
Calculate the Macaulay duration of Annuity B at the time of purchase is 1.369.
Step-by-step explanation:
First, we use 0.93 to calculate the v which equals 1/(1+i).
= 0.93
After rearranging the equation, we get 1.07
+ 0.07v - 0.93=0
So, v=0.9
Mac D: 
After substituting the value of v, we get Mac D = 1.369.
