I suppose
The vectors that span 
form a basis for 
if they are (1) linearly independent and (2) any vector in can be expressed as a linear combination of those vectors (i.e. they span ).
Compute the Wronskian determinant:
The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of is 3.
Write an arbitrary vector in as 
. Then the given vectors span if there is always a choice of scalars 
such that
which is equivalent to the system
The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives
so the vectors do span .
The vectors comprising form a basis for it because they are linearly independent.
The slope intercept form is y=mx+b. m being the rate of the slope (rise over run) so in this case 2/1, or simply 2. b is the y intercept, or where a line passes through the y intercept, in this case it is -1.
The linear equation to model the company's monthly expenses is y = 2.5x + 3650
<em><u>Solution:</u></em>
Let "x" be the units produced in a month
It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers.
Cost per unit = $ 2.50
The company has monthly operating expenses of $350 for utilities and $3300 for salaries
We have to write the linear equation
The linear equation to model the company's monthly expenses in the form of:
y = mx + b
Cost per unit = $ 2.50
Monthly Expenses = $ 350 for utilities and $ 3300 for salaries
Let "y" be the total monthly expenses per month
Then,
Total expenses = Cost per unit(number of units) + Monthly Expenses
Thus the linear equation to model the company's monthly expenses is y = 2.5x + 3650
Answer:
£67.78
Step-by-step explanation:
Bread - 6 x £2.87 = £17.22
Ham - 8 x £6.32 = £50.56
£17.22
+ <u>£50.56</u>
£67.78
Add all the new budget amounts:
510 + 254 + 295 + 51 + 0 + 100 + 100+ 0 + 100 = 1410
Her monthly total is 1410, which is less than her income of 1700
1700 - 1410 = 290
She has $290 extra each month.
So she can divide that amount by 2 to put an equal amount in each blank category, or add what ever amount less than that into each one.
