Let x equal the number of hours at the pharmacy and y equal the number of hours babysitting. Then
15x +10y = 90
Now the last part of your question did not show up above but I am assuming that the total hours where specified, let call that T. So the second equation is:
x + y = T
The potential energy of the pinecone before it drops is mgh (given the ground is used as the zero potential energy reference). After if falls the energy is all kinetic energy or (1/2)mv^2 Equating these gives v^2 = 2gh.
Note that you can now determine the energy loss due to air friction by the difference...
Just in case you are not taking a calculus level class, the position can be deterimined by the area under the curve of the velocity graph up to the time in question. If the graph drops below the x axis, count this as negative area.
We know from the first part that the distance is equal to the speed multiplied by the time
d = st, or d = (45 mi/hr)t
we also know from the last part this same distance is
d = (60 mi/hr)(43 mi - 10 mi - t), or (60 mi/hr)(33 hr - t).
Now elliminate the d
(45 mi/hr)t = (60 mi/hr)(33...
If A is the original amout deposited, the account balanece, B, after 1 period is B = A(1 + i), where i is the interest for the period. After two periods, B = A(1 + i)(1 + i) or A(1 + i)^2. And carrying this out to n periods you will obtain B = A(1 + i)^n.
This is the formula to use when the interest...
f(x) is a notation for a "function of x." Usually it is written as f(x)= "something", which is an expression with x as what we call the independent variable. Many times f(x) and y are the same thing.
In solving a quadratic equation you are looking for the roots of the expression in the form of a^2...
Good answer by Samuel. You should also ask yourself: in matrix multiplication is AB = BA? And the general answer is no.
The x coordinates are measured to the right of origin (or y axis) and y values are measured up from the origin (or the x axis).
First recall the formulas -(a - b) = (b - a) and x^2 + a^2 = (x + a)(x - a).
If you rearrange the equation with these formulas in mind you get:
1/(x-3) + 2/(x-3) = 4/[(x + 3)(x - 3)]
Now you can add the terms on the left hand side and multiply through by [(x + 3)(x - 3)].
That should give you...
Recall that the square root of a number is a number when squared equals the first number. mathematically if b = sqrt(a) then b^2 = a. So what you are looking for is the square root of 19. It turns out that this is an irrational number (a number continues in its decimal places forever) and usually...
It's always a good idea to check your answer by substituting your solution for x back into the original equation to see if it works. This will give you confidence that you have the right answer or let you know if you need to try again. All professionals
will do this.
In most practical problems...
It is a little out of the ordinary for me to see an equation with two equal signs but if we look at the first part (-7x - 2y = 11x - 2y) we can see by adding 2y to both sides that x must equal zero. By substituting x = 0 into a second equation, let's use 11x - 2y = 11 we can get the value for y.
A fraction is simply a division. Think of 7/42 as seven divided by 42. But before you do anything factor the denominator into 6(7). This way the 7's will cancel leaving you with 1/6. From here just do the long division i.e. 1 divided by 6. your answer will be less than 1 so you will have a decimal...
(a = b)^4
is the same as
(a + b)(a + b)(a + b)(a + b)
carrying out the first product
(a^2 + 2ab + b^2)(a + b)(a + b)
and keep going
(a^3 + 2(a^2)b + ab^2 + ba^2 + 2ab^2 + b^3)(a + b) or
(a^3 + 3ba^2 + 3ab^2 + b^3)(a + b)
Just carry out the last multiplication being careful with the...
Sounds like you've got it.
Since f(x) = 0, this is just the x axis, so this is the definite integral evaluated between the limits x = 2 and x = 10.
Hi Leanna, I'm going to take a quess at what you are after here. It looks like you are trying to find a number that will allow you to right this expression as a square of another expression in the form of
Ax + B.
In other words, we want
5x^2 + 11 + Blank = (Ax + B)^2
Is f(x) = 4x + .5 ? If so: Just multiply it by itself i.e. (f(x))(f(x)) = (4x + .5)(4x + .5). From here just carry out the multiplication.
Start by dropping the parenthesis then you will notice the 4s on the right side will cancel. Then add like terms. Get the x terms to one side and the constants to the other (by adding or subtracting the appropriate terms from both sides). Then divide by the coefficient of the x term.
Probably the easiest way to approch this one is to first subtract 7 from both sides, multiply through (both sides) by 5, collect like terms, and solve for t.