You need to take each quantity in the original recipe and multiply by 1/2.
(1/2 teaspoon)(1/2)= 1/4 teaspoon
(3 teaspoons)(1/2) ... just multiply 3 times 1/2 and the answer is the number of teaspoons of cinnamon.
(3 1/2 cups flour)(1/2) .... change 3...

David, thanks for your question. The two trinomials you used as examples are very similar : ax2+bx+c is the general form and x2+bx+c is the specific case where a = 1.
when c=0: ax2+bx+c --> ax2+bx
There is a common factor of x in both terms so x(ax+b)...

Let a=mass of 30% alloy
Let b= mass of 60% alloy
Since the total mass after mixing is 300 kg, a + b = 300 kg
The new mixture is a 50% alloy, so 0.3a + 0.6b = 0.5(300)
We have 2 equations with...

You should have learned something that sounds a lot like this:
Given two parallel lines and a transversal, alternate interior angles are congruent.
The key here is that you are told the two lines are parallel, and you have learned that the relationships between the...

Linda,
Your formula is perfect! On the left side is your total cost and on the right side is your brothers total cost. For some value of m they are equal. Solve for m and you will have your answer in months.
Jason

P = Probability of being defective = 0.03
1-P = Probability of not being defective = 0.97
12 C 5 = the number of combinations of 5 defects out of 12
(P)5(1-P)7= the probability for a single combination of 5 defects out of 12
The probability of...

In answering each of these questions remember how a function is defined in term the of input and output.
A function is a relationship in which each input has only one output. To check for a function look at the input and its output.
Is there another piece of data that has...

Since the probability for each seed is 0.8, and there are 50 seeds, the expected value would be the individual event probability multiplied by the number of events.
(0.8)(50) = 40 expected seedlings.

Total value = 4.00, let d = number of dimes, let q= number of quarters
We have also been given that d = 2q - 5
Total value = (0.10)(d) + (0.25)(q) = 4.00
Since d = 2q - 5, substitute for d
(0.10)(2q - 5) + 0.25q = 4.00
Distribute...

Make sure you draw a sketch to help you set up this problem.
The border will extend beyond the rectangle above, below, left, and right by the same amount, x.
Consider the border to be four thin rectangles along the sides and four little squares outside the four corners of the rectangle...

Remember that the formula for interest problems is: A = P(1+(i/n))nt
where A = amount
P = principal (the dollars you start with)
i = annual interest rate
n = number...

All the walls have the same height. Two of the walls will span a distance equal to the length and their areas will be l*h. Two of the walls will span a distance of the width, and their areas with be w*h.
a) Total area = 2(l*h) + 2(w*h) = 2h(l+w)
b) start...

So the domain is a set of all possible inputs, and the range is a set of all possible outputs.
To determine if your inputs are limited try to find a value of x which would result in an undefined value.
Is your function f(x) = sqr(2x2-1) or f(x) = sqr(2x2) - 1 ? because...

Remember that the goal is to isolate the k.
-3k + 12 = -6
We want to morph this into something that looks like k =
Subtract 12 from each side to eliminate the 12 on the left side of the equation:
-3k +...

There is another way to directly calculate square roots which is very similar to long division:
The first thing about this method is that numbers are "brought down" 2 at a time instead of 1 as in long division. Think of pairs of digits starting from the decimal point going each way...

The key in this problem is to apply the order of operations correctly.
P
E
MD
AS
[3*32+13*(-2)] + 7[8-(4-9)]
Parentheses: perform any operations within parentheses first
(4-9) = -5 --> [3*32+13*(-2)]...

If you sketch the parallelogram as described there will be triangles FTS and PTQ within. FS =5 and PQ= 8. Let TS =x and TQ = 10 - x, since SQ=10. There are 3 pairs of congruent angles.
Angle FTS is congruent to angle PTQ by vertical angles.
Angle TFS is congruent to angle TPQ by alternate...

The first step to factoring an expression is to look for a common factor. In this expression we can factor out a from each term to become
a(8a2+14a+3)
Now turn our attention to factoring the expression in the parentheses above
The 8a2 term could be factored...

If the "v" is really a square root symbol, the possible answers make much more sense.
sqr(6x-4) - sqr(2x + 10) = 0
There are 2 terms on the left side with square roots. If the whole left side was under one square root you could square each side, but it isn't. If you add sqr(2x...

(2.5 x 103)(4.2 x 102) = (2.5)(4.2)(103)(102)
= 10.5 x 105 (Multiply exponential expressions with the same base; add the exponents)
So answer c is an equivalent value but is not...