3c^3. This is probably it. I'm pretty positive.
The equation given is
where a is some number.
We can solve for x by taking the square root of both sides.
Now let's think through what happens for various values of a.
TWO SOLUTIONS
If a is a positive number the above yields two solutions. Take for example:
There will be two solutions (one positive and one negative) as there are two numbers (here -7 and +7) that when multiplied by themselves give 49. That is,
and
. The positive root is called the principal root and the negative root is called the secondary root. This will be the case anytime we take the root of a positive number.
ONE SOLUTION
If a = 0 there is only one solution. That is because
and
. Zero is neither positive nor negative and it has only one root which is 0 itself. So in this case there is only one solution and it is 0.
NO (REAL) SOLUTIONS
If a is negative we would be taking the square root of a negative number. There is no (real) number that when multiplied by itself gives a negative number. Take for example
which gives us
. The square root of -49 is not 7 because (7)(7)=49 which is positive. The square root of -49 is not -7 because (-7)(-7)=49 which is also positive. There is no real number that gives -49 when multiplied by itself. I say "real" numbers because there do exist imaginary/complex numbers but because of the way the questions was asked I imagine you may not know about these yet.
You are looking for the shaded region that would be contained in both of the inequalities.
You have:
If you graph an shade the correct half-plane for those equations, you will see there is a triangular region on the left side of the first quadrant.
Answer:
Graph D
Step-by-step explanation:
We can look at the number of pounds of pecans and cashews, shown on the x- and y-axis, respectively.
All of the graphs have an x-intercept of (4, 0), meaning that the number of pecans being bought is 4 lbs.
Since pecans cost $6 per lb, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
Let's look at the y-axis to see how many lbs of cashews Malik can buy. The y-intercept is (0, 3) for all graphs, meaning that 3 lbs of cashews are being bought.
Since cashews cost $8 per pound, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
The shaded area represents the values that can be used in the problem. Since we want $24 or less, the shaded region has to be below the line.
Malik can spend <u>no more than</u> $24, so the line should be solid since this means that the values the line touches are inclusive. 4 lbs of pecans and 3 lbs of cashews should be inclusive.
The graph that has all of these properties is Graph D.