D. some parallelograms are squares
Answer:
105 ways
Step-by-step explanation:
Because the order of selection does not matter, we know that we will be using a combination instead of a permutation.
₁₅C₂ = 15! / (2! * 13!)
= 15 * 14 * ... * 2 * 1 / 2 * 1 * 13 * 12 * ... * 2 * 1
= 15 * 14 / 2 * 1 (The 13! cancels out)
= 105
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Answer:
118 children
58 students
59 adults
Step-by-step explanation:
We can solve this problem by setting up a system of equations:
Let a = adults
2a = children (since double the # of adults were children), and
s = students
Set up the equations:
1704 = 5(2a) + 7s + 12(a)
1704 = 10a + 7s + 12a
235 = 2a + a + s
Simplify the equations:
1704 = 22a + 7s
235 = 3a + s
Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:
1704 = 22a + 7s
7(235 = 3a + s)
1704 = 22a + 7s
1645 = 21a + 7s
---------------------- (Subtract)
59 = a
This is the number of adults. Substitute this number into an equation to solve for the number of students:
235 = 3(59) + s
235 = 177 + s
s = 58.
Since the number of children is equivalent to 2a, solve:
2(59) = 118 children.
Therefore, the values for each group are:
118 children
59 adults
58 students.
We can rearrange 3x+y=9 to look more conventional by subtracting 3x from both sides and making it y= -3x+9.
Now we want to find a line that is parallel to this and goes through the point (0,-4). We know that -3 is the slope. With this in mind, if we want the other line to be parallel then it must have the same slope so that they never intersect. This gives us one of the numbers we need for the second line.
This means our second equation is looking like; y= -3x+b. This means we need to find b (the y-intercept) but we are also given a point it must go through and this is (0,-4). We simply plug this in into our new equation we need to solve and we get ; -4 = -3(0) + b . "since 0 is the x and -4 is the y" . From this we get that b= -4. This means the equation of a line parallel is:
y = -3x-4
Answer:
54
Step-by-step explanation:
