We need to find the expression for " number_of_prizes is divisible number_of_participants". Also there should not remain any remainder left. On in order words, we can say the reaminder we get after division is 0.
Let us assume number of Prizes are = p and
Number of participants = n.
If we divide number of Prizes by number of participants and there will be not remainder then there would be some quotient remaining and that quotent would be a whole number.
Let us assume that quotent is taken by q.
So, we can setup an expression now.
Let us rephrase the statement .
" Number of Prizes ÷ Number of participants = quotient".
p ÷ n = q.
In fraction form we can write
p/n =q ; n ≠ 0.
Answer:
The coordinates of the mid-point are :

Step-by-step explanation:
We know that, the coordinates of the mid-point (<em>x</em>, <em>y</em>) of a line segment joining the points (<em>x</em>₁, <em>y</em>₁) and (<em>x</em>₂, <em>y</em>₂) is given by

Now, we have the given points as (3, 5) and (-2, 0).
By using the above formula, coordinates of the mid-point (<em>x</em>, <em>y</em>) of the line-segment joining the points (3, 5) and (-2, 0) is given by,


∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is
.
This can be determined by finding the x-intercept. In doing so, we let y=0 to find the value of x.
y= 2x^2 -x -3
[0 = 2x^2 -x-3]÷2
0 = x^2 -1/2 x - 3/2
Complete the squares:
1/16 + 3/2 = x^2 - 1/2x + 1/16
25/16 = (x -1/4)^2
sqrt (25/16) = x - 1/4
+/- 5/4 = x - 1/4
Thus,
x = 1/4 + 5/4 = 3/2
x = 1/4 - 5/4 = -1
Thus, the graph crosses at x = 3/2 and x = -1.
The equivalent sets are <u>X n Y = { } and X U Y= {5, 6, 7,8, 9, 10, 12 ,14}</u>
<h3>Set theory and notation</h3>
Given the following sets expressed as;
X = {8, 10, 12, 14}
Y = {5, 6, 7, 8,9}
Since union means the combination of all the elements in both sets and intersection is the common elements in the set, hence;
X n Y = { }
X U Y= {5, 6, 7,8, 9, 10, 12 ,14}
Note that the intersection is an empty set since there is no common element
Learn more on set theory here: brainly.com/question/13458417
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Answer:
(-1,1)
Step-by-step explanation:
All you have to do is plug it in the equation:
(x,y)
For (-1,1)
1=2(-1)+1
Simplify:
1=-1 but you know that 1≠-1 so (-1,1) is not it
For (3,7)
7=2(3)+1
Simplify:
7=7
For (-3,-5)
-5=2(-3)+1
-5=-5
Simplify:
For (0,1)
1=2(0)+1
1=1