<span>ABCD is a parallelogram.
Looking at the quadrilateral ABCD, the first thing to do is to determine if the opposite sides are parallel to each other. So let's check that by looking at the opposite sides.
Line segment BA. When you go from point B to point A, you move to the right 1 space, and down 4 spaces. So the slope is -4. Looking at line segment CD, you also move to the right 1 space and down 4 spaces, which also means a slope of -4. So those two sides are parallel. When you compare line segments BC and AD, you'll notice that for both of them, you go to the right 5 spaces and up 2 spaces, so those too are parallel. So we can now saw that the quadrilateral ABCD is a parallelogram.
Since ABCD is a parallelogram, we now need to check if it's a rectangle (we know it can't be a square since the sides aren't all the same length). An easy way to test if it's a rectangle is to check of one of the angles is 90 degrees. And if we draw a line from B to D, we can create a triangle ABD. And in a right triangle, due to Pythagora's theorem we know that A^2 + B^2 = C^2 where A is the line segment AB, B is the line segment AD and C is the line segment BD. So let's calculate A^2, B^2, and C^2.
A^2: Line segment AB. We can construct a right triangle with A = 1 and B = 4. So C^2 = 1^2 + 4^2 = 1 + 16 = 17. So we have an A^2 value of 17
B^2: Line segment AD. We can construct a right triangle with A = 2 and B = 5. So C^2 = 2^2 + 5^2 = 4 + 25 = 29. So we have an B^2 value of 29
C^2: Line segment BD. We can construct a right triangle with A = 2 and B = 6. So C^2 = 2^2 + 6^2 = 4 + 36 = 40. So we have a C^2 value of 40.
Now let's check if the equation A^2 + B^2 = C^2 is correct:
17 + 29 = 40
46 = 40
And since 46 isn't equal to 40, that means that ABCD can not be a rectangle. So it's just a parallelogram.</span>
A direct variation is a mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. In other words, a direct variation is where
.
In answer a,
, so it is a direct variation.
In answer c,
, so it is a direct variation.
In answer d,
, so it is a direct variation,
Only answer b is left, which means the answer must be 'b'.
We also know 'b' is the answer because it cannot be expressed as <span>
. Instead, it is expressed as </span>
, which is not the same thing and is therefore not a direct variation.
Hope I helped, and let me know if you have any questions :)
To find the probability of both of these occurring, you will multiply the probability of choosing a blue marble by the probability of choosing a purple marble (with no replacement after the first one).
Probability of choosing a blue marble: 17/120
Probability of choosing a purple marble: 18/119
17/120 x 18/119 = 3/140
You will have a 3/140 chance of both of these occurring.
Answer:
0.61
Step-by-step explanation:
Pr (female) = total number of females(n')/Total number of students(n)
Where P(female) = probability of selectinga female
Pr(female) = n'/n................. Equation 1
Given: n = 44 students, n' = 15+12 = 27 females
Substitute into equation 1
Pr(female) = 27/44
Pr(female) = 0.61.
Hence the probability of selecting a female is 0.61
First we will change them on the same denominator which will be 12. If we do something to the denominator we must do the same to the numerator so :
For 1/3 we get 4/12 because (1/3)*4 = 4/12
And for 2/3 we get 8/12 because (2/3)*4 = 8/12
So 1/3 is the smaller fraction, 7/12 is in the middle and 2/3 is the bigger fraction.
