Answer:
The records can be select in 332,640 ways.
Step-by-step explanation:
Consider the provided information.
There are 11 records to select from and a disc jokey can play 6 records.
Here, we need to find the number of permutation of n = 11 records taken r = 6 at a time.
Use the formula:
Substitute the respective values in the above formula.
Hence, the records can be select in 332,640 ways.
Answer:
24 units
Step-by-step explanation:
Start by plotting on the rectangular coordinate system the four points given: (6,-3), (3,-6), (-1,-2) , and (2, 1)
Please see attached image for guidance with the answer.
These four points are represented with green dots in the image.
Notice that such rectangle can be viewed as inscribed in a larger square that is 7 units by 7 units, and on which these four points (the vertices of the rectangle) touch the square's perimeter.
So to make the calculation simple, we can find the area of the larger square (very simple to calculate since it is 7 times 7 = 49) and subtract from it the area of the four triangles that are depicted in yellow and in light green. Such result will give us the area of the rectangle (white background).
Out of the four triangles whose areas we need to extract, we notice that they are all right angle triangles with simple formulas to calculate their areas: base times height divided by 2.
The triangles in green have base 3 and height 3 so their areas are: (3 * 3) /2 = 4.5. since they are two of these the total area of the green triangles is 4.5*2 = 9
We do something similar with the yellow triangles, noticing that their base and heights are 4 and 4 respectively which gives an area of (4*4)/2 = 8
Again, since there are two of them, we multiply this by 2: 8 * 2 = 16
Now to calculate the area of the white rectangle we do:
Area of big square minus area of green triangles minus area of yellow triangles: 49 - 9 - 16 = 24
Answer:
x=15
Converse: If line x and y are parallel then angles on the same line are supplementary angles.
Step-by-step explanation:
<em><u>Converse:</u></em>
Let's start with the converse, so if line x and y are parallel then angles on the same line are supplementary angles. I'm not sure if that's the converse your teacher wants but my teacher taught me this.
<em><u>Finding x:</u></em>
Now we know that the angles are supplementary angles, that means if w add them together we get 180°. So our equation will be . Now we just solve it. We start by combining like terms, then adding the 15 to both sides, and lastly we divide the 13 to both sides and get...
x=15