Answer:
Step-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
The conclusion that can be made given the slopes of the quadrilateral is that: since the slopes of the opposite sides are equal, the opposite sides are parallel, therefore the quadrilateral is a parallelogram. (Option A is correct).
<em><u>Recall:</u></em>
- The slopes of the opposite sides of a parallelogram are always parallel.
- When two lines have a slope that is equal, the lines are said to be parallel to each other.
The slopes given shows are:
-1/2, 3/2, -1/2, and 3/2
This implies that the quadrilateral has two pairs of equal sides that are parallel to each other.
- Therefore, the conclusion that can be made given the slopes of the quadrilateral is that: since the slopes of the opposite sides are equal, the opposite sides are parallel, therefore the quadrilateral is a parallelogram. (Option A is correct).
Learn more about parallelogram on:
brainly.com/question/3050890
Sets and set operations are ways of organizing, classifying and obtaining information about objects according to the characteristics they possess, as objects generally have several characteristics, the same object can belong to several sets, an example is the subjects of a school , where students (objects) are classified according to the subject they study (set).
The <em>intersection</em> of sets is a new set consisting of those objects that simultaneously possess the characteristics of each intersected set, the intersection of two subjects will be those students who have both subjects enrolled.
The <em>union</em> of sets is a new set consisting of all the objects belonging to the united sets, the union of two subjects will be all students of both courses.
In this case there are three sets B, C and S of which we are given the following information:
Answer
n(BꓵSꓵC)=5
n(BꓵS)=10 – 5 = 5
n(BꓵC)=12 – 5 = 7
n[(BꓵC)ꓴ(BꓵS)ꓴ(CꓵS)]=21 – 5 – 5 – 7 = 4
n(B)=36 – 5 – 5 – 7 = 19
n(S)=30 – 5 – 5 – 4 = 16
n(C)=34 – 5 – 7 – 4 = 18
