Roxy has received the following quiz scores so far this year: 75, 88, 90, 96, 98, 100 Which box plot represents this data?
2 answers:
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Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS = = 57.5°
Now, tan(57.5°) =
⇒ 1.5697 =
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) =
⇒ tan65° =
⇒ QM =
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = () × (ST)
= () × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²
The answer is
first you must multiply or use the FOIL method (First, Outer, Inner, Last)
First you multiply the first terms
this gives you 3x^2, then you multiple the outer terms
this gives you -21x, then you multiply the inner terms
that gives you 2x, finally you multiply the last terms
that gives you 14, now you combine like terms
now you put all the terms together and end up with your solution
first you must multiply or use the FOIL method (First, Outer, Inner, Last)
First you multiply the first terms
this gives you 3x^2, then you multiple the outer terms
this gives you -21x, then you multiply the inner terms
that gives you 2x, finally you multiply the last terms
that gives you 14, now you combine like terms
now you put all the terms together and end up with your solution