A) Find KM∠KEM is a right angle hence ΔKEM is a right angled triangle Using Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides we can answer the
KM² = KE² + ME²KM² = 8² + (3√5)² = 64 + 9x5KM = √109KM = 10.44
b)Find LMThe ratio of LM:KN is 3:5 hence if we take the length of one unit as xlength of LM is 3xand the length of KN is 5x ∠K and ∠N are equal making it a isosceles trapezoid. A line from L that cuts KN perpendicularly at D makes KE = DN
KN = LM + 2x 2x = KE + DN2x = 8+8x = 8LM = 3x = 3*8 = 24
c)Find KN Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have the same height ME = LD.
∠K = ∠N Hence KE = DN the distance ED = LMhence KN = KE + ED + DN since ED = LM = 24and KE + DN = 16KN = 16 + 24 = 40
d)Find area KLMNArea of trapezium can be calculated using the formula below Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)substituting values into the general equationArea = 1/2 * ME * (KN+ LM) = 1/2 * 3√5 * (40 + 24) = 1/2 * 3√5 * 64 = 3 x 2.23 * 32 = 214.66 units²
Answer:
D
Step-by-step explanation:
if a<b,then b<a is the answer
Answer:
9.14285714286
Step-by-step explanation:
i dont know if you need to round it but heres the answer (hasnt been rounded)
Answer:
51*
Step-by-step explanation
I believe this correct only because 51 + <B + <A=180*
Because of that we will make <B equal to <C
Hope this helps!
Answer: Hello mate!
we know that p(x,y) means "Student x has taken class y"
and the used symbols are:
∃: this means "existence", you use this symbol to say that there exists at least one object that makes true the sentence.
∀: this means "for all", you use this symbol to say that the sentence is true for all the elements, then:
a) ∃x∃yP (x, y)
"exist at least one student x, that took at least one class y"
b) ∃x∀yP (x, y)
"exist at least one student x, that took all the classes y"
c) ∀x∃yP (x, y)
"every student x, took at least one class y"
d) ∃y∀xP (x, y)
"exist at least one class y, that has been taken by all the students x"
e) ∀y∃xP (x, y)
"for every class y, there is at least one student x that took the class"
f) ∀x∀yP (x, y)
"all the students x took all the classes y"
