In ΔDEF, d = 53 cm, ∠E=154° and ∠F=5°. Find the length of e, to the nearest 10th of a centimeter.

e = 64.8 cm

Step-by-step explanation:

The first thing to do here is to make a sketch of the triangle in question.

Please check the attachment for this.

The first thing to do here is to find the value of angle D.

Since it is a triangle, total angle there is 180

This means that;

D + E + F = 180

Thus 154 + 5 + D = 180

D + 159 = 180

D = 180-159

D = 21

The easiest way to find e is by the use of the sine rule.

Mathematically;

d/Sin D = e/Sin E

Thus;

53/sin 21 = e/Sin 154

e = 53Sin 154/Sin 21

e = 64.83

which is e = 64.8 cm to the nearest 10th of a centimeter

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.