Answer:
∠CDF = 54
Step-by-step explanation:
In ΔAEB,
AE ≅ AB
∠ABE = ∠E = x {Angles opposite to equal sides are equal}
∠EAB + ∠E +∠ABE = 180 {angle sum property of triangle}
26 + x + x = 180
26 + 2x = 180
2x = 180 - 26
2x = 154
x = 154/2
x = 77
∠ABE = ∠E = 77
In quadrilateral AECF
∠A + ∠E + ∠C + ∠F = 360
90 + 77 + ∠C + 90 = 360
∠C + 257 = 360
∠C = 360 - 257
∠C = 103
∠FCD + ∠BCD = ∠C
∠FCD + 67 = 103
∠FCD = 103 - 67
∠FCD = 36
ΔFCD,
∠FCD + ∠CDF + ∠CFD = 180
36 + ∠CDF + 90 = 180
∠CDF + 126 = 180
∠CDF = 180 - 126
∠CDF = 54
The answer is 5/8 milliliter are left in the bottle at lunch
Answer:
The number of ways of selection of 3 items taking 2 at a time in addition to the possible ways in which each girl selects the same style is 9 different ways. Since the list contains 9 different ways in which each of them can select a style, the list is complete.
Step-by-step explanation:
Here we have the number of ways the available styles can be arranged between each girl is given by the number of permutation of 3 items, taking two at a time plus the number of possible selections where both of them select the same style as follows
We note that the formula for permutation is
P =
Therefore ₃P₂ = = 6 different ways
The number of possible selections where both of them select the same style is given by
(T, T), (s, s), (L, L) = 3 different ways
Total number of ways = 6 + 3 = 9 ways
Number of different ways available in the list = 9 ways
Therefore the list is complete
Answer:
The age of the person who walked in the room is 44.
Step-by-step explanation:
The original mean age is 38 which means the total ages combined divided by the 5 people.
5 people x 38 (the mean age) = x
x = Total ages combined
x = 190 years old
Then another person came in, now totaling 6 people, and the mean age changed to 39 years old, an increase.
6 people x 39 (the new mean age) = y
y = Total ages combined
y = 234 years old
So, we are trying to figure out the age of the new person who came in. We have to subtract the new total age (y) by the original total age (x).
y - x = Age of new person in room
234 years old - 190 years old =
44 years old
Answer:
B) 3(2x+3)^2
Step-by-step explanation:
12x^2+36x+27
factor out the 3 first,
3(4x^2+12x+9)
factor out the trinomial 4x^2+12x+9,
3(2x+3)(2x+3)
3(2x+3)^2