Answer:
21, 42, 63, 84
Step-by-step explanation:
Numbers that have a star and a circle on them are all multiples of 3 and 7. As there are less multiples of 7 between 1-100 we should list the multiples of 7 and then check if they are also multiples of 3.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
A quick way of calculating if a number is a multiple of 3 is to see if its digital root is either 3, 6, or 9
7 is not as 7 is not a multiple of 3
14 is not as 1+4 = 5 is not a multiple of 3
21 is, as 2+1 = 3 is a multiple of 3
28 is not, as 2+8 = 10 is not a multiple of 3
35 not, 3+5=8
42 is, 4+2=6
49 is not, 4+9=13
56 is not , 5+6=11
63 is, 6+3=9
70 is not, 7+0=7
77 is not, 7+7=14, 1+4=5
84 is, 8+4=12, 1+2=3
91 is not, 9+1=10 1+0 = 1
98 is not, 9+8=17, 1+7=8
Let the cost of a chicken be x and the cost of a duck, y, then
50x + 30y = 550 . . . (1)
44x + 36y = 532 . . . (2)
(1) x 6 ⇒ 300x + 180y = 3,300 . . . (3)
(2) x 5 ⇒ 220x + 180y = 2,660 . . . (4)
(3) - (4) ⇒ 80x = 640
⇒ x = 640 / 80 = 8
From (1): 50(8) + 30y = 550
⇒ 30y = 550 - 400 = 150
⇒ y = 150 / 30 = 5
Therefore, the price of a chicken is $8 and the price of a duck is $5.
9514 1404 393
Answer:
(b) ... confirm ∠C≅∠E
Step-by-step explanation:
The first step is to read and understand the problem statement. It is asking for a way to prove ΔABC ~ ΔADE by AA similarity. That means you want to show any two of the three ...
For this purpose, lengths of line segments are irrelevant (eliminating the last two answer choices). The fact that ∠A≅∠A is given, so you only need to find an answer choice that will show one of the last two angle congruences.
Obviously, showing ∠B≅∠E (choice A) is not relevant to the problem.
The only answer choice that is relevant to the question is the second one, showing ∠C≅∠E.
