Answer:
bags of snack = x = 6
bottles of water = y = 5
Step-by-step explanation:
The system of equations can be used to determine how many of each item they bought.
20.00=2.50x+1.00y
11=x+y
how many bags of snack mix did they buy?
Let
bags of snack = x
bottles of water = y
20.00 = 2.50x + 1.00y (1)
11 = x + y (2)
From (2)
x = 11 - y
Substitute x = 11 - y into (1)
20.00 = 2.50x + 1.00y
20.00 = 2.50(11 - y) + 1.00y
20.00 = 27.5 - 2.50y + 1.00y
20.00 - 27.5 = -2.50y + 1.00y
-7.5 = -1.5y
y = -7.5/-1.5
y = 5
Substitute y = 5 into (2)
11 = x + y
11 = x + 5
11 - 5 = x
x = 6
bags of snack = x = 6
bottles of water = y = 5
Let's begin by breaking each number down into its prime factors: 4 = 2 x 2 5 = 5 6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number: common prime factors: 2 unique prime factors: 2,5,3 LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder): 10,000/60 = 166 and 2/3 Multiples of ALL 3 numbers (4,5,6) = 166 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number: common prime factors: none
unique prime factors: 2 x 2 x 5
LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
10,000/20 = 500
Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer: Multiples of ONLY numbers 4 and 5 (excluding 6): 500 - 166 = <span>334</span>
Answer:
(D)9 divided by sin 60 degrees
Step-by-step explanation:
From the given figure, using trigonometry
Substituting the given values, we get
Thus, The length of the support AB is 9 divided by sin 60 degrees.
Michelle: x
Ian: 5x
Joe: 7x
Michelle + Ian + Joe = 208 berries
x + 5x + 7x = 208
Combine like terms: 13x = 208
Divide both sides by 13: x = 16
Joe = 7x = 7*16=112
Joe picked 112 berries
