BC is 10 units and AC is 
units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵ 
∵ AB = 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (BC) × sin(30) = × sin(45)
∵ sin(30) = 0.5 and sin(45) = 
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵ 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (AC) × sin(30) = × sin(105)
∵ sin(105) = 
∴ 0.5 (AC) = 
- Divide both sides by 0.5
∴ AC = units
BC is 10 units and AC is units
Learn more:
You can learn more about the sine rule in brainly.com/question/12985572
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Answer:
$8.1
Step-by-step explanation:
Convert 45 yards of ribbon to feet through proper conversion factor.
(45 yards)(3 ft / 1 yard) = 135 feet
Divide this number by 5 to determine the number of 5-ft ribbon that customers can purchased.
n = 135 ft / 5 ft = 27
Then, multiply by $0.80.
R = (27)($0.80) = $21.6
The profit is equal to $21.6 and $13.50,
P = $21.6 - $13.50 = $8.1
Answer: $8.1
7/3x+1/3x=3x+6/3+5/3x
8/3x-5/3x=3x+6/3
3/3x=3x+6/3
x=3x+6/3
x-3x=6/3
-2x=2
-x=2/2
-x=1
x=-1
3tenths because 5tenths=50 And 2tenths=20 so if you do 50-20 you will get 30 or if u do 20+30 you will get 50 so either way is fine
Answer:
Proved
Step-by-step explanation:
From the given parameters, we have:
i.e. the length of each security numbers
i.e. 2 security numbers
Required
In 513 security numbers, 2 must have matching zeros
To do this, we make use of Pigeonhole principle.
First, we calculate the number of all security numbers not having matching zeros.
Each of the 9 digits can be selected in 2 ways.
2 ways implies that each digit is either 0 or not
So, total selection is:
Apply Pigeonhole principle
The principle states that: suppose there are n items in m containers, where 
, then there is at least one container that contains more than 1 item.
This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.
