SGA is doing a fundraiser to sell candles for project graduation. Small candles cost $4.00 and large candles cost $6.00. They ha
1 answer:
Given:
Cost of small candles = $4.00
Cost of large candles = $6.00
They have at most 50 candles, and want to make at least $100.
To find:
The system of linear inequalities represents the situation.
Solution:
Let x be the number of small candles and y be the number of large candles.
At most 50 candles means total candles must be less than or equal to 50.
Want to make at least $100. It means, the total sales must be greater than or equal to $100.
Therefore, the inequalities in the system of linear inequalities are and
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Answer:
AB = 75
BC = 60
AC = 45
m∠A = 53°
m∠B = 37°
m∠C = 90°
Step-by-step explanation:
<u>Trigonometric ratios</u>
where:
is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Given:
Therefore:
- side opposite angle A = BC = 60
- side adjacent angle A = AC = 45
To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AC² + BC² = AB²
⇒ 45² + 60² = AB²
⇒ AB² = 5625
⇒ AB = √5625
⇒ AB = 75
To find m∠A:
m∠C = 90° (as it is a right angle)
The interior angles of a triangle sum to 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 53° + m∠B + 90° = 180°
⇒ m∠B = 180° - 53° - 90°
⇒ m∠B = 37°