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°
Answer:
3*2*3^m*4^m=3^8*2^n
3^m+1*2^2m+1=3^8*2^n
m+1=8
m=7
2m+1=n
n=15
Step-by-step explanation:
The total number of persons standing in the line waiting for ordering pizza are 5.
Explanation:
There are 5 people in total so the first place can be occupied by any of the 5 persons.
Secondly the second place in the line can be occupied by any of the 4 persons left.
Then the third place will be occupied by any remaining 3 persons as the front two places are already occupied.
Similarly the fourth place will be taken by any of the remaining two people. And lastly the last place will b filled by the last remaining person.
So the total number of ways will be 5*4*3*2*1 = 120 ways that is given in the question.
Answer: 427 miles
Step-by-step explanation:
if the jeep averages 30.5 miles per gallon, and you have 14 gallons, then you will need to multiply 30.5*14 to get your answer, which is 427
<span>g(x)= 3x − 3
</span><span>g(−6)
g(-6) = 3(-6) - 3
g(-6) = -18 - 3
g(-6) = -21
The answer is -21.</span>
