The trig ratios are a set of numbers that are properties
of every angle.
When the angle is in a right triangle, they can be defined
like this:
Sine (sin) of the angle: (opposite leg) divided by (hypotenuse)
Cosine (cos) of the angle: (adjacent leg) divided by (hypotenuse)
Tangent (tan) of the angle: (opposite leg) divided by (adjacent leg)
Cotangent (cot) of the angle: (adjacent leg) divided by (opposite leg)
Secant (sec) of the angle: (hypotenuse) divided by (adjacent leg)
Cosecant of the angle: (hypotenuse) divided by (opposite leg).
The size of the right triangle doesn't matter, only the ratios of
pairs of sides. That will always be the same number for the
same angle, no matter how big or small the triangle is.
There's no easy way to calculate the numbers for an angle.
You just have to look them up, using tables in books, or online
(try 'cosine 29' on Google), or on most hand-calculators.
Step-by-step explanation:
A leap year occurs every 4th year.
So, 1875 - 1700 = 175
Now let us divide 175 by 4
So, 43 leap years occur between the years 1700 and 1875.
Answer: The cost of each pound of jellybean is $2.5
The cost for each pound of trail mix is $1.5
Step-by-step explanation:
Let the cost for each pound of jellybeans be x.
Let the cost of each pound of trail mix be y.
Based on the information given, we can form an equation which will be:
For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. This will be:
2x + 12y = 23 ...... i
For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. This will be:
5x + 3y = 17...... ii
2x + 12y = 23 ...... i
5x + 3y = 17...... ii
Multiply equation i by 5
Multiply equation ii by 2
10x + 60y = 115 ...... iii
10x + 6y = 34 ..... iv
Subtract iv from iii
54y = 81
y = 81/54
y = 1.5
The cost for each pound of trail mix is $1.5
From equation i
2x + 12y = 23
2x + 12(1.5) = 23
2x + 18 = 23
2x = 23 - 18
2x = 5
x = 5/2 = 2.5
The cost of each pound of jellybean is $2.5
Answer: they can rent the room for less than 6 hours.
Step-by-step explanation:
Let x represent the possible amounts of time in which they can rent the room.
There is a reservation fee of $47 and an additional hourly fee of $7.40. This means that the total cost of renting the room for x hours would be
47 + 7.4x
The math club wants to spend less than $91.40 on renting the room. This would be expressed as
47 + 7.4x < 91.4
7.4x < 91.4 - 47
7.4x < 44.4
x < 44.4/7.4
x < 6