Answer:
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y/x-5
Step-by-step explanation:
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
Answer: A cherry pie costs 9 and an apple pie cost 12
Step-by-step explanation:
Let an apple pie be represented by a
Let an cherry pie be represented by c
Jennifer sold 12 cherry pies and 3 apple pies for a total of 144. This can be written as:
12c + 3a= 144
Jacob sold 2 cherry pies and 9 apple pies for a total for 126. This can be written as:
2c + 9a = 126
12c + 3a= 144 ............. i
2c + 9a = 126 ........... ii
Multiply equation i by 2
Multiply equation ii by 12
24c + 6a = 288 ........ iii
24c + 108a = 1512 ...... iv
Subtract iv from iii
-102a = -1224
a = 1224/102
a = 12
An apple pie costs 12
From equation i
12c + 3a= 144
12c + (3×12) = 144
12c + 36 = 144
12c = 144 - 36
12c = 108
c = 108/12
c = 9
A cherry pie costs 9
The number line is a graph of the Integers
