Applying the trig formula: sin a = cos (90 - a)
cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x)
Property of the cosine function -->
(
2
x
+
8
)
=
±
(
53
−
x
)
a. 2x + 8 = 53 - x
3x = 45
x
=
15
∘
b. 2x + 8 = - 53 + x
x
=
−
61
∘
For general answers, add
k
360
∘
Check by calculator.
x = 15 --> sin (x + 37) = sin 52 = 0.788
cos (2x + 8) = cos (38) = 0.788. Proved
x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407
cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved
Let the number of runs made on the home run be x, then for the <span>two 3-run home runs, we have 2x
Let the number of runs made in each hit be y, then for the 4 hits that each scored 2 runs, we have 4y.
Thus the algebraic expression to model the total score is 2x + 4y.
Because, there are 3 runs per home run, then x = 3 and because there are 2 runs per hit, then y = 2.
Therefore, the total score is given by 2(3) + 4(2) = 6 + 8 = 14.
</span>
Answer:
1 5/9 OR 14/9
Step-by-step explanation:
First we need to find out what the question is asking. How much sugar will she need if she wants to make 2 1/3 batches?
Next, we must see if we need to divide, subtract, multiply, or add. We need to divide.
2 1/3 divided by 1 1/2
Convert mixed numbers to improper fractions: 2 1/3=7/3 1 1/3=3/2
Apply the fraction rule a/b/c/d=a*d/b*c: 7*2/3*3
14/9 OR 1 5/9
Answers:
Equation 1: B
Equation 2: D
Equation 3: A
Equation 4: C
*I am pretty sure are right
