By algebra properties we find the following relationships between each pair of algebraic expressions:
- First equation: Case 4
- Second equation: Case 1
- Third equation: Case 2
- Fourth equation: Case 5
- Fifth equation: Case 3
<h3>How to determine pairs of equivalent equations</h3>
In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:
First equation
(7 - 2 · x) + (3 · x - 11)
(7 - 11) + (- 2 · x + 3 · x)
- 4 + (- 2 + 3) · x
- 4 + (1) · x
- 4 + (5 - 4) · x
- 4 - 4 · x + 5 · x
- 4 · (x + 1) + 5 · x → Case 4
Second equation
- 7 + 6 · x - 4 · x + 3
(6 · x - 4 · x) + (- 7 + 3)
(6 - 4) · x - 4
2 · x - 4
2 · (x - 2) → Case 1
Third equation
9 · x - 2 · (3 · x - 3)
9 · x - 6 · x + 6
3 · x + 6
(2 + 1) · x + (14 - 8)
[1 - (- 2)] · x + (14 - 8)
(x + 14) - (8 - 2 · x) → Case 2
Fourth equation
- 3 · x + 6 + 4 · x
x + 6
(5 - 4) · x + (7 - 1)
(7 + 5 · x) + (- 4 · x - 1) → Case 5
Fifth equation
- 2 · x + 9 + 5 · x + 6
3 · x + 15
3 · (x + 5) → Case 3
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Answer:
B: 4 liters of soda
Step-by-step explanation:
16 / 4 = 4
Therefore,
The snack committee mixed 4 liters of soda per liter of fruit punch.
Answer:
0.38268343
Step-by-step explanation:
cos(
67.5
)
Rewrite
67.5
as an angle where the values of the six trigonometric functions are known divided by 2
.
cos
(
135\
2)
Apply the cosine half-angle identity.
±
√
1
+
cos
(
135
)
2
Change the
±
to
+
because cosine is positive in the first quadrant.
√
1
+
cos
(
135
)
2
Simplify
√
1
+
cos
(
135
)
2
√
2
−
√
2
2
The result can be shown in multiple forms.
Exact Form:
√
2
−
√
2
2
Decimal Form:
0.38268343
…
Yes, this looks to be done correctly.
Just divide 2,099,451 by 3501. Houston`s area is 599 square miles
