Which best proves why the expressions 4 (x + 3) + 2 x and 6 (x + 2) must be equivalent expressions?
2 answers:
Answer:
A. When x = 3, both expressions have a value of 30.
Step-by-step explanation:
The first expression is 4(x+3)+2x
The second expression is 6(x+2).
When we substitute x=3 into the first equation, we get:
When we substitute x=3 into the second expression we get:
This proves that the two expressions are equivalent.
The correct choice is A
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Answer:
- x = 1
Step-by-step explanation:
From the given right-angle triangle
The angle = ∠60°
- The adjacent to the angle ∠60° is 1/2.
- The opposite to the angle ∠60° is y.
The hypotenuse = x
<u>Determining the value of x:</u>
Using the trigonometric ratio
cos 60° = adjacent / hypotenuse
substituting adjacent = 1/2 and hypotenuse = x
∵ cos (60°) = 1/2
Dividing both sides by 2
Simplify
Thus, the value of hypotenuse x is:
x = 1
<u>Determining the value of y:</u>
Using the trigonometric ratio
sin 60° = opposite / hypotenuse
As we have already determined the value of hypotenuse x = 1
substituting opposite = y and hypotenuse = 1
sin 60° = y/1
y = 1 × sin 60°
∵
Therefore, the value of y is:
Summary:
- x = 1