Answer:
92 attendees had activity cards
Step-by-step explanation:
Let x be the number of students with activity cards. Then 130-x is the number without, and the total revenue is ...
7x +10(130 -x) = 1024
7x +1300 -10x = 1024 . . . . eliminate parentheses
-3x = -276 . . . . . . . . . . . . . collect terms; subtract 1300
x = 92 . . . . . . divide by 3
92 students with activity cards attended the dance.
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<em>Comment on the solution</em>
Often, you will see such a problem solved using two equations. For example, they might be ...
Let 'a' represent the number with an activity card; 'w' the number without. Then ...
- a+w = 130 . . . . the total number of students
- 7a +10w = 1024 . . . . the revenue from ticket sales
The problem statement asks for the value of 'a', so you want to eliminate w from these equations. You can do that using substitution. Using the first equation to write an expression for w, you have ...
w = 130-a
and making the substitution into the second equation gives ...
7a +10(130 -a) = 1024
This should look a lot like the equation we used above. There, we skipped the extra variable and went straight to the single equation we needed to solve.
Answer:
D
Step-by-step explanation:
You have to have exactly the same thing underneath the radical. So for example in choice A you have sqrt(2) and sqrt(3) underneath the radical. They are not the same. Choice A is not the answer.
Choice B has the same problem sqrt(5) is not the same thing as sqrt(3) and choice B is not the answer.
Choice C has sqrt(5) and sqrt(6) as your choice. They are not the same. C is not correct.
D is the answer. Both choices have sqrt(7) as the radicals. They are both 7. They are the same.
Answer: 
Step-by-step explanation:
Since we have given that
And we know that θ is in the Fourth Quadrant.
So, Except cosθ and sec θ, all trigonometric ratios will be negative.
As we know the "Trigonometric Identity":
It must be negative due to its presence in Fourth quadrant.
Hence,
Answer:
C
Step-by-step explanation:
AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.
The standard form is Ax + By = C
Given the linear equation, y = x + 10, we must transpose x to the left-hand side of the equation:
- x + y = x — x + 10
- x + y = 10
Next, we must multiply both sides by (-1) because A must be positive:
(-1) (- x + y) = 10 (-1)
This leads to:
x — y = -10 in standard form, Ax + By = C
