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:
The reflected point would be (3,-7)
Answer:
C
Any time you have a subtraction and a negitive right next to eachother, it means to add. So, you would add 13 and 1 to get 14, then keep the denominator 19 to get 14/19.
Step-by-step explanation:
Answer:
minimum
Step-by-step explanation:
Given a quadratic function in vertex form
f(x) = a(x - h)² + k
• If a > 0 then f(x) is a minimum
• If a < 0 then f(x) is a maximum
f(x) = 0.25(2x - 15)² + 150 ← is in vertex form
with a = 0.25 > 0
Thus f(x) has a minimum turning point
Given:
To find:
The value of x and measure of ∠A.
Solution:
Let C be angle the vertically opposite to ∠A.
The reference image for answer is attached below.
By vertical angle theorem:
m∠A = m∠C
m∠C = 10x + 24°
By the corresponding angle theorem:
m∠C = m∠B
Subtract 24° on both sides.
Subtract 6x from both sides.
Divide by 4 on both sides.
The value of x is 12°.
The measure of ∠A is 144°.
