Answer:
39 tickets were given to the employees
Step-by-step explanation:
1. Approach
First, list the given information, then form an equation based on the given information. Finally, solve the equation with simplification and inverse operations.
2.Given
A total of 234 tickets were given away
5 times as many tickets were given away to listeners compared to employees
-Call the number of tickets given away to employees (x)
3. Form an equation
(Tickets_given_to_employees) + (Tickets_given_to_listeners) = (Total_tickets)
Substitute,
x + 5x = 234
Simplify,
6x + 234
Inverse operations,
6x = 234
/6 /6
x = 39
Hey there! :)
Answer:
a) 32 sticks.
b) 5n + 2 sticks.
Step-by-step explanation:
Solve this by finding the pattern.
Pattern # 1 = 7 sticks.
Pattern #2 = 12 sticks
Pattern #3 = 17 sticks.
We can see an increase of 5 sticks within each. We can use this to write an equation:
f(n) = 7 + 5(n-1)
***Where n is the term number
You can simplify the equation to become:
f(n) = 7 + 5n - 5
f(n) = 5n + 2.
Use this equation to solve for pattern # 6:
f(6) = 7 + 5(n-1)
f(6) = 7 + 5(5)
f(6) = 7 + 25
f(6) = 32.
Answer:

Step-by-step explanation:
To complete the square, we first have to get our equation into
form.
First we add 16x to both sides:

And now we subtract 62 from both sides.

We now have to add
to both sides of the equation. b is 16, so this value becomes
.

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because
and
.

We can now take the square root of both sides.

We can now isolate x on one side by subtracting 8 from both sides.

So our solutions are
Hope this helped!
Answer:
27 and 23
Step-by-step explanation:
We can solve this problem as a system of equations. X is the first number and Y is the second number.
The first equation is x+y = 50 and the second equation is x-y=4
Now we solve the system, using elimination method:
x+y=50
x-y=4
2x = 54
x = 54/2
x = 27
And from any of the equations we can find Y
27 + y = 50
y = 50 - 27
y = 23
Answer:
TRUE
Step-by-step explanation:
A quadratic equation can be found that will go through any three distinct points that ...
- satisfy the requirements for a function
- are not on the same line
_____
The key word here is "may." You will not be able to find a quadratic intersecting the three points if they do not meet both requirements above.