Answer:
$ 15.79
Step-by-step explanation:
Let x be the price of full ticket,
∵ Total number of tickets = 4000,
Quarter of 4000 tickets = = 1000,
Remaining tickets = 4000 - 1000 = 3000,
Since, if the price of each ticket is reduced by 20%,
Then the new price of each ticket = (100 - 20)% of x
= 80% of x
= 0.80x,
According to the question,
The total price of quarters of ticket + total price of remaining tickets = $ 60000
= 0.80x × 1000 + x × 3000 = 60,000
800x + 3000x = 60,000
3800x = 60,000
⇒ x ≈ 15.79
Hence, the price of full ticket is approximately $ 15.79.
Find the area and perimeter of the following triangle with the given vertices:
(1, 2), (8, 2) and (3, 6)
Explain your reasoning; show all your work for full credit!
Answer:
9. Always true
10. Always true
11. Never true
12. Always true
13. Always true
14. Never true
Step-by-step explanation:
An inverse is defined as the reflection across the line y=x. Algebraically this means that x and y switch place in the inverse equation and in the coordinate points of a function.
A line will always give a line.
Example: y = 2x -2
Inverse: x = 2y -2 which when rearranged is y = 1/2 x +1.
This also means that the slope if greater than 1 for the function will have a slope less than 1 for its inverse.
Answer:
"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the -coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a <em>polynomial</em> of degree 2, which is a fancy way of saying that something is a quadratic), the -coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve , which gives (the 'V' stands for 'or'). We can take the average of the two roots to get the -coordinate of the minimum point of the graph (which, in this case, is ).
Having the -coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the -coordinate of the extremum.