Question 1. Midpoint
Answer: M(-2,4)
Explanation:
1) The coordinates of the midpoint, M (x,y) between two points (x₁,y₁) and (x₂, y₂) are:
x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2
2) Replacing the coordinates of the given points P (-4, 1) and Q (0,7) you get:
x = (- 4 + 0) / 2 = - 2, and
y = (1 + 7) / 2 = 4
So, the answer is M (-2,4)
Question 2: The distance between the two midpoints is:
Answer: 7.21
Explanation:
1) Use the formula of distance, which is an application of Pythagora's theorem:
d² = (x₂ - x₁)² + (y₂ - y₁)²
2) Substitute values:
d² = (0 - (-4))² + (7 - 1)² = 4² + 6² = 16 + 36 = 52 ⇒ d = √52 ≈ 7.21
Answer:
The vertex is (-1, 4)
Not sure what the table looks like, but just plug the x values into the equation to get a complete point
Graph the points on a graph
Step-by-step explanation:
One piece at a time:
4(p+2) means 4 times everything inside the parentheses.
That's
4(p) + 4(2) = 4p + 8 .
3(2p-3) means 3 times everything inside the parentheses.
That's
3(2p) + 3(-3) = 6p - 9 .
Now add everything up:
4p + 8 + 6p - 9 .
Add all the p's together: 4p + 6p = 10p
Add all the plain numbers together: 8 - 9 = -1
The final result is: 10p - 1 .
Answer:
99 units.
Step-by-step explanation:
The cost function for manufacturing <em>x</em> units of a certain product is:
We want to find the number of units manufactured at a cost of $8350. Therefore:
Subtract 8350 from both sides:
This equation can be a bit difficult to factor, if even possible, so we can use the quadratic formula:
In this case, a = 1, b = -15, and c = -8316. Thus:
Simplify:
Evaluate:
Therefore, our solutions are:
We cannot produce negative items, so we can ignore the second answer.
Therefore, for a cost of $8350, 99 items are being produced.
Answer:
Step-by-step explanation:
