We would find the midpoint by applying the formula for determining the midpoint of a segment which is expressed as
Midpoint = (x1 + x2)/2, (y1 + y2)/2
From the given points,
x1 = 4, y1 = - 5
x2 = 6, y2 = 1
Midpoint = (4 + 6)/2, (- 5 + 1)/2
Midpoint = 10/2, - 4/2
Midpoint = 5, - 2
-9 times -7 will get you the same product as 9 times 7 which is 63...
remember when multiplying two negatives you get a positive.
Answer: There are 418 sheets needed to cut all the required apples and leaves.
Explanation:
Since we have given that
Number of apples = 1045
Number of leaves = 1463
From a sheet of paper,
Number of apples can be cut = 5
Number of leaves can be cut = 7
Let the number of sheets of paper be x
So,
Number of sheets of paper required to cut 1045 apples is given by
Similarly,
Number of sheets of paper required to cut 1463 leaves is given by
So, total number of sheets is required to cut 1045 apples and 1463 leaves is given by
Hence, there are 418 sheets needed to cut all the required apples and leaves.
Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
Answer:
(x−3)(x+8)
Step-by-step explanation:
The middle number is 5 and the last number is -24.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 5
Multiply together to get -24
Can you think of the two numbers?
Try -3 and 8:
-3+8 = 5
-3*8 = -24
Fill in the blanks in
(x+_)(x+_)
with -3 and 8 to get...
(x-3)(x+8)