Answer:
Replace “the height of a tree” with a variable, x
Replace “increased by” with an addition symbol
Replace “seven inches” with the number 7.
Write the expression X + 7
Step-by-step explanation:
we have the phrase
“The height of a tree is increased by seven inches”
so
Let
x------> the height of a tree
1) Replace “the height of a tree” with a variable, x
2) Replace “increased by” with an addition symbol (+)
3) Replace “seven inches” with 7.
4) Write the expression X + 7
therefore
The algebraic expression is

Answer:
The minimum average cost is $643.75
It should be built 62.5 machines to achieve the minimum average cost
Step-by-step explanation:
The equation that represents the cost C to produce x DVD/BLU-ray players is C = 0.04x² - 5x + 800
To find the minimum cost differentiate C to equate it by 0 to find the average cost per machine and to find the value of the minimum cost
∵ C = 0.04x² - 5x + 800
- Differentiate C with respect to x
∴ 
∴ 
- Equate
by 0
∴ 0.08x - 5 = 0
- Add 5 to both sides
∴ 0.08x = 5
- Divide both sides by 0.08
∴ x = 62.5
That means the minimum average cost is at x = 62.5
Substitute the value of x in C to find the minimum average cost
∵ C = 0.04(62.5)² - 5(62.5) + 800
∴ C = 643.75
∵ C is the average cost
∴ The minimum average cost is $643.75
∵ x is the number of the machines
∴ It should be built 62.5 machines to achieve the minimum
average cost
If you were on a number line you go over 10 numbers to the left. Therefore, you will pass all of these numbers...
-7,-6,-5,-4,-3,-2,-1,0,1,2. Your answer will be 2.