Answer:
the company must sell 15 bracelets to break even.
Step-by-step explanation:
To find the profit made from selling x bracelets, we need to subtract the cost of producing x bracelets from the revenue earned from selling x bracelets.
The cost of producing x bracelets is given by the function C(x) = 180 + 8x.
The revenue earned from selling x bracelets is given by the function R(x) = 20x.
To find the profit, we subtract the cost from the revenue: P(x) = R(x) - C(x).
Substituting the given functions:
P(x) = 20x - (180 + 8x).
To simplify the expression, we combine like terms:
P(x) = 20x - 180 - 8x.
Simplifying further, we combine the x terms and the constant terms:
P(x) = 12x - 180.
So, the function P(x) represents the profit made from selling x bracelets: P(x) = 12x - 180.
To find the number of bracelets the company must sell to break even, we set the profit (P(x)) equal to zero, since profit is zero at the break-even point:
12x - 180 = 0.
Adding 180 to both sides of the equation:
12x = 180.
Dividing both sides by 12:
x = 15.
8x = 5x + 27 Add 12 to both sides
3x = 27 Subtract 5x from both sides
x = 9 Divide both sides by 3
Answer:
x-5+10 = 2x-7
the 2 lengths are equal
x+5 = 2x-7
x-2x=-7-5
-x=-12
x= 12
Your friend is not correct.
It takes the cheetah Approximately 21.67 seconds to run at 90 ft/s to reach the moving antelope.
Given that, a cheetah can run at top speed for only about 20 seconds and the top speed of a cheetah is 90 feet per second.
The formula to find the speed of an object is Speed = Distance / Time.
From the given question in 20 seconds cheetah will cover a distance of:
20 × 90 = 1800 feet
In 20 seconds cheetah will cover a distance of 1800 feet.
It is given that the antelope runs 60 feet per sec
That means in 20 seconds antelope will cover a distance of:
20 × 60 = 1200 feet
In 20 seconds antelope will cover a distance of 1200 feet.
Now add the distance ran initially, because the antelope was ahead of the cheetah from 650 feet.
1200 feet + 650 feet = 1850 feet
But the maximum distance cheetah can cover is 1850 feet. Thus the antelope is still 50 ft ahead of the cheetah.
Therefore, the antelope is probably safe.
Hence, your friend is not correct.
The speed of a cheetah is 30 feet per second more than antelope.
Cheetahs need to cover 50 feet to catch antelope.
So, 50/30 =1.67 seconds
20 seconds + 1.67 second = 21.67 seconds
Therefore, it takes the cheetah approximately 21.67 seconds to run at 90 ft/s to reach the moving antelope.
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