The area of the rectangle MNPQ is 588 cm^2.
1 answer:
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Answer:
f(x) = -5x + 250
Step-by-step explanation:
* Lets explain how to solve the problem
- In week 10 the manufacturer fixed 200 cars
- In week 15, the manufacturer fixed 175 cars
- the reduction in the number of cars each week is linear
- The form of the linear equation is y = mx + c, where m is the slope of
the line which represent the equation and c is the y-intercept
- The slope of the line m =
where (x1 , y1) and (x2 , y2) are two points on the line
* Lets solve the problem
- Assume that the weeks' number is x and the cars' number is y
∴ (10 , 200) and (15 , 175) are two points on the line which represent
the linear equation between the cars' numbers and the weeks
numbers
∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)
∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175
- Use the rule of the slope above to find m
∴
- Substitute the value of x in the form of the linear equation above
∴ y = -5x + c
- To find c substitute x and y by one the coordinates of one of the
two points
∵ x = 10 when y = 200
∴ 200 = -5(10) + c
∴ 200 = -50 + c
- Add 50 to both sides
∴ 250 = c
- Substitute the value of c by 250
∴ y = -5x + 250, where the number of cars seen each week is y and
x is the number of the week
∵ f(x) = y
∴ f(x) = -5x + 250
Answer:
The cost is $9.70 per kilogram.
Step-by-step explanation:
This can be solved by a rule of three.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.
Solution:
The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:
1 pound - xkg
2.2 pound - 1 kg
kg
Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?
$4.40 - 0.45kg
$x - 1kg
The cost is $9.70 per kilogram.