Which relation is a function?A. {(2, 3), (1, 5), (2, 7)}
B. {(-1, 5), (-2, 6), (-3, 7)}
C. {(11, 9), (11, 5), (9, 3)}
D.{(3, 8), (0, 8), (3, -2)}
Answers
Answer: Option B
Step-by-step explanation:
A function has a rule, for each point in the domain, there can be only one point associated in the range.
This means that f(x) can have only one value y that is associated to the point x in the domain.
now, with this in mind, let's analyze the options, where the pairs are always written as (x, y)
A) Here we can see the pairs (2,3) and (2, 7), so we have the point in the domain, 2, that is associated with two different values in the range, so this relation can not be a function.
B) In this set, there are no problems because we do not have ani point in the domain with more than one value in the range, so this can be a function.
C) here point 11 has two different values in the range, so this can not be a function.
D) here point 3 has two different values in the range, so this can not be a function.
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y shirts at £12 each. Total = 12*y = £12y
Total cost = £15x + £12y
Total cost = £(15x + 12y)
Final answer:
The total cost, in pounds, for X jumpers at £15 each and Y shirts at £12 each can be written as the mathematical expression: 15X + 12Y, where X and Y are the quantities of jumpers and shirts respectively.
Explanation:
To write an expression for the total cost of X jumpers at £15 each and Y shirts at £12 each in pounds, you need to multiply the cost per item by the quantity of each items and then add these two products together.
So, the total cost can be given as:
15X + 12Y
where
- X represents the number of jumpers
- Y represents the number of shirts
In this expression, '15X' stands for the total cost of the jumpers and '12Y' stands for the total cost of the shirts.
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Answer:
The horizontal distance from the starting point when rocket lands is:
168.83 meters.
Step-by-step explanation:
We are given a function that models the height of the rocket when it is 'x' meters away from the starting point.
The function is:
Now we are asked to find the horizontal distance from the starting point when the rocket will land.
i.e. we are asked to find 'x' ; when y=0
i.e.
Let y=0
on solving the quadratic equation we obtain:
As the distance can't be negative.
Hence, the viable solution is:
x=168.83
y=-0.06x²+10.1x+5
==>6x²-1010x-500=0
Δ=1010²+4*6*500=1032100=(1015,92...)²
x=(1010-1015.92...)/12 <0 exclude
or x=(1010+1015.92..)/12=168.826935... (m)
Answers
Answer:
The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
If the height is increased by 0.2
then
The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)
Final answer:
The overall change in surface area when the height of a rectangular prism is increased by 0.2 cm can be calculated with the formula 0.4w + 0.4l.
Explanation:
In this question, we are looking at the surface area of a box that is a rectangular prism and how it will change if the height of the box is increased by 0.2 cm. The surface area of a prism is given by the formula 2lw + 2lh + 2wh, where l, w and h are the length, width and height respectively.
Now, if the height is increased by 0.2 cm, the difference in the surface area will be 2lw (because there are two ends with area lw that do not change) plus the change in the area of the sides. The sides' areas will increase by 2w x 0.2 and 2l x 0.2 respectively (since we have two opposing sides that both increase by 0.2 cm in height).
Therefore, the overall change in surface area when the height is increased by 0.2 cm is simply the sum of these two parts, which is 2w x 0.2 + 2l x 0.2. This can also be simplified to 0.4w + 0.4l.
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The rate of change is (amount of the change) / (time it took to change) .
Amount of the change = (3 - 1) = 2 .
Rate of change = (2) / (time it took to change from 1 to 3) .