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3 years ago

The table below shows the outputs y for different inputs x:

Mathematics

2 answers:

vovangra [49]3 years ago

4 0

<h2>Answer with explanation:</h2>

Part A:

A relation is said to be a function where each input has only a single output.

We usually take the input variable as 'x' and the output variable as 'y'.

In the given table, we can see that 1 is the input value corresponding to 4 and 2 both.

i.e. one input value corresponds to two different output values that contradicts the definition of the function.

Thus the given table doesn't represent any function.

Part B: Given : The total cost f(x), in dollars, for renting a paddle-boat for x hours is shown below:

$f(x) = 20 + 10x$

At x= 120 , $f(120) = 20 + 10(120)=20+1200=1220$

It represents that the total cost for renting a paddle-boat for 120 hours is $1220.

igor_vitrenko [27]3 years ago

3 0

Part A)
The table doesn't represent y as a function of x.
Why? <span>One reason is that 1 or 3 is the first element in more than one ordered pair.
Part B)
f(x) = 10x + 20
f(120)= 10*120 + 20 = 1200 + 20 = 1220
</span><span>f(120) represents cost of boating for 120 hours.</span><span>
</span>

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Serhud [2]

Answer: The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )

is (x , y) → (x - 5 , y + 8)

Step-by-step explanation:

Let us revise the translation

If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)

If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)

If the point (x , y) translated vertically up by k units then its image is (x , y + k)

If the point (x , y) translated vertically down by k units then its image is (x , y - k)

(x , y) → (x ± h , y ± k) the right arrow symbol used to show the

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Example:

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Let us find the translation rule that maps point D ( 7 , − 3 ) onto

point D' (2 , 5)

∵ Point (x , y) = (7 , -3)

∵ Its image after translation (x + h , y + k) = (2 , 5)

∴ x + h = 2

∵ x = 7

∴ 7 + h = 2

- Subtract 7 from both sides

∴ h = -5

∵ y + k = 5

∵ y = -3

∴ -3 + k = 5

- Add 3 to both sides

∴ k = 8

∴ The rule of translation is (x , y) → (x - 5 , y + 8)

The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )

is (x , y) → (x - 5 , y + 8)

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<u>Step-by-step explanation:</u>

Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.

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Now we have:

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