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3 years ago

If y varies directly as x, and y is 12 when x is 1.2, what is the constant of variation for this relation?

Mathematics

2 answers:

Georgia [21]3 years ago

8 0

Hello,

y=k*x ; if x=1.2,y=12
==>12=k*1.2==>k=12/1.2==>k=10

Answer B

erik [133]3 years ago

7 0

Answer:

constant of variation is 10.

Second option is correct.

Step-by-step explanation:

We have been given that y varies directly as x. Thus, we have

y = kx.............(1)

k is the constant of variation

Now, it has been given that when y is 12 then x is 1.2.

Hence, substituting x = 1.2 and y = 12 in equation (1)

12 = 1.2 k

Divide both sides by 1.2

k = 12/1.2

k = 10

Therefore, constant of variation is 10.

Second option is correct.

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The length of a swimming pool is 3 feet longer than it’s width. The swimming pool is surrounded by a deck that is 2 feet wide an

Firlakuza [10]

Answer:

The Length of swimming pool is 8.35 feet

The width of swimming pool is 5.35 feet

Step-by-step explanation:

Given as :

The length of swimming pool is 3 feet longer that its width

Let The width of swimming pool = w feet

So, The Length of swimming pool = L = (w + 3) feet

Now, The swimming pool is surrounded by deck of 2 feet wide

The width of deck = w' = w + 2 + 2 = (w + 4) feet

The area of deck = 116 feet²

The length of deck = L' = L + 2 + 2 = (L + 4) feet

So, L' = (w + 3 + 4) feet

I.e L' = (w + 7) feet

∵ The area of deck = 116 feet²

So , L' × w' = 116 feet²

(w + 7)× (w + 4) = 116

Or, w² + 4 w + 7 w + 28 = 116

Or, w² + 11 w - 88 = 0

Solving the quadratic equation as

ax² + bx + c = 0

So, w = $\dfrac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, w = $\dfrac{-11\pm \sqrt{11^{2}-4\times 1\times (-88)}}{2\times 1}$

Or, w = $\dfrac{-11\pm \sqrt{473}}{2}$

or, w = $\dfrac{-11\pm 21.7}{2}$

or, w = 5.35 , -16.35

The width of swimming pool = w = 5.35 feet

The Length of swimming pool = L = (5.35 + 3) feet = 8.35 feet

Hence, The Length of swimming pool is 8.35 feet

And The width of swimming pool is 5.35 feet

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A roster for a baseball team has 12 players. the coach is randomly making the batting order for 9 players. what is the probabili

andrey2020 [161]

The probability of you being the leadoff hitter is 8.3%.

Explanation:

The number of possible rosters can be calculated with permutations, knowing that the coach can choose the first hitter among all 12 players, then the second hitter among the 11 players remaining and so on until the 9th hitter among the remaining 4 players.

Therefore:
Possible rosters = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 79833600

The leadoff hitter is the first player in the batting order, therefore the number of possible rosters in which you are chosen as the first one is:
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