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natulia [17]
3 years ago
10

The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10

Mathematics
1 answer:
navik [9.2K]3 years ago
7 0
\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------

\bf \textit{we also know that }
\begin{cases}
y=5.4\\
x=9
\end{cases}\implies 5.4=k9\implies \cfrac{5.4}{9}=k
\\\\\\
\cfrac{\quad \frac{54}{10}\quad }{9}=k\implies \cfrac{54}{10}\cdot \cfrac{1}{9}=k\implies \cfrac{3}{5}=k\qquad thus\qquad \boxed{y=\cfrac{3}{5}x}
\\\\\\
\textit{when x = -10, what is \underline{y}?}\qquad y=\cfrac{3}{5}(-10)
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A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at
valina [46]

Answer:

P(Same)=\frac{61}{190}

Step-by-step explanation:

Given

Red = 5

White = 6

Black = 9

Required

The probability of selecting 2 same colors when the first is not replaced

The total number of ball is:

Total = 5 + 6 + 9

Total = 20

This is calculated as:

P(Same)=P(Red\ and\ Red) + P(White\ and\ White) + P(Black\ and\ Black)

So, we have:

P(Same)=\frac{n(Red)}{Total} * \frac{n(Red) - 1}{Total - 1} + \frac{n(White)}{Total} * \frac{n(White) - 1}{Total - 1}  + \frac{n(Black)}{Total} * \frac{n(Black) - 1}{Total - 1}

<em>Note that: 1 is subtracted because it is a probability without replacement</em>

P(Same)=\frac{5}{20} * \frac{5 - 1}{20- 1} + \frac{6}{20} * \frac{6 - 1}{20- 1}  + \frac{9}{20} * \frac{9- 1}{20- 1}

P(Same)=\frac{5}{20} * \frac{4}{19} + \frac{6}{20} * \frac{5}{19}  + \frac{9}{20} * \frac{8}{19}

P(Same)=\frac{20}{380} + \frac{30}{380}  + \frac{72}{380}

P(Same)=\frac{20+30+72}{380}

P(Same)=\frac{122}{380}

P(Same)=\frac{61}{190}

4 0
2 years ago
Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How
aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood  = K hrs

So, the per hour rate of Dwight  = (\frac{1}{K})

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood  = (K- 3) hrs

So, the per hour rate of Joe  = (\frac{1}{K-3})

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them  = (\frac{1}{2})

⇒ Per hour rate of ( Dwight  + Joe)  =(\frac{1}{2} )

\implies (\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})

Now, solving for the value of K , we get:

(\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})\\\implies  \frac{(K-3) + K}{K (K-3)}  = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K  + 6=  0\\\implies K^2 - 6K - K  + 6=  0\\\implies K(K-6) -1(K - 6)=  0\\\implies (K-6)(K-1) = 0

Implies either K = 6 Or K = 1

But if K = 1, (K-3)  = 1- 3  = -2 hours would be A CONTRADICTION.

⇒ K  = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0
2 years ago
The points J, K, L and M all lie on the same line segment, in that order, such that the ratio of JK:KL:LMJK:KL:LM is equal to 1:
RideAnS [48]

Answer: JL = 25

Step-by-step explanation: Segment JM is the total measure of the line segment and it equals 45.

Suppose first segment JK measures d.

The total ratio is the sum of each part

d + 4d + 4d = 9d

The sum of each part corresponds to the total measure of the line segment. Then:

9d = 45

d = 5

Segment JL is

JL = d + 4d

JL = 5d

JL = 5.5

JL = 25

Segment JL measures 25 units.

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3 years ago
Every delivery order from a pizzeria has a delivery charge of $1.50. How many dollars b is the total bill for a delivery of one
Charra [1.4K]

Answer:

p+1.50=b

Step-by-step explanation:

Hope it helps (;

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3 years ago
G(a) = 3a + 2<br> f(a)=2a-4<br> Find (g/f)(3)
Basile [38]

Answer:(gf)(3)=g(3)f(3) g(a)=3a+2 or g(3)=3(3)+2=9+2 =11 f(a)=2a−4 f(3)=2(3)−4=6−4=2 g(3)f(3)=112. Answer  

Step-by-step explanation:

7 0
2 years ago
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