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marin [14]
3 years ago
14

Write an equation of the line that passes through (2,−5) and is parallel to the line 2y=3x+10

Mathematics
1 answer:
LenaWriter [7]3 years ago
8 0

Step-by-step explanation:

Divide two on both sides to get rid of it and the make the equation in the form y = mx + c

\frac{2}{2} y = \frac{3}{2} x +  \frac{10}{2}

y = 3/2x + 5

since both lines are parallel they must have the same gradient which is 3/2

y = 3/2x + c

All you have to do now is to replace x and y with (2, -5) to find c

x = 2

y = -5

-5 = 3/2 × 2 + c

-5 = 3 + c

c = -5-3

c = -8

y  = \frac{3}{2} x  - 8

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Find the value of x.
valentina_108 [34]

Answer:

  x = 100

Step-by-step explanation:

The ratios of long side to hypotenuse are the same for all these triangles.

  x/(x+10) = (x+10)/(x+21)

  x^2 +21x = x^2 +20x +100 . . . . . multiply by (x+10)(x+21), expand

  x = 100 . . . . . . . . . . . . . . . . subtract x^2 +20x

5 0
3 years ago
HURRY!!! Given the function find f(-1), f(0), f(2)
Zolol [24]

Answer:

f(-1) = -10

f(0) = -6

f(2) = 8

Step-by-step explanation:

As the function says, when x is below 0, the part that we have to use is 7x-3, and when is equal or greater we use 7x-6.

We do so and just replace de values of x in each equation.

f(-1)=7(-1)-3=-10\\f(0)=7(0)-6=-6\\f(2)=7(2)-6=8\\

7 0
3 years ago
Let X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes. If the random vari
Gelneren [198K]

Answer:

Probability that the wait time is greater than 37 minutes is 0.3474.

Step-by-step explanation:

We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.

<u><em>Let X = waiting time for a car to pass by on a country road</em></u>

The probability distribution function of exponential distribution is given by;

f(x) = \lambda e^{-\lambda x}  , x >0     where, \lambda = parameter of distribution.

Now, the mean of exponential distribution is = \frac{1}{\lambda}  which is given to us as 35 minutes that means  \lambda = \frac{1}{35}  .

So, X ~ Exp( \lambda = \frac{1}{35} )

Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;

F(x) = P(X \leq x) = 1 - e^{-\lambda x}  , x > 0

Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X \leq 37 min)

  P(X \leq 37 min) = 1 - e^{-\frac{1}{35} \times 37}        {Using CDF}

                         = 1 - 0.3474 = 0.6525

So, P(X > 37 min) = 1 - 0.6525 = 0.3474

Therefore, probability that the wait time is greater than 37 minutes is 0.3474.

4 0
3 years ago
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boyakko [2]

Answer:

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Step-by-step explanation:

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