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2 years ago

Write an equation of a line perpendicular to y=4x-3 that contains the point (0,7)

Mathematics

1 answer:

ExtremeBDS [4]2 years ago

8 0

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have

$y=4x-3\to m_1=4$

Therefore

$m_2=-\dfrac{1}{4}$

We have the equation of a line:

$y=-\dfrac{1}{4}x+b$

Put the coordinates of the point (0, 7) to the equation of a line:

$7=-\dfrac{1}{4}(0)+b\\\\\7=b\to b=7$

Answer: $\boxed{y=-\dfrac{1}{4}x+7}$

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Solve the equation 2x^{2}+9x-1=x to the nearest 10th

Scilla [17]

Answer:

2x2+9x−1=x

Step 1: Subtract x from both sides.

2x2+9x−1−x=x−x

2x2+8x−1=0

Step 2: Use quadratic formula with a=2, b=8, c=-1.

−b±√b2−4ac

−(8)±√(8)2−4(2)(−1)

2(2)

−8±√72

x=−2+

√2 or x=−2+

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Step-by-step explanation:

This is what I got but I'm not 100% positive. I checked it on a calculator and it seemed to check out.

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3 years ago

3n-5=19

alina1380 [7]

Answer:

n=8

Step-by-step explanation:

3n-5=19

3n=19+5

3n=24

n=24/3

n=8

6 0

2 years ago

Find the area <br> Plz help

Katena32 [7]

To calculate the area of a triangle, multiply the base and the height, then divide the product by 2.

7*8=56

56/2=28

Area=28 feet squared

5 0

2 years ago

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Identify the circumference of ⊙S in which A=64π ft^2. HELP ASAP!!

Vika [28.1K]

Answer:

C = 16π ft

Step-by-step explanation:

If we know the area

A = pi r^2

64 pi = pi r^2

Divide each side by pi

64 = r^2

Take the square root of each side

8 = r

The radius is 8

Now we can find the circumference

C = 2 *pi*r

C = 2*pi*8

C = 16pi

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2 years ago

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A player tosses a die 6 times.If gets a number 6 Atleast two times he wins 2 dollars ,otherwise he looses 1 dollar.. Find the ex

swat32

Answer:

$E(x)=-0.2101$

Step-by-step explanation:

The expected value for a discrete variable is calculated as:

$E(x)=x_1*p(x_1)+x_2*p(x_2)$

Where $x_1$ and $x_2$ are the values that the variable can take and $p(x_1)$ and $p(x_2)$ are their respective probabilities.

So, a player can win 2 dollars or looses 1 dollar, it means that $x_1$ is equal to 2 and $x_2$ is equal to -1.

Then, we need to calculated the probability that the player win 2 dollars and the probability that the player loses 1 dollar.

If there are n identical and independent events with a probability p of success and a probability (1-p) of fail, the probability that a events from the n are success are equal to:

$P(a)=nCa*p^a*(1-p)^{n-a}$

Where $nCa=\frac{n!}{a!(n-a)!}$

So, in this case, n is number of times that the player tosses a die and p is the probability to get a 6. n is equal to 6 and p is equal to 1/6.

Therefore, the probability $p(x_1)$ that a player get at least two times number 6, is calculated as:

$p(x_1)=P(x\geq2)=1-P(0)-P(1) \\\\P(0) =6C0*(1/6)^{0}*(5/6)^{6}=0.3349\\P(1)=6C1*(1/6)^{1}*(5/6)^{5}=0.4018\\\\p(x_1)=1-0.3349-0.4018\\p(x_1)=0.2633$

On the other hand, the probability $p(x_2)$ that a player don't get at least two times number 6, is calculated as:

$p(x_2)=1-p(x_1)=1-0.2633=0.7367$

Finally, the expected value of the amount that the player wins is:

$E(x)=x_1*p(x_1)+x_2*p(x_2)\\E(x)=2*(0.2633)+ (-1)*0.7367\\E(x)=-0.2101$

It means that he can expect to loses 0.2101 dollars.

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2 years ago

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