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3 years ago

An experiment involves rolling two dice and counting the number of 6s.FInd the experimental probability obtaning

Mathematics

1 answer:

VikaD [51]3 years ago

3 0

I believe your answer would be 1 ÷ 6 = 0.167, or a 16.7% percent chance :]

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find the equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(

aliina [53]

The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2

<h3>Solution:</h3>

Given, two points are A(-5, 5) and B(3, -3)

We have to find the perpendicular bisector of segment AB.

Now, we know that perpendicular bisector passes through the midpoint of segment.

The formula for midpoint is:

$\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

$Here x_1 = -5 ; y_1 = 5 ; x_2 = 3 ; y_2 = -3$

$\text { So, midpoint of } A B=\left(\frac{-5+3}{2}, \frac{5+(-3)}{2}\right)=\left(\frac{-2}{2}, \frac{2}{2}\right)=(-1,1)$

Finding slope of AB:

$\text { Slope of } A B=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { Slope } m=\frac{-3-5}{3-(-5)}=\frac{-8}{8}=-1$

We know that product of slopes of perpendicular lines = -1

So, slope of AB $\times$ slope of perpendicular bisector = -1

- 1 $\times$ slope of perpendicular bisector = -1

Slope of perpendicular bisector = 1

We know its slope is 1 and it goes through the midpoint (-1, 1)

The slope intercept form is given as:

y = mx + c

where "m" is the slope of the line and "c" is the y-intercept

Plug in "m" = 1

y = x + c ---- eqn 1

We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1

1 = -1 + c

c = 2

Now substitute c = 2 in eqn 1

y = x + 2

Thus y = x + 2 is the required equation in slope intercept form

7 0

4 years ago

In the figure, m ║ n and p is a transversal. Which of the following are alternate interior angles?

Lyrx [107]

The answer is c. Because there inside and opposite

8 0

3 years ago

Which box plot correctly displays the data set with a maximum of 24, a minimum of 3, a median of 15, an upper quartile of 19, an

sashaice [31]

Answer:

its C

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Please help me with these questions and show how u got them! i will mark you brainliest

Goshia [24]

Step-by-step explanation:

There aren't any like terms in the situations to solve then

7 0

3 years ago

I need help with number 7, and the second part of number 8. Thank you!

tangare [24]

Answer:

7. $\dfrac{\pi }{3},\ \pi ,\ \dfrac{5\pi }{3}$

8. b. $0,\ \dfrac{2\pi }{3},\ \pi,\ \dfrac{4\pi }{3}$

Step-by-step explanation:

7. Solve the equation

$\cos x+\cos 2x=0$

First, note that

$\cos 2x=2\cos^2x-1$

Hence,

$\cos x+2\cos ^2x-1=0$

Use substitution

$t=\cos x,$

then

$2t^2+t-1=0\\ \\D=1^2-4\cdot 2\cdot (-1)=1+8=9\\ \\\sqrt{D}=\sqrt{9}=3\\ \\t_{1,2}=\dfrac{-1\pm 3}{2\cdot 2}=-1,\ \dfrac{1}{2}$

Now,

$\cos x=-1\ \text{or}\ \cos x=\dfrac{1}{2}$

Solve each equation separately for $0\le x$

$\cos x=-1\\ \\x=\pi+2\pi k, \in Z\\ \\\text{only } x=\pi \in [0,2\pi)$

$\cos x=\dfrac{1}{2}\\ \\x=\pm\arccos \dfrac{1}{2}+2\pi k,\ k\in Z\\ \\x=\dfrac{\pi }{3}\ \text{and}\ x=\dfrac{5\pi }{3}$

8. b. Solve the equation

$\sin x+2\sin x\cos x=0$

Rewrite it:

$\sin x(1+2\cos x)=0$

By zero product property,

$\sin x=0\ \text{or}\ 1+2\cos x=0$

Solve each equation separately.

$\sin x=0\\ \\x=\pi k,\ k\in Z\\ \\\text{for}\ x\in [0,2\pi),\ \ \ \ x_1=0\ \ x_2=\pi$

$1+2\cos x=0\\ \\\cos x=-\dfrac{1}{2}\\ \\x=\pm \arccos \left(- \dfrac{1}{2}\right)+2\pi k,\ k\in Z\\ \\x=\dfrac{2\pi }{3}\ \text{and}\ x=\dfrac{4\pi }{3}$

5 0

4 years ago