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stiv31 [10]
3 years ago
14

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

Mathematics
1 answer:
Sedbober [7]3 years ago
6 0

Answer:   \bold{y=-\dfrac{1}{3}x-1}

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\

Next, find the midpoint of (4, 1) and (2, -5):

Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\


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The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of peopl
Sholpan [36]

Answer:

1.) .399

2.) {.369, .429}

Step-by-step explanation:

The proportion of criminals in this sample that were caught was \frac{286}{716}=.39944, .399 rounded to three decimal places.

To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.

The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.

The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.

Finally, we need the standard error. The formula for standard error for a proportion with a single population is \sqrt{\frac{(proportion)(1-proportion)}{sample size} }so in this situation it would be \sqrt{\frac{(.399)(.601)}{716} }=.0183.

The confidence interval would be .399±.018×1.645 or .399±.030 {.369, .429}

5 0
3 years ago
Suppose that the inside bottom of a box is painted with three colors: 1/3 of the bottom area is red, 1/6 is blue, and 1/2 is whi
7nadin3 [17]

Answer:

1/18 (5.5%)

Step-by-step explanation:

You have a 1/3 chance to get red the first time and a 1/6 to get blue the second. So to find the compound probability of this you multiply 1/3*1/6.

6 0
3 years ago
PLEASE, I NEED THIS NOW!!!!
11111nata11111 [884]

Answer:

For the first one

x= About 32.02

y= About 27.58

z= About 55.16

For the second one

x= 6

y= 12

z= about 16.97

Step-by-step explanation:

Their all really simple

These are special right triangles, a 45, 45, 90 and a 30, 60, 90 triangle. The formla for these triangles are shown in the picture below.

Now for the first one ]

Lets find Z first

Now this is a 45 special right triangle so we know the other side s 39 but the hypotenuse is n\sqrt{2} (I’m using N becuase x and y is taken) So n is basically 39 (look at the image below) and just solve that. Now for x and y. We know its a 30, special right triangle. We know that 39 here is already the answer for  N\sqrt{3} so make an equation to find the n and you’ll get 27.58 for y. Now For x, its just doubled the y.

For the second one this is easier

We know that the x is (6) becuase its already in the radical number, now to find the hypotnuse, we double that and get 12. Now we know what y is becuase since the 2nd triangle is a 45/45/90, we know that 12 is y, the hypotnuse is just N\sqrt{2} and we just plug in the n with 12 and solve it!

6 0
3 years ago
2x-y=-1 in slope intercept form
AnnyKZ [126]

Answer:

y=-2x+1

Step-by-step explanation:

y=Mx+b is the slope formula. You want to move y over to the other side to get the equation equal to y

4 0
3 years ago
You move down 6 units. You end at (10, 4). Where did you start?
Alexandra [31]

Answer:

(10,10)

Step-by-step explanation:

coordinates are (x,y)

x is horizontal(left and right), y is vertical (up and down)

going down 6 means subtracting 6 from the second number

lets reverse that to go up and add 6 back

4+6=10

so the original point was (10,10)

8 0
2 years ago
Read 2 more answers
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