1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
OverLord2011 [107]
3 years ago
9

Find k so that the distance from (–1, 1) to (2, k) is 5 units. k= k= *there are two solutions for 2*

Mathematics
2 answers:
dalvyx [7]3 years ago
7 0

Answer:

k = -3

k =5

Step-by-step explanation:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\

5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\

\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3

Ierofanga [76]3 years ago
5 0

A = (-1, 1) and B = (2, k) so:

d(A,B)=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(2-(-1))^2+(k-1)^2}=\\\\=\sqrt{3^2+(k-1)^2}=\sqrt{9+k^2-2k+1}=\sqrt{k^2-2k+10}\\\\\\d(A,B)=5\\\\\sqrt{k^2-2k+10}=5\quad|(\ldots)^2\\\\\big|k^2-2k+10\big|=25\\\\k^2-2k+10=25\qquad\vee\qquad k^2-2k+10=-25\\\\k^2-2k-15=0\qquad\vee\qquad k^2-2k+35=0\\\\\\\Delta_1=(-2)^2-4\cdot1\cdot(-15)=64>0\qquad\text{two solutions}\\\\\Delta_2=(-2)^2-4\cdot1\cdot35=-136

k_2=\dfrac{2+\sqrt{64}}{2}=\dfrac{2+8}{2}=\dfrac{10}{2}=\boxed{5}

You might be interested in
Help por fav vorrrrrr
Viefleur [7K]

Answer:

The slope PV is:

  • m = -4

Step-by-step explanation:

Given

  • P(2, 4)
  • V(3, 0)

Determining the slope of PV

(x₁, y₁) = (2, 4)

(x₂, y₂) = (3, 0)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [0 - 4] / [3 - 2]

               = -4 / 1

               = -4

Thus, the slope PV is:

  • m = -4
8 0
2 years ago
What is the point-slope form of a line with slope -3 that contains the point<br> (10, -1)?
Advocard [28]

Answer:

y - (-1) = -3(x-10)

y+1= -3x+30

y= -3x+30-1

y= -3x+29

8 0
2 years ago
Given an equation y= -8x -4. Identify the slope and y-intercept
Naddika [18.5K]

Answer:

Slope = - 8

y-intercept = - 4

Step-by-step explanation:

y= -8x -4 \\  \\ equating \: it \: with \\  \\ y = mx + b \\  \\ slope \: (m) =  - 8 \\  \\ y - intercept \: (b) =  - 4

8 0
2 years ago
Question number eight answer
sergiy2304 [10]

Answer:

22 shots.

Step-by-step explanation:

90 shots times 24.6% = 22.14

<u>He missed </u><u>22 </u><u>shots.</u>

3 0
3 years ago
Read 2 more answers
What is the volume of this composite solid <br><br>​
Rufina [12.5K]
There is no picture attached.
explanation:
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following coordinates of point C would make triangle ABC similar to triangle LMP ? Look at pic attached :) thank yo
    10·1 answer
  • HELP PLEASE!!!
    14·1 answer
  • Write the equivalent decimal and fraction for each percent.
    12·1 answer
  • Sean's school raised $32,578. Leslie's school raised $18,749. How much more money did Sean's school raise?
    13·2 answers
  • Factorized the expression 8+16
    11·2 answers
  • Julio has 5 more dollars than Dan. Altogether, Julio and Dan have $19. Write and solve an equation to represent the situation. H
    14·1 answer
  • -8y + 6 + 4y &gt;14
    8·2 answers
  • Spencer's bedroom has an area of 48 square feet. The bedroom is 8 times as many square feet as Spencer's closet. Of the closet i
    13·1 answer
  • Last year, there sugar factories in a town
    12·1 answer
  • A data set is made up of these values. 4, 6, 7, 8, 9, 12, 15 Find the interquartile range. O A. 6 - 4 = 2 O B. 12- 6 = 6 O C. 15
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!