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
Anni [7]
3 years ago
9

Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point

(6, -7) are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
Mathematics
1 answer:
Maksim231197 [3]3 years ago
3 0

Answer: (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

or  (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]

Taking square on both the sides , we get

(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0

Using quadratic formula : x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}

so, (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

since \sqrt{3}=1.732

so, (6+7(1.732),0)\text{ and }(6-7(1.732),0) are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

You might be interested in
How is 2y(z(z+5)+10) gotten from 2yz^2 +10yz +20y ? Please help!!!
Harrizon [31]

Answer:

Adding like terms! Hope this Helps!

6 0
2 years ago
Which explains why the graph is not a function?
torisob [31]

Answer:

56

Step-by-step explanation:

6 0
2 years ago
The head track coach for PCTVS has a big track meet coming up. He knows that his biggest rival is Clifton and the entire track m
frutty [35]

Answer:

ookkkkk

Step-by-step explanation: i have no clue about what u saying

7 0
3 years ago
6 points are placed on the line a , 4 points are placed on the line b . How many triangles is it possible to form such that thei
BaLLatris [955]

Answer:

96

Step-by-step explanation:

Using side b as the base, 4 points makes 3 bases (the space in between).  With three bases, you can have 3 bases of 1 segment, 2 bases of 2 segments, and 1 base of 3 segments.  This equals 6 bases. Each of these can connect to a point on line a. 6x6=36

Using side a as the base, 6 points makes 5 bases.  With 5 bases, you can have 5 bases of 1 segment, 4 bases of 2 segments, 3 bases of 3 segments, 2 bases of 4 segments, and 1 base of 5 segments.  This equals 15 bases.  Each of these can connect to a point on line b.  15x4=60

36+60=96

5 0
3 years ago
Read 2 more answers
Which angle is supplementary to ∠1?
Hatshy [7]
Answer: angle 2 is supplementary to angle 1
4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve for x: 2|2x − 2| + 4 = 20.
    14·2 answers
  • How do I solve 5 + 6y = 9y + 2 + 3(1 - y)
    12·1 answer
  • A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along
    5·1 answer
  • A pole vaulter uses a 15 foot long pole. she grips the pole so that the segment below her left hand is twice the length of the s
    13·1 answer
  • The sum of two numbers is 83. The sum of 2 times the first number and 3 times the second number
    13·1 answer
  • Which direction does the graph of f(x) = −18 + x2 − 3x open?
    7·1 answer
  • Solve the perimeter formula of a rectangle for w and use the resulting formula to find the width of a rectangle with a length of
    10·1 answer
  • The triangles are congruent by the SSS congruence theorem. Triangles B C D and W X Y are shown. Triangle B C D is shifted up and
    12·2 answers
  • Can someone explain step by step?
    10·2 answers
  • I need the steps and answers pleass
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!