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
What is the answer 1 plus 1
AnnZ [28]

Answer:

the answer is 4, just kidding it's 2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Pls help me on number 5
Alekssandra [29.7K]
Answer is A trust me
7 0
2 years ago
Read 2 more answers
Val walks 2 3/5 miles each day . Bill returns 10 miles once every 4 days . In 4 days, who covers the greatest distance
julia-pushkina [17]
Val by 4/10 walk longer
7 0
3 years ago
(x^4)^2 perform the indicated operation
erica [24]

Answer:

x^8

Step-by-step explanation:

Since you are doing x^4 squared, you have to multiply the exponents.

4 * 2 = 8

x^8

8 0
3 years ago
Read 2 more answers
Please help im very confused!!!
OleMash [197]

Answer:

1/2 ×4 ×3=6

base is 4

and 3 is height

the answer is 6 as you multiply 1/2 ×base ×height

4 0
3 years ago
Read 2 more answers
Other questions:
  • write an equation of the line that passes through the given point(-2,5) and is parallel to the given line 2y=4x-6
    10·1 answer
  • What is cd? please answer
    6·1 answer
  • Quadrilateral ABCD is a square and the length of BE¯¯¯¯¯ is 6 cm.
    13·2 answers
  • Give formula to calculate Selling price when profit is given in percentage. ​
    11·1 answer
  • The diagonals of rhombus ABCD intersect E.find m
    10·2 answers
  • Solve 1/3 x = -4/5????
    15·2 answers
  • How many ounces in a gallon?
    5·2 answers
  • U should rly help plz
    14·1 answer
  • What is 3 feet + 14 inches
    6·1 answer
  • I'm not sure what this is can anyone lend a hand?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!