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
allsm [11]
2 years ago
5

Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​​

Mathematics
2 answers:
Len [333]2 years ago
5 0

Given equation of the Circle is ,

\sf\implies x^2 + y^2 = 25

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

Anna11 [10]2 years ago
4 0

inside the circle

Step-by-step explanation:

we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,

  1. if \displaystyle (x-h)^2+(y-k)^2>r^2 then the given point lies outside the circle
  2. if \displaystyle (x-h)^2+(y-k)^2 then the given point lies inside the circle
  3. if \displaystyle (x-h)^2+(y-k)^2=r^2 then the given point lies on the circle

step-1: define h,k and r

the equation of circle given by

\displaystyle  {(x - h)}^{2}  + (y - k) ^2=  {r}^{2}

therefore from the question we obtain:

  • \displaystyle  h= 0
  • \displaystyle  k= 0
  • {r}^{2}  = 25

step-2: verify

In this case we can consider the second formula

the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula

\displaystyle  {( - 4  - 0)}^{2}  + (2 - 0 {)}^{2} \stackrel {?}{ < }  25

simplify parentheses:

\displaystyle  {( - 4 )}^{2}  + (2  {)}^{2} \stackrel {?}{ < }  25

simplify square:

\displaystyle  16 + 4\stackrel {?}{ < }  25

simplify addition:

\displaystyle  20\stackrel { \checkmark}{ < }  25

hence,

the point (-4, 2) lies inside the circle

You might be interested in
11. What is the approximate distance
nekit [7.7K]
A is the approximate distance
6 0
2 years ago
PLS HELP ME UNDERSTAND THIS
katovenus [111]

Answer:

-1

Step-by-step explanation:

can be soled by substitution remember BEDMAS

can also be written like this

((-2)-2*(-0.5))^3

6 0
2 years ago
Read 2 more answers
LMNO~QRST find the value of x.
adelina 88 [10]
Since both trapezoids are similar, so LMNO is a scaled version of QRST by some magnitude
so we can easily use the concept of ratios to find x
in other words: x÷2=6÷5
so x=6×2÷5=12/5=2.4
x=2.4
4 0
3 years ago
The layer of gold coating on a ring should be 0.03 millimeters thick when the ring is completed. A coating of 0.021 millimeters
Arisa [49]
The amount of gold coating in millimeters needed for the ring is the difference between the total coating and the coating that has already been applied. From the given above, that would be,
                                    0.03 mm - 0.021 mm = 0.009 mm
Thus, the answer to this question is letter B. 
6 0
3 years ago
Read 2 more answers
Lexi2984 can u help me with this question
arsen [322]

9514 1404 393

Answer:

  see the attachment

Step-by-step explanation:

The x- and y-intercepts are easily found:

<u><em>X-intercept</em></u>

Set y = 0 and divide by the coefficient of x.

  -x +0 = 8

  x = -8

__

<u><em>Y-intercept</em></u>

Set x = 0 and divide by the coefficient of y.

  0 -2y = 8

  y = -4

__

Now, we have two points on the graph: (-8, 0) and (0, -4). A third point can be one that is halfway between these: (-4, -2). The graph is attached.

7 0
2 years ago
Other questions:
  • What is the estimated age of Earth?
    9·2 answers
  • A​ cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to five dash sixths i
    6·1 answer
  • Can someone help me with this
    6·1 answer
  • Is it is it possible to have 43 pencils and divide the pencils into groups with the same number of pencils with none left over
    15·2 answers
  • Solve (1/6+2 2/3)x(1 1/4-1/2)
    13·1 answer
  • I have no idea how to do this stuff.
    9·1 answer
  • 22.A large round pizza has a radius of r = 15 inches, and a small round pizza has a
    9·1 answer
  • Working together, Karen and Darren can mow their yard in 40 minutes if they each have a mower and mow at the same time. If Karen
    14·1 answer
  • Greatest common factor of 26m^4n^2, m^2n
    11·1 answer
  • a sixth grade student can complete 20 multiplication facts in one minute if you works at the same rate how long should it take h
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!