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Naya [18.7K]
3 years ago
12

Where does the point (6,2) lie on a circle centered at (7,8) with a radius of 6

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer:

<em>The point lies barely outside of the circle</em>

Step-by-step explanation:

<u>Equation of a Circle</u>

Given its center (h,k) and radius r, the equation of a circle is given by

(x-h)^2+(y-k)^2=r^2

The circle given in the question is centered at (7,8) and has a radius of 6, thus its equation is

(x-7)^2+(y-8)^2=6^2

(x-7)^2+(y-8)^2=36

To find out if a point (a,b) is outside or inside the circle area, the following conditions apply.

if (a-7)^2+(b-8)^2>36 then the point lies outside of the circle area

if (a-7)^2+(b-8)^2 then the point lies inside of the circle area

Let's use the point as given (6,2)

(6-7)^2+(2-8)^2=1+36=37

Thus the point lies barely outside of the circle

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Answer:

Step-by-step explanation:

The correct answer would actually be 15 because (-5) multiplied by -3 makes it positive 15.

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3 years ago
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If the point (2, 5) is a solution to the system of equations shown below, then determine the missing values of b and m. Show how
antoniya [11.8K]

Complete Question:

If the point (2, 5) is a solution to the system of equations shown below, then determine the missing values of b and m. Show how you arrive at your answer.

1. y = 3x + b

2. y = mx + 9

Answer:

1. Intercept, b = -1

2. Slope, m = -2

Step-by-step explanation:

Given the following data;

Points on the line (x, y) = (2, 5)

To find the missing values;

Mathematically, the equation of a straight line is given by the formula;

y = mx + b

Where;

  • m is the slope.
  • x and y are the points
  • b is the intercept.

1. y = 3x + b

Substituting the value of x and y, we have;

5 = 3(2) + b

5 = 6 + b

b = 5 - 6

<em>Intercept, b = -1</em>

2. y = mx + 9

Substituting the value of x and y, we have;

5 = m(2) + 9

5 = 2m + 9

2m = 5 - 9

2m = -4

m = -4/2

<em>Slope, m = -2</em>

6 0
3 years ago
Alfie has a £10 note
Nana76 [90]

Answer:

4 pencils

Step-by-step explanation:

3*1.45 = 4.35 ---> spent for the pens

( 10 -[ 4.35 + 2.05] ) = money spent on pencils

0.9x= 3.6

x=3.6/0.9 = 4

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Step-by-step explanation:

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2 years ago
Convert 5 square root of a into exponential form?
stich3 [128]

Answer:

The answer is:  " 5a^\frac{1}{2} "  .

_____________________________________________

Step-by-step explanation:

______________________________________________

We are asked to convert "5 square root of a"  ;  into "exponential form".

Note that "5 square root of a" ;

             or;  " 5 root a " ;

means:    " 5 times the {square root of the variable, "a" };

      or :    " 5 multiplied by the {square root of the variable, "a" }.

_______________________________________________

This can be written as:   " 5\sqrt{a} " .

_______________________________________________

<u>Note the following property of exponents</u>:

\sqrt[n]{a^m} = (\sqrt[n]{a})^m = a^m^n .

_____________________________________________

So;  to write:  " √a "  ;  <u> </u><em><u>as an exponent</u></em><u> </u> :

______________________________________________

<u>Note</u>:  

" \sqrt{a}  = \sqrt[2]{a} =   \sqrt[2]{a^1} = (\sqrt[2]{a})^1 =  a^\frac{1}{2} " .

_______________________________________________

<u>So</u>:

" \sqrt{a}  =  a^\frac{1}{2} "  ;

_______________________________________________

<u>And</u>:

________________________________________________

" 5\sqrt{a}  =  5a^\frac{1}{2} " .

________________________________________________

   →   The answer is:  " 5a^\frac{1}{2} " .

________________________________________________

Hope this helps!

   Best wishes in your academic endeavors

           — and within the "Brainly" community!

________________________________________________

6 0
3 years ago
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