MATHEMATICS MIDDLE SCHOOL

Find the radius of the circle whose equation is x² - 10x + y² - 10y = -1.1
7
49

Answers

Answer 1

Answer:

Answer:

radius = 7 units

Step-by-step explanation:

We are given the equation;

x² - 10x + y² - 10y = -1

We are required to determine the radius of the circle;

We are going to use completing square method to solve for the radius and the center of the circle.

First we make sure the coefficient of x² and y² is 1

x² - 10x + y² - 10y = -1

Then we add the square of half the coefficient of x and y on both sides of the equation;

That is;

$x^2- 10x+((-10)/(2))^2 + y^2+- 10y +( (-10)/(2))^2= -1 +((-10)/(2))^2+ ((-10)/(2))^2$

Simplifying the equation, we get;

$(x-(10)/(2))^2 + (y-(10)/(2))^2= -1+25+25$

Thus;

$(x-(10)/(2))^2 + (y-(10)/(2))^2= 49$

That is;

$(x-5)^2 + (x-5)^2 = 49$

The equation of a circle is written in the form of;

$(x-a)^2+(x-b)^2=r^2$

Then (a, b) is the center and r is the radius.

Therefore;

In our case; $(x-5)^2+(y-5)^2=49$

Then, center = ( 5, 5)

radius = √49

= 7 units

Related Questions

Please answer ASAP! An explanation is a MUST requirement in order to receive points and the Brainliest answer. Thank you.
Stuart is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%, what is the sale price of the jeans including tax?a. $21.60 b. $34.56 c. $42.34 d. $44.16
What is the radical form of the square root of 1450?
{8x [1+(20-6)]}÷ 1/2=
Find the percent equvalent to 18 over 30

The roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.

Answers

The possible values of k are -11 and 11

Solution:

Given that equation is:

$x^2 - kx + 28 = 0$

Roots are:

$\alpha\n\n\alpha + 3$

To find: value of x

The general quadratic equation is:

$ax^2 + bx + c = 0$

$\text{ Product of roots } = (c)/(a)\n\n\text{ Sum of roots } = (-b)/(a)$

From given,

$x^2 - kx + 28 = 0$

a = 1

b = -k

c = 28

Therefore,

$Product\ of\ roots = (28)/(1) = 28$

$Sum\ of\ roots = (-k)/(1) = -k$

Given roots are:

$\alpha\n\n\alpha + 3$

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, sum of roots are:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11

What number is 32% of 1,000

Answers

It is 320 because if you divide 1000 by 10, you would get 100 (which would be equal to 10% of 1000) So if you multiply 100x3=300. then, 2% of 100 is 20, so you add that to 300 then you 320

One half gallon is equilvalent to 4 pints. How many gallons are the equilvalent of 72 pints

Answers

There are 9 gallons in 72 pints. If a half gallon equals 4 pints then a whole gallon would equal 8 pints. 72 divided by 8 would equal 9 Gallons

Find an equation of the line that (a) has y-intercept of -8 and (b) is parallel to the line 6 x − 1 y = 7 6x-1y=7 . Write your answer in the form y = m x + b y=mx+b .

Answers

Answer:

The equation of the line in the slope-intercept form is:

$\:y=6x-8$

Step-by-step explanation:

The slope-intercept form of the equation of a line is

$y\:=\:mx\:+\:b$

As y intercept is -8, we have

$y\:=\:mx\:-8$

Since the line is parallel to $6x-y=7$ , then it has the same slope.

Let's put this equation in $y\:=\:mx\:+\:b$ form and find the slope

$6x-y=7$

$y=6x-7$

Thus, the slope is :

$m = 6$

Now we can finish the equation of the line in the slope-intercept form

$y\:=\:mx\:+\:b$

$\:y=6x-8$ ∵ $m = 6$ , b = -8

Therefore, the equation of the line in the slope-intercept form is:

$\:y=6x-8$

maria is buying a digital camera on layaway for $193. if she makes a down payment of $25 and pays $24 each week, how many weeks will it take maria to pay for the digital camera.

Answers

Price of the digital camera that Maria is buying from layaway = $193
Amount of money that Maria pays as down payment = $25
Amount of money that Maria pays each week = $24
Let us assume the number of weeks required by Maria to pay for the digital camera = x
then
25 + 24x = 193
24x = 193 - 25
24x = 168
x = 168/24
= 7
So Maria will require 7 weeks to pay for the digital camera.

anwer will be 7 weeks ok and thank u

Smith drives his car and covers 450 miles in 10 hours.At the same speed, how many hours will it take to cover 540 miles?Plz help

Answers

$450\ miles\ in\ 10\ hours\n\n540\ miles\ in\ x\ hour\n\nmaking\ proportion:\n450-10\n540-x\n\ncross\ multiplication\n\n450=540*10\n\n450x=5400\ \ \ \ \ | divide\ by\ 450\n\nx=12\n\nIt\ will\ take\ 12\ hours.$