Solve, using linear combination. 4x + y = 5 3x + y = 3

the point 3,2 lies on a circle.what is the exact length of the radius of this circle if the center is located at (-1,-4)

Crazy boy [7]

You can use the distance formula to solve this.

Distance Formula:
$d = \sqrt{(X_2 -X_1)^2 + (Y_2 - Y_1)^2}$

I am going to use point (3,2) as point 1 and (-1,-4) as point 2
Insert the points into the formula
$d = \sqrt{(X_2 -X_1)^2 + (Y_2 - Y_1)^2}$
$d = \sqrt{((-1) - 3)^2 + ((-4) - 2)^2}$
Solve:
$d = \sqrt{((-1) - 3)^2 + ((-4) - 2)^2}$
$d = \sqrt{(-4)^2 + (-6)^2}$
$d = \sqrt{16 + 36}$
$d = \sqrt{52}$
$d = \sqrt{52} = \sqrt{4}\sqrt{13}$
$d = \sqrt{52} = 2 \sqrt{13}$
$d = 2 \sqrt{13}$
$radius = 2 \sqrt{13} = 7.2111$

5 0

3 years ago

Write the equation of a line that meets all the following requirements:

LuckyWell [14K]

9514 1404 393

Answer:

x + y = 5
y = -x + 5

Step-by-step explanation:

We can start with the point-slope form of the equation for a line. To meet the given requirements, we can use a point of (5, 0) and a slope of -1. Then the equation in that form is ...

y -0 = -1(x -5)

Simplifying gives the slope-intercept form:

y = -x +5 . . . . . . . use the distributive property to eliminate parentheses

Adding x to both sides gives the standard form:

x + y = 5

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Explanation

We know the line has the required intercept and slope because we chose those values to put into the point-slope form. Conversion from one form to another made use of the rules of equality, the additive identity element (y-0=y), and the distributive property.