To work out the equation of a straight line the slope and an (x, y) coordinate must be given
15x + y =65divide by 65 b/s3x/13 + y/65=1ORx/4.33 + y/65=1HENCE X INTERCEPT=4.33 AND Y=65
x= # of pencils that cost .45 y= # of pencils that cost .65 So now you need 2 equations for 2 variables: 15= x+y This equation is saying: 15 total pencils bought= pencils that cost .45 + pencils that cost .65 The second equation is: 7.75= .45x + .65y This equation is saying: total money spent (7.75)= price of pencils (.45) times # of pencils + price of pencils (.65) times # of pencils Then you combine these two equations, but first switch around the first equation to look like: y=15-x Then you replace the "y" in the second equation by putting in what y equals the first equation: 7.75= .45x + .65(15-x) Then distribute and solve for x: x = 10 Then enter 10 into the first equation for x to figure out y: y= 15- 10 y= 5 So your answer is-- Ray bought 10 pencils that cost .45 and 5 pencils that cost .65
-(60x) 5-65=-60 0x-1x=-1x 1y-1y=0y
About 175
t - 17 = 48 The first step is to move the -17 to the right side of the equation and end up with: t = 48 + 17. (When you switch sides, the sign changes) To solve the equation: t = 65
Given the equation y = 45x + 65, the y-intercept is 65. We know this because the equation is already in the form y = mx + b, where m is the slope, and b is the y-intercept.
that is one point, you need at least two for a line.
subtract the x to the other side to get y=-x+65. its a straight line crossing the y-axis at 65 with a slope of -1.
Equation of circle: x^2 +10x +y^2 -2y -39 = 0 Completing the squares: (x+5)^2 +(y-1)^2 = 65 Center of circle: (-5, 1) Slope of radius: 1/8 Slope of tangent line: -8 Point of contact: (3, 2) Equation of tangent line: y-2 = -8(x-3) => y = -8x+26 Note that the tangent line meets the radius of the circle at right angles.
Let 'S' represent the sum. Then the equation isS = 198 + 65
First find the slope of the circle's radius as follows:- Equation of circle: x^2 +10x +y^2 -2y -39 = 0 Completing the squares: (x+5)^2 + (y-1)^2 -25 -1 -39 = 0 So: (x+5)^2 +(y-1)^2 = 65 Centre of circle: (-5, 1) and point of contact (3, 2) Slope of radius: (1-2)/(-5-3) = 1/8 which is perpendicular to the tangent line Slope of tangent line: -8 Tangent equation: y-2 = -8(x-3) => y = -8x+26 Tangent equation in its general form: 8x+y-26 = 0
A line with slope m and a point (x0, y0) on it has equation: y - y0 = m(x - x0) The slope of the tangent is perpendicular to the slope of the radius to the point (3, 2) The product of the slope of a line and a line perpendicular to it is -1. A circle with centre (X, Y) and radius r has equation: (x - X)² + (y - Y)² = r² For x² + 10x + y² - 2y - 39 = 0 and the point (3, 2): x² + 10x + y² - 2y - 39 = 0 → x² + 10x + (10/2)² - (10/2)² + y² - 2y + (2/2)² - (2/2)² - 39 = 0 → (x + 5)² - 25 + (y - 1)² - 1 - 39 = 0 → (x - -5)² + (y - 1)² = 65 → the circle has centre (-5, 1) and radius √65. The slope m' of the radius to (3, 2) from the centre of (-5, 1) is given by: slope = change_in_y / change_in_x → m' = (2 - 1) / (3 - -5) = 1/8 → slope m of the tangent is: mm' = -1 → m = -1/m → m = -1/(1/8) = -8 Thus the tangent has equation: y - 2 = -8(x - 3) → y - 2 = -8x + 24 → y + 8x = 26
The
198+65= ?
It is not an equation and no solution is possible.
60
Equation: 5x = 65 5x / 5 = 65 / 5 x = 13