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What is the equation of a line that passes through the point 0 2 and is perpendicular to a line with a slope of 3?
Slope of line: 3 Perpendicular slope: -1/3 Equation: y-2 = -1/3(x-0) => y = -1/3x+2
Y equals -5x plus 5 and 3x plus 2y equals 3 solve this equation using substitution?
y = -5x+5 (Equation 1)3x+2y = 3 (Equation 2)you see the the first equation is equal to y. just put that into the second equation.3x + 2(-5x+5) = 3 (now do algebra and find x)3x - 10x + 10 = 3-7x = -7-x = -1x = 1Now put x into one of the equations to find yy = -5(1) + 5 (Equation 1)y = -5 + 5y = 0Now put both the x and y into both equations to see if it is truee.0 = -5(1) + 5 (Equation 1)0 = -5 + 50 = 0 CORRECT3(1) + 2(0) = 3 (Equation 2)3 + 0 = 33 = 3 CORRECTTherefore your answers arex = 1y = 0
What equation gives 25 using 8 6 1 2 3 0?
It is: 6*(2+3-1)+80 = 25
How do you solve the Relationship between the coefficient and roots of quadratic equations?
TO FIND THE RELATION BETWEEN ROOTS AND COEFFICIENTS OF A QUADRATIC EQUATION:Let us take the general form of a quadratic equation:ax2 + bx + c = 0 (1)where a(≠0) is the coefficient of x2 , b is the coefficient of x and c is a constant term. If and ß be the roots of the equation, then we have to find the relations of and ß with a, b and c.Since a ≠0, hence multiplying both sides of (1) by 4a we get,4a2x2 + 4abx + 4ac = 0 or (2ax)2 + 2.2ax.b + b2 - b2 + 4ac = 0Or, (2ax + b)2 = b2 - 4ac2ax + b = b2 - 4acx =Hence, the roots of (1) areLet, = and ß =Hence, + ß = +Or + ß = = - b/a = - (2)Again ß = xOr ß = =Or ß = = = (3)Equations (2) and (3) represent the required relations between roots (that is, and ß) and coefficients (that is, a, b and c) of equation (1).Example 1:If the roots of the equation 2x2 - 9x - 3 = 0 be and ß, then find + ß and ß.Solution:We know that + ß = - = - =And ß = = (Answer)Example 2:If one root of the quadratic equation x2 - x - 1 = 0 is a, prove that its other root is 3 - 3.Solution:x2 - x - 1 = 0 (1)Let ß be the other root of the equation (1). Then,+ ß = = 1 or ß = 1 -Since is a root of the equation (1) hence, 2 - - 1 = 0 or 2 = + 1Now, 3 - 3 = . 2 - 3 = ( + 1) - 3 [Since 2 = + 1]= 2 + - 3 = + 1 - 2 = 1 - = ß [Since ß = 1 - ]Hence, the other root of equation (1) is 3 - 3. (Proved)Example 3:If a2 = 5a - 3 and b2 = 5b - 3, (a ≠b), find the quadratic equation whose roots are and .Solution:Given (a ≠b) and a2 = 5a - 3 and b2 = 5b - 3, hence it is clear that a and b are the roots of the equation x2 = 5x - 3 or x2 - 5x + 3 = 0.Hence, a + b = - = 5 and ab = = 3.Now, the sum of the roots of the required equation= + = = = = =And the product of the roots of the required equation = . = 1.Hence, the required equation is x2 - x + 1 = 0 or 3x2 - 19x + 3 = 0. (Answer)
What is the equation of the line that passes through 2 2 and 6 3 in standard form?
Points: (2, 2) and (6, 3) Slope: 1/4 Equation: y = 1/4x+3/2 In standard form: x-4y+6 = 0
What is the equation of a line that passes through points (0 -1) and (2 3)?
As Slope=m=3-(-1)/2-0=2 So equation is y-(-1)=2×(x-0) y+1=2x 2x-y-1=0
Which equation has the solution set 1 and 3?
An equation with the solution set 1 and 3 can be written in factored form as (x-1)(x-3) = 0. When expanded, this equation becomes x^2 - 4x + 3 = 0. Therefore, the equation x^2 - 4x + 3 = 0 has the solution set 1 and 3.
What is the equation of a line that passes through the point 0 2 and is perpendicular to a line with a slope of 3?
Slope of line: 3 Perpendicular slope: -1/3 Equation: y-2 = -1/3(x-0) => y = -1/3x+2
What is the equation of (62) and (00)?
If you mean points (6, 2) and (0, 0) then the slope is 1/3 and the equation is y = 1/3x
What is the equation of the line that passes through the points 0 5 and 2 3?
Points: (0. 5) and (2, 3) Slope: -1 Equation: y = -x+5
How many different equations can be made with the numbers 0123?
A huge number. 0 + 1 + 2 = 3 0 + 2 + 1 = 3 1 + 0 + 2 = 3 1 + 2 + 0 = 3 2 + 0 + 1 = 3 2 + 1 + 0 = 3 -0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3 0 - 1 + 3 = 2 0 + 3 - 1 = 2 -1 + 0 + 3 = 2 -1 + 3 + 0 = 2 3 + 0 - 1 = 2 3 - 1 + 0 = 2 -0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2 0 - 2 + 3 = 1 0 + 3 - 2 = 1 -2 + 0 + 3 = 1 -2 + 3 + 0 = 1 3 + 0 - 2 = 1 3 - 2 + 0 = 1 -0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1 1 + 2 - 3 = 0 1 - 3 + 2 = 0 2 + 1 - 3 = 0 2 - 3 + 1 = 0 -3 + 1 + 2 = 0 -3 + 2 + 1 = 0 For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on. Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3 As you can see, the number of equations is huge!
What are four solutions of the equation y equals -3x-6?
3
What is a number times iself plus 1 equals 10 in an equation?
x^2+1=10 x^2-9=0 (x-3)(x+3)=0 x=±3 the top line is the equation you are looking for
Solve |- 2 x + 2| - 3 = -3?
The equation to solve is given by. |-2 x + 2| -3 = -3 Add 3 to both sides of the equation and simplify. |-2 x + 2| = 0 |-2 x + 2| is equal to 0 if -2 x + 2 = 0. Solve for x to obtain. So, x = 1
Y equals -5x plus 5 and 3x plus 2y equals 3 solve this equation using substitution?
y = -5x+5 (Equation 1)3x+2y = 3 (Equation 2)you see the the first equation is equal to y. just put that into the second equation.3x + 2(-5x+5) = 3 (now do algebra and find x)3x - 10x + 10 = 3-7x = -7-x = -1x = 1Now put x into one of the equations to find yy = -5(1) + 5 (Equation 1)y = -5 + 5y = 0Now put both the x and y into both equations to see if it is truee.0 = -5(1) + 5 (Equation 1)0 = -5 + 50 = 0 CORRECT3(1) + 2(0) = 3 (Equation 2)3 + 0 = 33 = 3 CORRECTTherefore your answers arex = 1y = 0
Solve the following system of equations What is the value of y when x - y - z equals 0 3x plus y - z equals 2 x plus 2y plus z equals 0?
x = -1, y = 2, z = -3.x - y - z = 03x + y - z = 2x + 2y + z = 0Adding equation 3 to equations 1 and 2 gives new equations 1 & 2:2x + y = 04x + 3y = 2Doubling the [new] equation 1 and subtracting from the [new] equation 2 gives:y = 2Substituting back into [new] equation 1 gives:2x + 2 = 0 ==> x = -1Substituting back into the original equation 1 gives:-1 - 2 - z = 0 ==> z = -3Check by substituting back into original equations:3x + y - z = 3(-1) + (2) - (-3) = -3 + 2 + 3 = 2x + 2y + z = (-1) + 2(2) + (-3) = -1 + 4 - 3 = 0
What equation gives 25 using 8 6 1 2 3 0?
It is: 6*(2+3-1)+80 = 25
