Chapter 1: Linear Systems
What method is used to solve a system of equations by eliminating one variable?
The elimination method.
What is the equation of a circle with a center at (4, -1) and a radius of 6?
(x-4)squared + (y+1)squared = 36
What is the sum of the interior angles in a quadrilateral?
The sum of the interior angles in a quadrilateral is 360 degrees.
Factor the expression x squared - 4
(x−2)(x+2).
Write the quadratic relation y= (x-3)(x+4) in expanded form.
y = x squared + x - 12
Solve the system of equations 3x - 2y = 5 and 2x + y = 8 using the method of substitution
x = 3 , y = 2
Find the midpoint of the line segment connecting points A(3, 2) and B(7, 8).
The midpoint of the line segment connecting points A(3, 2) and B(7, 8) is (5, 5).
What are the properties of a rectangle.
A rectangle has four right angles, opposite sides of equal length, and diagonals that are equal in length.
Factor 3x squared - 12x + 12.
3(x−2) squared
Graph the relation y= -2(x-1)squared +3
It is a downward parabola that opens with vertex at (1, 3).
What does it mean for two linear relations to be equivalent?
They represent the same line.
Determine the length of the line segment with endpoints (1, 3) and (5, 7).
The length of the line segment is 4squareroot2.
Investigate and confirm the properties of an isosceles triangle.
An isosceles triangle has two equal sides and two equal angles.
Solve the quadratic equation 2x squared - 5x - 3 = 0 using any method
x = 3 and x = -0.5
Complete the square to find the vertex form of the quadratic y = xsquared - 6x + 2
y = ( x - 3 ) squared - 7
Connect the equation y = 2x + 3 with its corresponding line on the coordinate plane
The line passes through the point (0, 3) and has a slope of 2.
What are the coordinates of the midpoint of a line segment with endpoints (2, -1) and (8, 3)?
The coordinates of the midpoint are (5, 1).
What are the properties of a rhombus?
A rhombus has equal sides and diagonals. Opposite angles are equal, and the diagonals bisect each other at right angles.
Find the common factors in the expression 4x squared - 8x
4x(x−2).
Determine the equation of a quadratic relation with roots r = 2 and s = -5
The equation of the quadratic relation is y = x squared + 3x - 10
Use substitution to solve the system x + y = 7 and 2x - y = 3.
x = 2, y = 5
Define analytic geometry and explain its applications.
Analytic geometry combines algebra and geometry, using equations and coordinates to study shapes. Its applications include graphing, solving equations, and analyzing geometric properties in fields like physics, engineering, and computer graphics.
Prove that the diagonals of a parallelogram bisect each other.
In a parallelogram, opposite sides are parallel, and the opposite angles are equal. Due to these properties, it can be observed that the diagonals bisect each other.
Determine the product in the expression (a-b)squared.
a squared −2ab + b squared
Explore the transformation of the quadratic y = x squared after a vertical stretch by a factor of 3
a = 3, It is a vertical stretch by a factor of 3
h = 0 it has no horizontal shift
k = 0 it has no vertical shift