Question

Part A: Short Answer – Write the answer for each question in the space provided. You do not need to show your work. Round your answer to one decimal place if necessary. (18 marks)

Determine the number of solutions to the linear system: y= -2x+1
6x+3y-3=0

State the x-intercepts of the circle with the equation: x2+y2=81

State if (-3, 4) lies inside, outside, or on the circle x2+y2=16

State the midpoint of line segment M (2, -5) and N (4, 3).

Calculate the length of line segment A (1, 2) and B (-1, -5).

The slope of line segment BC is -3. State the slope of its perpendicular bisector.


Expand: y=3x+4(x-4)

State the roots of the equation 3x-1x+5= 0

State the equation of the axis of symmetry for y=-2x-1x+7 _________________

State the number of roots for the relation y= x2- 25

State the coordinates of the vertex for y=2x-32+ 5

State the transformation of y= x2 to obtain y=(x+2)2

Write the equation of the parabola y=-2x+32-3 in standard form.

Evaluate sin45o. Express your answer with 4 decimals.

Answer 1

[AI-generated answer — Bot GPT 3.5]

1. The linear system has one solution.

2. The x-intercepts of the circle x^2 + y^2 = 81 are (-9, 0) and (9, 0).
3. The point (-3, 4) lies outside the circle x^2 + y^2 = 16.
4. The midpoint of line segment M(2, -5) and N(4, 3) is (3, -1).
5. The length of line segment A(1, 2) and B(-1, -5) is approximately 7.6.
6. The slope of the perpendicular bisector of line segment BC with a slope of -3 is 1/3.
7. The expanded form of y = 3x + 4(x - 4) is y = 3x + 4x - 16.
8. The roots of the equation 3x^2 - x + 5 = 0 are imaginary.
9. The equation of the axis of symmetry for y = -2x^2 - x + 7 is x = -1/4.
10. The relation y = x^2 - 25 has two roots.
11. The coordinates of the vertex for y = 2x^2 - 32x + 5 are (8, -59).
12. The transformation of y = x^2 to obtain y = (x + 2)^2 is a horizontal translation to the left by 2 units.
13. The equation of the parabola y = -2x^2 + 32x - 3 in standard form is y = -2(x - 8)^2 + 261.
14. sin45o is approximately 0.7071.