Linear Systems
What is a parallel and perpendicular line?
Parallel lines will never touch.
Perpendicular lines will meet at a 90 degree angle.
Common factor the following
3ab+a+2b
4a+5b
If a parabola opens up, the vertex is the ____point.
Minimum
What form must a quadratic be in to be factored?
ax2+bx+c=0
Prove this triangle is similar
90 degree angle
Shared angle
Corresponding angles
Solve without graphing x+y=2 and 3x=6-3y
y=x+2
There are infinite solutions
Factor this equation
x2+8x+15
(x+3) (x+5)
Stat the transformations that occur
y=2(x-3)+5
Vertical stretch of 2
Horizontal shift of 3 units to the right
Vertical shift of 5 units up
Graph using x-intercepts
y=x2+13x+120
(x+12) (x+20)
Calculate the following sin24 and tan14.
0.4067 and 0.2493
Use substitution method to solve 3x+4y=2 and 9x+12y=6
Infinite points of intersection
Factor this hard trinominal
5x2+14x+8
(5x+10) (x+4)
Find the x-intercepts y=(x+3) (x-1)
The x-intercepts are 3 and 1
Solve the following quadratic using quadratic formula x2+4x+3=0
x=-1.175
x=-6.825
Solve for missing side
x=6.92
Use elimination method to solve x+1/2y=6 and 3/2x+2/3y=17/2
The point of intersection is (3,6)
Factor using perfect square
x2-20x+100
(x-10)2
Find the x-intercepts, axis of symmetry, and vertex of y+3x(x-4)
X-intercepts are (0,0) (4,0)
A.O.S. is 2
Vertex is (2,-12)
The equation h=-16t2+128t+2 represents the path of a toy rocket being launched from a platform. How long does it take for the toy to hit the ground? What is the maximum height?
It takes the toy 126.87 seconds to hit the ground. The max height is 114 centimeters.
Solve for missing angle
The sum of two numbers is 39 their difference is 9. Find the numbers.
The numbers are 24 and 15
Factor using difference of square
9x2-16y2
(3x+4y) (3x-4y)
The arch hallway is approximately 24m tall and 15m wide, determine an equation to model the arch and solve.
y=25/-144 x(x-24)
A small business sells 110 notebooks in a week for $20 each. Each $2 decrease results in 3 more being sold. What is the max revenue.
The max revenue is $1,065.68
A ladder is placed leaning against a building and makes an angle of 52 with level ground. If the distance between the wall and the foot of the ladder is 5ft, how far up the wall will the ladder be?
The ladder will be 6.3ft up the wall