Quadratic Equations
x^2=-7x-10
x^2+7x+10=0
x^2+2x+5x+10
x(x+2)+5(x+2)
5x2=10 5+2=7
(x+2)(x+5)=0
x+2=0 or x+5=0
-2 -5
Solve the following system using the substituton method. 2x+y=2 and 3x + 2y =5
POI (-1,4)
What is the answer to this binomial
Hint use special products
(3y+7x)(3y-7x)
9y^2-49x^2
sin(30)
=1/2
A ladder is leaning against a wall. The ladder forms an angle of 60 degrees with the ground, and the bottom of thr ladder is 4 metters away from the basef the wall. how long is the ladder?
8 metters
Identify the vertex of x^2-2x-15
Identify the x intercepts x=-1 x=5
The Midpoint between x=-1 x=5
-1+5/2 = 4/2 =2
Subsitute x=2 into the equation
y=(2+1)(2-5)=(3)(-3)=-9
Therefore the vertex is (2,-9)
Solve the following by using the elimination method.
5x-4y=18
3x+4y=62
The solution is (10,8)
Factor Out the greatest Common Factor
-5mn4 + 15m^2 - 10n^3
5n^2
sin^-1(1/2)
30 degrees
Two friends Alice and Bobo went to a bookstore. Alice bought 3 books and 2 bookmars and her total was 23 dollars. Bon bought 5 books and 3 book marks and his total was 37 dollars.
What is the price for one book and one bookmark?
5 dollars for a book and 4 dollars for a bookmark
Use the Quadratic Formula 0=3x^2+8x-5
x1 = -0.52
x2 =-3.19
2x+3y=16
4x-y=3
x=25/14
y=29/7
Factor the following trinomial if possible
x^2-17xy-27^2
(x+y)(x-27)
solve for x in the equation
sin(x)=1
x=90 degrees
A toy rocket is launched from the ground with an inital height of 0 meters and an initital velocity of 20m per second, the height h(t) of the rocket in meters after t seconds is given by the equation h(t) = -5t^2+20t
at what time will the rocket hit the ground
4 seconds after
Does this Equation have a solution?
0=x^2-5x+11
this equation has no real solutions
3x + 4y =24
2x-y=1
x=28/11
y=45/11
Factor the following: 25x^2 -60xy +36y^2
25x^2-60xy+36y^2= (5x-6y)^2
in triangle ABC angle A 40 degrees and B 60 degrees and side a= 12cm find the length of side b
b=14.37
a tree casts a shadow that is 15 metters long. the angle of the sun is 30 degrees. how tall is the tree?
8.66m tall
The Equation h(t) =-4.9t^2+60t+3 represents the path of a frisbee where h is height in meters and t is time in seconds after it has been thrown
what is the height of the Frisbee when it is launched?
The height of the frisbee was 3m when it was launched
maria bought 3 apples and oranges for $5.50. john bought 2 apples and 3 oranges for 5 dollars how much does each apple and each orange cost
1 apple is 1.30 dollars
1 orange is 0.80
Factir the following expression 4x^2 - 12x - 9 =0
x= 3+3 square root of 2/2
in trianle ABC side a = 8cm sibe b= 6 cm and angle C=60 degrees find the length of side c
c=7.21cm
The area of a rectangular garden is 96 square metters. the length of the garden is 4 metters more than twice its width. what are the dimensions of the garden?
width 6 meters
length 16 meters