System of Equations
When solving a system of equations, you are trying to find whether or not two or more lines __________.
Intersect
____
Possibility 1:
The two lines intersect each other resulting in an (x, y) pair.
Possibility 2:
The results of the system of equations is: 0 = n, where n is any number other than 0. This means there is no solution. Think of parallel lines.
Possibility 3:
The result of the system of equations is: 0 = 0. This means the lines are identical. There is an infinite number of solutions. Think of one line lying on top of the other line.
How do you test if a graph is a function?
a) Vertical line test
b) Horizontal line test
c) Function line test
VERTICAL LINE TEST
If a vertical line drawn anywhere on the graph of a relation only intersects the graph at one point, then that graph represents a function. If a vertical line can intersect the graph at two or more points, then the graph does not represent a function.
What is the quadratic formula?
X=_______________
X= -b +- √(b24ac)/ 2a
Which of these is trinomial?
a) 3x+4x+5x
b) 3x + 3y
c) 3x+ 3y+4z
c) 3x+ 3y+4z
a trinomial is a polynomial consisting of three terms or monomials.
How many boroughs are there in NYC?
1) 10
2) 5
3) 50
2) 5
True or False:
these lines will be parallel on a graph because the slopes are the same.
line 1: 5x + 24 = 72
line 2: 5x + 2 = 10
True
Find the GCF: 4x3 and 10x2
2x2
4x3 = 2x2(2x)
10x2 = 2x2(5)
The common factors between 4x3 and 10x2 are 2x2
If the domain is the set of real numbers, what is the solution set for the equation x2+4=0?
1) {-2}
2) {2,-2}
3) {}
3) {}
the square root of -4 is an imaginary number which is not a real number
Combine the like terms to simplify:
2x2-6+3x2+10
5x2+4
(2x2+3x2) = 5x2
(-6+10) = 4
What is the largest organ on the human body?
A) pancreas
B) brain
C) skin
c) skin
When solved graphically, which system of equations will have exactly one point of intersection?
A) y = x + 2
y = x - 2
B) y = 3/6x + 5
y = 1/2x + 20
C) y = -2x + 19
y = 2x - 3
C) y = -2x + 19
y = 2x - 3
If two lines have different slopes, they will intersect at a single point. The point of intersection is the solution to the system of equations formed by the two lines.
Factor the following:
x2-3x-18
(x-6) (x+3)
we need to find two binomial factors that, when multiplied, give us the original expression.
We are looking for two numbers that multiply to -18 and add up to -3
What is the solution set of the equation 3x2=48?
1) {-2,-8}
2) {2,8}
3) {4,-4}
3) {4,-4}
the square root of 16 is -4/+4
Which polynomial function has zeros at -3, 0, and 4?
1) f(x)=(x+3)(x2+4)
2) f(x)=(x2-3)(x-4)
3) f(x)=x(x+3)(x-4)
3) f(x)=x(x+3)(x-4)
zeros of a root:
x-3=0
x=3
x+4=0
x=-4
x+0=0
x=0
What is the chemical symbol for gold on the periodic table?
A) Au
B) Ag
C) Fe
Solve the system of equations:
**DAILY DOUBLE**
x = 3
5x + 4y = -9
-x + 4y - 2z = -25
A) y = -6, z = -1, x = 3
B) y = 5, z = 1, x = 3
C) y = 6, z = -1, x = 3
A) y = -6, z = -1, x = 3
Substituting the value of x from Equation 1 into Equations 2 and 3:
Equation 2:
5(3) + 4y = -9
15 + 4y = -9 4y = -9 - 15
4y = -24 y = -6
Equation 3:
-(3) + 4(-6) - 2z = -25
-3 - 24 - 2z = -25
-27 - 2z = -25
-2z = -25 + 27
-2z = 2
z = -1
Therefore, the solution to the system of equations is x = 3, y = -6, and z = -1. In the format (x, y, z), the solution is (3, -6, -1).
(4)
the x value of 6 pairs with both y values of 10 and 12
rule when it comes to functions: "x cannot cheat on y"
Which of the following is the correct solution set for the quadratic equation
2x2 - 5x + 2 = 0?
A) {-1, 2}
B) {-2, 1}
C) {1/2, 2}
C) {1/2, 2}
use the quadratic formula to plug in numbers
Which planet is known as the "Red Planet"?
A) Venus
B) Mars
C) Saturn
b) Mars
At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax.
Write a system of equations, in terms of a and c, that models this situation
equation 1: 4a+2c=325.94
equation 2: 2a+3c=256.95
Equation 1: 2a + 4c = 325.94
Explanation: In a group of six people, which includes two children, there are four adults. The total cost of their admissions is $325.94.
Equation 2: 3a + 2c = 256.95
Explanation: In a group of five people, which includes three children, there are two adults. The total cost of their admissions is $256.95.
The function f has a domain of {1,3,5,7} and a range of {2,4,6}. Could f be represented by {(1,2), (3,4), (5,6), (7,2)}? Justify your answer.
Yes, because every element of the domain is assigned one unique element in the range, or, there are no repeated values of x assigned to y.
A rocket is shot vertically into the air. Its height, h, at any time, t, in seconds, can be modeled by the equation h=-16t2+184t. Determine algebraically, the number of seconds it will take the rocket to reach a height of 529 feet.
hint: rearrange into the correct format of ax2+bx+c=0 then use quadratic formula
5.75 seconds
Given that the height, h, is given by the equation h = -16t2 + 184t, we can substitute 529 for h and solve for t algebraically.
-16t2 + 184t = 529
Rearranging the equation:
-16t2 + 184t - 529 = 0
Now, we have a quadratic equation in the form of at2 + bt + c = 0, where:
a=-16 b=184 c=-529
then
use the quadratic formula
Express in simplest form:
(3x2+4x-8) - (-2x2+4x+2)
5x2-10
To simplify the expression (3x2 + 4x - 8) - (-2x2 + 4x + 2), we can distribute the negative sign to the terms inside the second parentheses and then combine like terms:
(3x2 + 4x - 8) - (-2x2 + 4x + 2) = 3x2 + 4x - 8 + 2x2 - 4x - 2
Now, let's combine the like terms:
(3x2 + 2x2) + (4x - 4x) + (-8 - 2) = 5x2 + 0 + (-10) = 5x2 - 10
Which scientist is known for proposing the theory of evolution through natural selection?
A) Isaac Newton
B) Marie Curie
C) Charles Darwin
C) Charles Darwin