Answer & Step-by-step explanation:
If a point is reflected across the x-axis, then the points will be like this...
(x,y) → (x,-y)
If a point is reflected across the y-axis, then the points will be like this...
(x,y) → (-x,y)
So, in order to solve this problem, first we will reflect (1,2) across the x-axis and then across the y-axis.
(2,1) → (2,-1) → (-2,-1)
So, your final coordinate point will be (-2,-1).
So PEMDAS is order of operations basicly.
P=Parenthesis
E=Exponets
M=Multiplication
D=Division
A=Addition
S=Subtraction
For example: 2x4+(9x9)-1
When solving order of operations you ALWAYS start with the problem in the parentheses.
(9x9)=81
Now multiplication comes next so, 2x4=8
Then addition, 8+81=88
Lastly subtraction, 88-1=81
1- the answer is b and d 2- the answer is a and b 3- the answer is b
Answer:
The pair of lines in (c) are parallel; so are the pair in (d).
Step-by-step explanation:
Rule: Two lines are parallel if their slopes are equal. If the slopes of two different lines are equal, then the lines are parallel.
Let's look at these four possible answer choices with that in mind:
a) the slopes are not equal; they are negative reciprocals. These lines are not parallel.
b) The slopes are not equal; one is positive and one is negative. These lines are not parallel.
c) Both of these lines have the slope 4; that is, their slopes are equal. Therefore these two lines are parallel.
d) y = 9 and y = 18 are both horizontal lines, and are therefore parallel. 9 and 18 do not represent slopes; rather, they represent y-intercepts.
Answer:
See below.
Step-by-step explanation:
Equation of parabola:
y = some expression in x^2
To translate the parabola vertically, substitute y with y - k.
The translation is k units vertically. If k is positive, the translation is up. If k is negative the translation is down.
Example 1:
original parabola: y = x^2 - 2x + 5
To translate it 3 units up, we need k = 3.
Substitute y with y - 5 to get
y - 3 = x^2 - 2x + 5
y = x^2 - 2x + 8 is the equation of the parabola translated 3 units up.
Example 2:
original parabola: y = 2x^2 + 4x - 6
To translate it 5 units down, we need k = -5.
Substitute y with y - (-5), or y = 5 to get
y + 5 = 2x^2 + 4x - 6
y = 2x^2 + 4x - 11
y = 2x^2 + 4x - 11 is the equation of the parabola translated 5 units down.