Step-by-step explanation:
as I don't see any equations or graphs here I can only answer in general :
f(x) is the patent function.
g(x) is the transformed function.
g(x) = -6f(x-7)
the "-" reflects the curve over the x-axis (what was positive is now negative and vice versa).
the factor 6 stretches the curve up and down by the factor 6 (everything is now 6 times larger or smaller).
and the argument "x-7" relates x (for the new function) with "x-7", meaning that now things are happening at x, that were originally happening at x-7, so they happen now "later" (more to the right on the x-axis) than before - hence a shift to the right.
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Slope of the line =(7- -5) / (-3-1) = 12 / -4 = -3
a. point slope form is y + 5 = -3(x - 1) Answer
b rearrange to slope-intercept form:-
y = -3x + 3 - 5
y = -3x - 2 Answer
If line A and B are parallel, then both angle 6 and 8 are corresponding angles, which mean they are the same.
SInce angle 6 is 127 degrees, then angle 8 is also 127 degrees
Answer:
K (-1,-1)
Step-by-step explanation:
