A dilation is a transformation
, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.
In a dilation of
the scale factor, k is mapping the original figure to the image in such a way that the
distances from O to the vertices of the image are k times the distances
from O to the original figure. Also the size of the image are k times the
size of the original figure.
Thus for a dilation using the rule
results in the distance of the image form O being twice the distance of the original point from O.
Therefore, it can be observed that the scale factor of the dilation, k, is 2.
<span>Simplifying
x4 = 16
Solving
x4 = 16
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Simplifying
x4 = 16
Reorder the terms:
-16 + x4 = 16 + -16
Combine like terms: 16 + -16 = 0
-16 + x4 = 0
Factor a difference between two squares.
(4 + x2)(-4 + x2) = 0
Factor a difference between two squares.
(4 + x2)((2 + x)(-2 + x)) = 0
Subproblem 1
Set the factor '(4 + x2)' equal to zero and attempt to solve:
Simplifying
4 + x2 = 0
Solving
4 + x2 = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + x2 = 0 + -4
Combine like terms: 4 + -4 = 0
0 + x2 = 0 + -4
x2 = 0 + -4
Combine like terms: 0 + -4 = -4
x2 = -4
Simplifying
x2 = -4
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:
Simplifying
2 + x = 0
Solving
2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2
Combine like terms: 0 + -2 = -2
x = -2
Simplifying
x = -2
Sub-problem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:
Simplifying
-2 + x = 0
Solving
-2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2
Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2
Combine like terms: 0 + 2 = 2
x = 2
Simplifying
x = 2Solutionx = {-2, 2}</span>
Answer:
x = 19
Step-by-step explanation:
(5x + 4)° + (x - 2)° + (3x + 7)° = 180°
(5x + x + 3x)° + (4 - 2 + 7)° = 180°
9x° + 9° = 180° → ÷9
x + 1 = 20
x = 20 - 1
x = 19
Consecutive integers are 1 aparrt
they are
x,x+1,x+2,x+3
the 2nd and 4th sum is x+1 and x+3
sum is 34
x+1+x+3=34
2x+4=34
minus 4
2x=30
divide 2
x=15
x+1=16
x+2=17
x+3=18
the numbers are 15,16,17,18
Answer:x=3
Step-by-step explanation:
D( x )
x+2 = 0
x = 0
x+2 = 0
x+2 = 0
x+2 = 0 // - 2
x = -2
x = 0
x = 0
x in (-oo:-2) U (-2:0) U (0:+oo)
(9*x-7)/(x+2)+15/x = 9 // - 9
(9*x-7)/(x+2)+15/x-9 = 0
(x*(9*x-7))/(x*(x+2))+(15*(x+2))/(x*(x+2))+(-9*x*(x+2))/(x*(x+2)) = 0
x*(9*x-7)+15*(x+2)-9*x*(x+2) = 0
9*x^2-9*x^2+8*x-18*x+30 = 0
30-10*x = 0
(30-10*x)/(x*(x+2)) = 0
(30-10*x)/(x*(x+2)) = 0 // * x*(x+2)
30-10*x = 0
30-10*x = 0 // - 30
-10*x = -30 // : -10
x = -30/(-10)
x = 3
x = 3
