The distributive property of division over addition and substraction is idk
F(x)=-1x-1
1) Pick 2 points on the line (i chose (-4,3) and (3,-4)
2) Find slope of the line using the 2 points. (work below)
3) Find y-intercept, which is the point where y-axis and the line cross (y-intercept is -1).
4) Place both slope and y-intercept into slope-intercept form, y=mx+b (m=slope and b=y-intercept.)
5) Change y to f(x) (meaning function of x).
Work:
3-(-4)/-4-3=3+4/-4-3=7/-7=-1
y-intercept equals -1 also.
y=mx+b
y=-1x+(-1)
y=-1x-1
f(x)=-1x-1<---Answer
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
Answer:
6
Step-by-step explanation:
12/2=6/1=6
Answer:
The GCF for the variable part is
k
Step-by-step explanation:
Since
18
k
,
15
k
3
contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.
Steps to find the GCF for
18
k
,
15
k
3
:
1. Find the GCF for the numerical part
18
,
15
2. Find the GCF for the variable part
k
1
,
k
3
3. Multiply the values together
Find the common factors for the numerical part:
18
,
15
The factors for
18
are
1
,
2
,
3
,
6
,
9
,
18
.
Tap for more steps...
1
,
2
,
3
,
6
,
9
,
18
The factors for
15
are
1
,
3
,
5
,
15
.
Tap for more steps...
1
,
3
,
5
,
15
List all the factors for
18
,
15
to find the common factors.
18
:
1
,
2
,
3
,
6
,
9
,
18
15
:
1
,
3
,
5
,
15
The common factors for
18
,
15
are
1
,
3
.
1
,
3
The GCF for the numerical part is
3
.
GCF
Numerical
=
3
Next, find the common factors for the variable part:
k
,
k
3
The factor for
k
1
is
k
itself.
k
The factors for
k
3
are
k
⋅
k
⋅
k
.
k
⋅
k
⋅
k
List all the factors for
k
1
,
k
3
to find the common factors.
k
1
=
k
k
3
=
k
⋅
k
⋅
k
The common factor for the variables
k
1
,
k
3
is
k
.
k
The GCF for the variable part is
k
.
GCF
Variable
=
k
Multiply the GCF of the numerical part
3
and the GCF of the variable part
k
.
3
k
