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
The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
<h3>How to determine the
x-intercept?</h3>
The function is given as:
g(x) = -5(x - 3)^2
Set g(x) to 0, to determine the x-intercept.
-5(x - 3)^2 = 0
Divide through by -5
(x - 3)^2 = 0
Take the square root of both sides
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)
<h3>How to determine the vertex?</h3>
The function is given as:
g(x) = -5(x - 3)^2
A quadratic function is represented as:
g(x) = a(x - h)^2 + k
Where, the vertex is
Vertex = (h, k)
By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have
(h, k) = (3, 0)
Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
Read more about x-intercept and vertex at
brainly.com/question/1305604
#SPJ1
Answer:
0.06
Step-by-step explanation:
0.42 ounces is enough for 14 plants. After watering 12 plants, there will be enough plant food left over for 2 plants. Write a proportion:
0.42 / 14 = x / 2
Cross multiply:
14x = 0.84
Solve:
x = 0.06
Answer:
Fractional form, y = 1/27, y = -1/7
Decimal form, y = 0.037 bar, y = -0.037 bar
To get a feel for where those two radicals fall on the number line, take a look at the perfect square roots they fall between. Both sqrt(7) and sqrt(8) fall between the perfect square roots sqrt(4) and sqrt(9); since sqrt(4) = 2 and sqrt(9) = 3, we know that sqrt(7) and sqrt(8) are somewhere in between 2 and 3. This means we know that sqrt(7) > 2. What about sqrt(8)/2 though? Well, sqrt(4)/2 = 2/2 = 1, and sqrt(9)/2 = 3/2 = 1 1/2, so sqrt(8)/2 has to be between 1 and 1 1/2, both of which are less than 2. Putting those all in order:
sqrt(8)/2, 2, sqrt(7)
