<em><u>The expressions that are polynomial are:</u></em>
6 + w
z + 1
<em><u>Solution:</u></em>
A polynomial is an expression with variables and coefficients with the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables
1) 6 + w
Here "w" is a variable, hence it is a polynomial expression
This is a polynomial, since it has variables and coefficients and variable with non negative exponent
3) z + 1
This is also a polynomial with variable "z" and has addition operation
Since it has root so it is not a polynomial
I think its 28 because 308 divided by 11 is 28 to find how many gallons were used per mile
Answer:
69 feet
Step-by-step explanation:
we have
where
h(t) is the height of the ball
t is the time in seconds
we know that the given equation is a vertical parabola open downward
The vertex is the maximum
so
the y-coordinate of the vertex represent the maximum height of the ball
Convert the quadratic equation into vertex form
The equation in vertex form is equal to
where
(h,k) is the vertex of the parabola
the vertex is the point (2,69)
therefore
The maximum height is 69 ft
In the given diagram, we can note that the tree divides the hypotenuse of the triangle as well as the side where the tree is based into halves.
In a triangle, when a line is drawn joining between the midpoints of two sides, this line is always parallel to the third side and equals half its length.
Applying this concept to the given diagram here, we will find that the tree is joining the midpoints of two sides of the triangle. this means that the tree is parallel to the building and the height of the tree is half the height of the building.
Therefore:
height of tree = 0.5 * 120 = 60 ft
X=2
2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=
2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=
2
