Transcript Equations & Polynomials

Equations & Polynomials
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To find area and perimeter
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Find the area of the following rectangle.
x+2
Formula for area of a rectangle.
2x + 4
Multiply 2 and 4 you get 8.
Multiply 2 and 2x you get 4x.
Multiply x and 4 you get 4x.
area = length (x) width
2x + 4
(x) x + 2
+ 4x + 8
2x^2 + 4x
Multiply x and 2x you get 2x^2.
Combine Like Terms
2x^2
+
8x
+
8
Find the perimeter of the following
rectangle.
Formula for perimeter
of a rectangle.
x+2
2x + 4
Perimeter = 2(length) + 2(width)
P = 2(x + 2) + 2(2x + 4)
Multiply to eliminate parenthesis
P = 2x + 4 + 4x + 8
Combine like terms
P = 6x + 12
Find the area of the
following:
width = (2x - 3)
x+2
(x) 2x - 3
- 3x - 6
2x^2 + 4x
-3 times 2 is equals to -6
2x^2
length = (x + 2)
+
x - 6
First let’s draw the figure.
-3 times x is equals to -3x
2x times 2 is equals to 4x
2x times x is equal to 2x^2
Combine Like Terms
x+2
2x - 3
Find the area of a triangle whose height
if 2x + 1 and base is 2x + 2.
Formula for area of a triangle.
A = ½ bh
2x + 1
2x + 2
Multiply 2 times 1 you get 2.
Multiply 2 times 2x you get 4x.
Multiply 2x times 1 you get 2x.
Multiply 2x times 2x you get 4x^2.
Combine Like Terms
Since it is a triangle we must take ½
our answer.
2x + 1
(x)
2x + 2
4x + 2
4x^2 + 2x
4x^2
2x^2
+
+
6x
3x
+
+
2
1
a. Find the area of a square whose side
is 2x + 4. b. Then find the perimeter.
a.
2x + 4
Multiply 4 times 4 you get 16.
Multiply 4 times 2x you get 8x..
Multiply 2x times 4 you get 8x.
Multiply 2x times 2x you get 4x^2.
Combine Like Terms
b.
2x + 4
(x)
2x + 4
8x + 16
4x^2 + 8x
4x^2 + 16x + 16
2x + 4
(x) 4
Multiply 4 times 4 you get 16.
Multiply 4 times 2x you get 8x.
8x + 16
Find the area of the region below.
2x
x
b
a
Now we have created 3 rectangles. Let’s call
them a, b and c to help us.
x+5
x+2
x^2 + 5x
2x^2
2x^2 + 4x
5x^2 + 9x
First let’s find the formula we need to find the
area. Since there is no formula for this type of
figure, lets make rectangles so we can use the
x rectangle formula. a = l (x) w
c
2x
Now lets find the area of a. x(x + 5)
Now let’s find the area of b. Since the width of
a is x then the length of b is x. Since the
length of c is 2x then the length of b is 2x.
Now we can find the area 2x times x.
Now let’s find the area of c. 2x times x + 2.
Now let’s combine our like terms.
Find the area of the blue region.
First let’s find the area of the whole
region, since it is a rectangle, let’s
use the rectangular formula. A = lw
x+4
x-4
x
x-2
-2 times 4 is 8.
x times -4 is -4x.
-2 times x is -2x.
x times x is x^2.
x times 4 is 4x.
x times x is x^2.
Combine Like Terms
x^2 + 2x - 8
-x^2
x^2 +- 4x
6x - 8
Remember to change the signs of the
bottom rectangle since you are subtracting.
(x + 4)(x – 2) = you must use the foil,
the box or the multiplication method.
x+4
(x) x - 2
- 2x - 8
x^2 + 4x
x^2 + 2x - 8
Now let’s find the area of the smaller
rectangle. a = lw
x - 4
(x)
x
x^2 - 4x
Now let’s subtract our smaller
rectangle from our larger one.
Find the area of a rectangle whose length is 4 more than
the width. Let “x” represent your width.
First let’s draw the figure.
L=x+4
w=x
Since it wants us to represent x as our width, let’s
set w = x. Remember we must set the unknown
to a variable until we know it’s value. Since the
length is 4 more than the width and more than
means add our length is represented by x + 4.
The area formula for a rectangle is a = lw.
So let’s multiply x(x + 4) we get x^2 + 4x as our
answer.
Find the perimeter of a rectangle whose length is 4 more
than the width. Let “x” represent you width.
First let’s draw the figure.
L=x+4
w=x
Since it wants us to represent x as our width, let’s
set w = x. Remember we must set the unknown
to a variable until we know it’s value. Since the
length is 4 more than the width and more than
means add our length is represented by x + 4.
The perimeter formula for a rectangle is
p = 2l + 2w.
So let’s substitute and solve, p = 2(x + 4) + 2(x):
Distribute to eliminate your parenthesis
p = 2x + 8 + 2x:
Then combine your like terms if any
p = 4x + 8
If the length of a rectangle is 4 less than the width
and the perimeter is 48. Find the a. width b.
Length c. Area of the rectangle.
L=x-4
P = 48
w=x
48 = 2(x – 4) + 2(x)
48 = 2x – 8 + 2x
48 = 4x - 8
+8
+8
56 = 4x
4 = 4
14 = x
c. Now we can find our area by
multiplying 14 and 10 is 140.
First let’s draw the figure.
Now let’s represent the width and length. We
will call the unknown width as x, the length as
x – 4 and the perimeter as 48.
Now we must use the perimeter formula to
find the length and width values. P = 2l + 2w.
Substitute and solve. P = 2l + 2w (l = x – 4) (w = x)
Distribute to eliminate parenthesis.
Combine Like Terms
Add 8 to both sides.
Divide both sides by 4
Substitute our x value into the equations and
we can find our length and width.
a. Since w = x we know our width is 14.
b. Since L = x – 4 by substituting 14 in for x
we can find our length is 14 – 4 is 10.
Find the perimeter of the following equation.
Definition of perimeter, the distance
around a figure.
2 ways to solve: either add all sides
since all sides are equal or multiply by
the number of sides.
2x + 4
2x + 4
2x + 4
2x + 4
(x) 6
2x + 4
2x + 4
2x + 4
2x + 4
12x + 24
12x + 24