Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
Answer:
B
Step-by-step explanation: because this negative
Answer:
a. 
b. His teacher will receive more pencils (See explanation).
Step-by-step explanation:
a. The total number of pencils Louis brings to school is:
Then, in order to calculate the number of pencils Louis’s teacher will receive after he gives each of his 15 classmates an equal number of pencils, you need to solve the division show in the picture attached.
Notice that the remainder obtained is: 
.
<em>This means that Louis’s teacher will receive 4 pencils.</em>
b. If Louis decides instead to take an equal share of the pencils along with his classmates, his teacher will receive more pencils; because the amount of pencils each classmate will receive will be less. This means that the number of pencils leftover will increase, leaving more pencils for his teacher.
Answer:
Length = 9units
Width = 7units
Step-by-step explanation:
It is said that the length is 2units more than the width
Assume that the width is x, then the length will be 2 + x
ie
Width = x
Length = 2 + x
Area of the rectangle = 63units
Area of rectangle = l * b
l - length of the rectangle
b - width of the rectangle
A = l * b
63 = (2 + x) * x
63 = ( 2 + x) x
63 = 2x + x^2
Let's rearrange it
x^2 + 2x - 63 = 0
Let's find the factor of 63
A factor that can be multiplied to give -63 and that can be added to give +2
Let's use -7 and +9
x^2 - 7x + 9x - 63 = 0
Separate with brackets
( x^2 - 7x) + ( 9x - 63) = 0
x( x - 7) + 9(x - 7) = 0
( x + 9)(x - 7) = 0
( x + 9) = 0
( x - 7) = 0
x + 9 = 0
x = -9
x - 7 = 0
x = 7
Note: the length of a rectangle can not be negative
So therefore,
x = 7
Length = 2 + x
= 2 + 7
= 9units
Width = x
= 7units
