Area of the rectangle is determined by Binomial Multiplication as given below.
Binomial Multiplication follows FOIL method , Firsts , Outer terms , Inner Terms , Last Terms.
A rectangle is given and area of the rectangle has to be determined by splitting it into smaller rectangles.
Let the rectangle is of 5*3 ft
To determine the area the rectangle has been split into rectangles of 15 rectangles as seen in the figure attached.
Area of the smaller rectangle is given by Length * Breadth = 1*1
Let us consider x = 1
Then
The side of the rectangle will be ( x+4) ( x+2)
On solving this by FOIL
x² + 6x +8
Area = x² + 6x +8
Area = 1 + 6 + 8 = 15 sq.ft
Area of the bigger rectangle =
= ( Area of 1st rectangle + Area of 2nd Rectangle + ...... + Area of 15th Rectangle)
= 15 * ( Area of the smaller rectangle)
Area of the bigger rectangle = 15 * ( 1 * 1)
To know more about Binomial Multiplication
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Use the sample space of possible outcomes to determine the following probabilities.
1. Probability of drawing two odd numbers.
2. The sum of the two numbers drawn is less than 5.
3. The sum of the two numbers is less than 6 or greater than 8.
Answer:
Step-by-step explanation:
1. 1/2 x 1/2, 1/4
2. (2,2) is the only way to have a sum less than 5, so 1/16
3. 3 ways to be less than 6 and 3 ways to be greater than 8, so 6/16 or 3/8
The property that explains why these two expressions are equal is the distributive property. Option C is correct.
Given that:
A distributive property takes the form of distributive law where each algebraic expression is an equal variable.
i.e.
5(g+h) = 5g + 5h
An associative property simply means a rearrangement of algebraic terms in the bracket which doesn't affect the solution of the algebraic expression.
e.g
x + (y+z) = (x+y) + z
So, option A is not correct.
A commutative property means the addition or multiplication of variables by just changing their order without the result being changed.
e.g.
x + y = y + x
So, option B is incorrect.
Learn more about distributive property here:
Answer:
To solve the system of linear equations using Gaussian elimination, we'll write the augmented matrix and perform row operations to transform it into row echelon form.
The given system of equations:
-2x_1 + 3x_2 + x_3 = 2
-3x_1 + 4x_2 + 2x_3 = 2
x_1 - 5x_2 + 4x_3 = -9
-2x_1 + 4x_2 - 4x_3 = 8
Writing the augmented matrix:
[ -2 3 1 | 2 ]
[ -3 4 2 | 2 ]
[ 1 -5 4 | -9 ]
[ -2 4 -4 | 8 ]
1. Row 1 Ã (-3) + Row 2 â Row 2:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ 1 -5 4 | -9 ]
[ -2 4 -4 | 8 ]
2. Row 1 Ã (1/2) + Row 3 â Row 3:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 (3/2) 2 | -5/2]
[ -2 4 -4 | 8 ]
3. Row 1 Ã (-1) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 (3/2) 2 | -5/2]
[ 0 7 -3 | 6 ]
4. Row 2 Ã (-9/7) + Row 3 â Row 3:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 7 -3 | 6 ]
5. Row 2 Ã (2/3) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 0 (-11/7) | 0 ]
6. Row 3 Ã (-14/11) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 0 1 | 0 ]
7. Row 3 Ã (1/2) + Row 1 â Row 1:
[ -1 3/2 3/2 | (4/7) ]
[ 9 -13 -5 | -6 ]
[ -1 0 1 | 0 ]
[ 0 0 1 | 0 ]
8. Row 3 Ã (9/7) + Row 2 â Row 2:
[ -1 3/2 3/2 | (4/7) ]
[ 0 -26/7 -14/7 | -42/7 ]
[ -1 0 1 | 0 ]
[ 0 0 1 | 0 ]
9. Row 3 Ã (1/2) + Row 4 â Row 4:
[ -1 3/2 3/2 | (4/7) ]
[ 0 -26/7 -14/7 | -42/7 ]
[ -1 0 1 | 0 ]
[ 0 0 1 |
Divisibility rule of 2: All even numbers are divisible by 2 means no remainder will be left. For example- 4,6,10,18,26 etc
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3. For example- 15,54,213,699 etc
Divisibility rule of 5: A number is divisible by 5 if the number's last digit is either 0 or 5. For example- 40,85,255,3600,6510 etc
Divisibility rule of 10: The last digit must be zero. For example-100,450,2500,3010,5860 etc
Divisibility rule of 7: To know if a given number is divisible by 7, we will take the last digit of the number and double it. Then we will subtract the result from the rest of the number. If the resulting number is evenly divisible by 7, then the original number is also divisible by 7. For example: 2555, 5509,203, 287 etc
Lets check for 2555. double the last digit. 5 is doubled to 10. Then subtract 10 from 255 this gives 245. 245 is divisible by 7, so 2555 is divisible by 7.
this is the reason, divisibility rule of 7 is complicated as compared to other given number.
price of a belt and a hat.