Is there a chart involved
Answer:
Options (1), (3) and (5)
Step-by-step explanation:
Equation that represents the relationship between the three sides of a triangle is,
a² + b² = c²
Where c = longest side of the triangle
If the length of the given sides satisfy the equation, triangle formed by the sides will be a right triangle.
Option A.
27 in, 36 in, 45 in
(45)² = (27)² + (36)²
2025 = 729 + 1296
2025 = 2025
True.
Option 2.
18 in, 22 in, 28 in
(28)² = (18)² + (22)²
784 = 324 + 484
784 = 808
False.
Option 3
10 in, 24 in, 26 in
(26)² = (10)² + (24)²
676 = 100 + 576
676 = 676
True.
Option 4
20 in, 21 in, 31 in
(31)² = (20)² + (21)²
961 = 400 + 441
961 = 841
False.
Option 5
28 in, 45 in, 53 in
(53)² = (28)² + (45)²
2809 = 784 + 2025
2809 = 2809
True.
Therefore, Options (1), (3) and (5) will be the correct options.
Answer:
1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)
2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)
3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)
4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)
Step-by-step explanation:
To obtain the answer to the question, first let us factorise each expression. This is illustrated below:
1. 15x^7y^2 + 4x^3
Common factor is x^3, therefore the expression is written as:
x^3(15x^4y^2 + 4)
2. 15x^7y^2 + 3x
Common factor is 3x, therefore the expression is written as:
3x(5x^6y^2 + 1)
3. 15x^7y^2 + 6xy
Common factor is 3xy, therefore the expression is written as:
3xy(5x^6y + 2)
4. 15x^7 + 10y^2
Common factor is 5, therefore the expression can be written as:
5(3x^7 + 2y^2)
X + 8 >= 14
x >= 14 -8
x> = 6
Answer:
a = -19
b = -35
c = -180
d = -81
Step-by-step explanation: