Answer:
Rearrange the equations that result from use of the Pythagorean theorem.
Step-by-step explanation:
Transversal AB crossing parallel lines AD and BC makes supplementary interior same-side angles A and B. Since A = 90°, B must be 90°. The Pythagorean theorem then applies in the right triangles ABC and ABD.
We can use that theorem to write two expressions for AB^2:
BD^2 -AD^2 = AB^2 = AC^2 -BC^2
The middle expression, AB^2, isn't needed beyond this point. Adding (AD^2 -AC^2) to both sides of the equation gives the desired result:
BD^2 -AC^2 = AD^2 -BC^2
Answer:
Step-by-step explanation:
The sum of the ages of a Mother and her son is 78 , three years ago the mother is five times as old as the son, what is their present ages?
To solve this , let the age of the mother be x and the age of the son be y , from the first statement :
x + y = 78
Three years ago , the mother will be x- 3 and the son will be y - 3 , from the second statement:
x - 3 = 5 ( y-3)
x- 3 = 5y - 15
x - 5y = -12
The resulting equations are
x + y = 78
x - 5y = -12
This is called a simultaneous linear equation , that means it is a linear equation.
The side of a square is xcm , if the difference between the area and the perimeter is 12 , find the legth of its side.
Interpretation:
The formula for the area of a square is and the perimeter is 4l , from the question , we have
- 4x = 12
This is not a linear equation , it is simply a quadratic equation , so the situation is non linear
The expression that is a prime polynomial is:
B. .
<h3>What is a prime polynomial?</h3>
A prime polynomial is a polynomial that cannot be factored.
In this problem, item b gives a prime polynomial, as:
- In item a, 3 is a common factor, hence the polynomial can be factored.
- In item c, x is a common factor, hence the polynomial can be factored.
- In item d, the polynomial can be factored according to it's roots.
More can be learned about prime polynomials at brainly.com/question/26388060
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