What is the simplified form of the expression? 2√18-5√32

5 sqrt 2

Step-by-step explanation:

Using the rule of radicals

sqrt a ×  sqrt b ⇔ sqrt ab

Simplify each radical

5 sqrt 8

= 5 sqrt 4(2)

= 5 × sqrt 4 × sqrt 2

= 5 × 2 × sqrt 2  = 10 sqrt 2

sqrt 18

= sqrt 9(2)

=  sqrt 9 × sqrt 2  = 3 sqrt 2

Putting it all together

10 sqrt 2 - 3 sqrt 2 - 2 sqrt 2

Collect like terms

=  sqrt 2 (10 - 3 - 2 ) = 5 sqrt 2

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: