The pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula a2 + b2 = c2. if a is a rational number and b is a rational number, why could c be an irrational number?

the square of rational numbers is irrational, and sum of two irrational numbers is irrational.

the product of two rational numbers is rational, and the sum of two rational numbers is irrational.

the left side of the equation will result in a rational number, which is a perfect square.

the left side of the equation will result in a rational number, which could be a non-perfect square.

Last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.

Step-by-step explanation:

Given that the Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula

we have to tell if a is a rational number and b is a rational number, why could c be an irrational number.

As, a and b both are rational then their squares are also rational and the addition of two rational numbers are also rational.

Therefore, the only option which gives the c irrational is the square root of .

Hence, last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet