Explanation

To find the degree of the polynomial:

Add the exponents of x and y:

Degree = exponent of x + exponent of y

= 3 + 2

= 5

Explanation

To find the time it takes for the amount to reach Rs. 784:

Use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A = 784, P = 700, r = 4% = 0.04, n = 1 (compounded annually)

784 = 700(1 + 0.04/1)^(1t)

Divide both sides by 700:

1.1286 ≈ (1.04)^t

Take the logarithm of both sides:

t ≈ log(1.1286) / log(1.04)

≈ 3

So, it will take approximately:

3 years

Explanation

To find the perimeter of the square-shaped field:

First, find the side length of the square:

Area = side²

2704 = side²

Take the square root:

side = √2704

side = 52

Now, find the perimeter:

Perimeter = 4 × side

= 4 × 52

= 208

Explanation

√15129 = 123, which has 3 digits.

So, the number of digits in the square root of 15129 is 3.

Explanation

In negative fractions, the greater the denominator (for the same numerator), the closer the fraction is to zero, making it larger.

Comparing:

• -1/3 = -0.333
• -2/3 = -0.666
• -4/9 = -0.444
• -5/6 = -0.833

-1/3 is the greatest among them as it is closest to zero.

Explanation

When 5/3 is divided, it gives 1.666..., where 6 repeats infinitely.

Since the decimal never ends but follows a repeating pattern, it is non-terminating and recurring.

Explanation

A monomial is an algebraic expression with only one term (no addition or subtraction signs).

4ab²c² is a single term, so it is classified as a monomial.

Explanation

Vertical angles are always equal. Given that one angle is 2x and the other is 80°, we set up the equation:

2x = 80°

Solving for x:

x = 80° / 2 = 40°

Explanation

To find the surface area of the cylinder:

Use the formula:

Surface Area = 2πr(h + r)

where r = 7 cm and h = 33 cm:

Surface Area = 2π(7)(33 + 7)

= 2π(7)(40)

≈ 2 × 3.14 × 7 × 40

≈ 1760 cm²

Explanation

To find (A ∪ B)':

First, find A ∪ B:

A ∪ B = {2, 3, 4} ∪ {1, 3, 5}

= {1, 2, 3, 4, 5}

Now, find the complement of A ∪ B:

(A ∪ B)' = U - (A ∪ B)

= {1, 2, 3, 4, 5} - {1, 2, 3, 4, 5}

= {}