Explanation

Supplementary angles add up to 180°. Given:

One angle = 122°

Let the other angle be x. Then:

x + 122° = 180°

Subtract 122° from both sides:

x = 58°

Explanation

The surface area of a sphere is given by the formula: 4πr².

Substituting r = 7 cm, we get 4 × 3.1416 × (7)² = 616 cm².

Explanation

Vertical angles are equal. Given:

80° = 4x

Divide both sides by 4:

x = 80° / 4

x = 20°

Explanation

The traveler covers:

First journey: x km

Second journey: y km

Third journey: x km

Total distance = x + y + x = 2x + y

Explanation

Given:

Sum of numbers = -8

Product of numbers = 15

The algebraic expression representing this is:

x^2 - (sum)x + (product) = 0

x^2 - (-8)x + 15 = 0

x^2 + 8x + 15 = 0

The correct answer is: x^2 + 8x + 15

Explanation

A sphere is a 3D (three-dimensional) shape because it has depth, along with height and width.

Circle, rectangle, and triangle are 2D (two-dimensional) shapes as they have only length and width.

Explanation

1 / (2/3)

= 1 × (3/2)

= 3/2

Explanation

When you multiply two numbers with different signs (one positive and one negative), the result is always negative. In this case, (-2) multiplied by (+3) equals (-6).

Here's the calculation:

(-2) x (+3) = -2 x 3 = -6

So, the correct answer is -6.

Explanation

P(A) is the power set of A = {1, 2}, which includes all subsets: ∅, {1}, {2}, {1, 2}.

So, {2} is one of the subsets, hence it is an element of P(A).

Explanation

Cost per student: 1 3/8 = 11/8

Total amount: 13 3/4 = 55/4

Now, divide the total amount by the cost per student:

Number of students = Total amount ÷ Cost per student

= (55/4) ÷ (11/8)

= (55/4) × (8/11)

= 55 × 2 / 11

= 110 / 11

= 10