Explanation

 The subject is "One", which is singular.

"Of the boys" is a prepositional phrase and does not affect the verb.

Explanation

The Scissors' handle just snapped off.

Scissors is a plural noun (even though it refers to a single object).

To show possession for a plural noun ending in s, we add only an apostrophe: Scissors' handle.

Explanation

Total parts = 2 + 3 + 7 = 12

Each part = 129,000 ÷ 12 = 10,750

Largest share = 10,750 × 7 =  75,250

Explanation

"China is on the way to becoming one of the strongest economies in the world."

On the way to is followed by a noun or gerund (verb+ing), so "becoming" is correct.

Explanation

Work = Men × Days = 120 × 30 = 3600 man-days

If 80 men work: 3600 ÷ 80 = 45 days

Explanation

Explanation

 If each value of 'x' determines exactly one value of 'y', then:

The variable y depends on x

For every input x, there is a unique output y

This is the definition of a function in mathematics.

Explanation

The point where two boundary lines of a solution region (in linear programming or systems of inequalities) intersect is called a  Vertex

Explanation

Step 1: Identify the first term and common difference

• First term $a = 7$

• Common difference $d=11-7=4$

Step 2: Use the formula for the n
th term of an A.P.:

$$a_n = a + (n - 1)d$$

For the 21st term:

$$a_{21} = 7 + (21 - 1) times 4 = 7 + 20 times 4 = 7 + 80 = 87$$

Explanation

$$\text{Fans}\propto \text{Machines}\times \text{Days}$$

Let $x$ be the number of fans produced in 12 days with 16 machines.

Set up the proportion:

560/20×7=x/16×12​

560/140​=x/192​
4=x/192​⇒x=4×192=768​