Explanation

1) 3x - 6y = 15  

2) -2x + 4y = -10

Step 1: Multiply equation (2) by 1.5 to align y coefficients with equation (1):

-2x + 4y = -10  

× 1.5 →  

-3x + 6y = -15

Step 2: Add equation (1) and the modified equation (2):

(3x - 6y) + (-3x + 6y) = 15 + (-15)  

0 = 0

This means the two equations are dependent — they represent the same line.

Step 3: Express x in terms of y from equation (1):

3x - 6y = 15  

3x = 15 + 6y  

x = (15 + 6y) / 3 = 5 + 2y

Since infinitely many solutions exist, pick y = 0:

x = 5 + 2(0) = 5  

y = 0

x = 5, y = 0

Explanation

Time at original speed = 240 / x  

Time at increased speed = 240 / (x + 4)  

Given:  

240/x - 240/(x + 4) = 0.5

Multiply through by x(x + 4) to eliminate denominators:

240(x + 4) - 240x = 0.5x(x + 4)  

240x + 960 - 240x = 0.5x² + 2x  

960 = 0.5x² + 2x  

Multiply both sides by 2:  

1920 = x² + 4x  

x² + 4x - 1920 = 0

Solve the quadratic:  

x² + 4x - 1920 = 0  

Using quadratic formula:  

x = [-4 ± √(16 + 7680)] / 2  

x = [-4 ± √7696] / 2  

√7696 ≈ 87.7  

x ≈ (-4 + 87.7)/2 ≈ 83.7/2 ≈ 41.85

Approximate correct option is 40 km/h

Explanation

We are given:

- 3rd term = 8  

- 6th term = 17  

- We need to find the 8th term.

Formula for nth term of an AP:  

Tₙ = a + (n - 1)d

Let’s form equations:

1) T₃ = a + 2d = 8  

2) T₆ = a + 5d = 17  

Subtract (1) from (2):  

(a + 5d) - (a + 2d) = 17 - 8  

⇒ 3d = 9  

⇒ d = 3  

Now plug back to find a:  

a + 2(3) = 8  

⇒ a + 6 = 8  

⇒ a = 2

Now find the 8th term:  

T₈ = a + 7d = 2 + 7(3) = 2 + 21 = 23

Explanation

Let's try to find the consistent difference between numbers:

- 54 → 43 → difference = -11  

- 43 → 34 → difference = -9  

- 34 → 26 → difference = -8  

- 26 → 22 → difference = -4  

- 22 → 19 → difference = -3  

- 19 → 18 → difference = -1

The differences are not follow a regular pattern.

Now assume correct pattern:  

Try subtracting odd numbers in decreasing order:

- 54 - 11 = 43  

- 43 - 9 = 34  

- 34 - 7 = 27  

- 27 - 5 = 22  

- 22 - 3 = 19  

- 19 - 1 = 18

So if the intended pattern was subtracting odd numbers in sequence (11, 9, 7, 5, 3, 1):

The correct sequence should be:  

54, 43, 34, 27, 22, 19, 18

So the number 26 in the original sequence is wrong.  

It should have been 27 instead of 26.

Correct wrong number: 26  

Correct sequence: 54, 43, 34, 27, 22, 19, 18

Explanation

2√(x + 2) = 3√2

Step-by-step solution:

Step 1: Divide both sides by 2

√(x + 2) = (3√2)/2

Step 2: Square both sides

x + 2 = [(3√2)/2]²  

= (9 × 2) / 4  

= 18 / 4  

= 4.5

Step 3: Subtract 2 from both sides

x = 4.5 − 2  

x = 2.5

Explanation

Let the number be x.  

40% of x = 380  

⇒ (40/100) × x = 380  

⇒ 0.4x = 380  

⇒ x = 380 ÷ 0.4  

⇒ x = 950

Explanation

11 + 8 = 19

19 + 10 = 29

29 + 12 = 41

41 + 14 = 55.

Explanation

Area = Length × Width

30 = 5 × Width

Width = 30 / 5

Width = 6

Explanation

Explanation

A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere, which means the sphere is inscribed in the cylinder.

The diameter of the sphere is equal to the diameter of the circular base of the cylinder, which is 2r cm.