Explanation

 Calculate the discount amount:

Original Price - Selling Price = Discount

$1500 - $1200 = $300

Calculate the discount percentage:

(Discount / Original Price) * 100%

($300 / $1500) * 100%

0.20 * 100% = 20%

Explanation

 The point (0, -7) lies on the Y-axis because the x-coordinate is 0, and only the y-coordinate has a non-zero value (-7). Points on the Y-axis do not belong to any specific quadrant but are considered as lying directly on the axis itself.

Quadrant I contains points where both x and y are positive.

Quadrant II contains points where x is negative and y is positive.

Quadrant III contains points where both x and y are negative.

Quadrant IV contains points where x is positive and y is negative.

Since the x-coordinate is 0, this point is on the Y-axis.

Explanation

Given:
$x^2 - 3x - 10 = 0$

We are told that one factor is $(x - 5)$.
So, we divide the quadratic by $(x - 5)$ to find the other factor:

Method:
Use factoring:

We want two numbers that multiply to $-10$ and add to $-3$.
These numbers are -5 and 2.

Thus,

$$x^2 - 3x - 10 = (x - 5)(x + 2)$$

Explanation

Let "x" be the number.

Three-fourths of the number is (3/4)x.

When we multiply the number by three-fourths of itself,

we get: x * (3/4)x = 10700.

This simplifies to (3/4)x² = 10700.

Solving for x, we get x = 70. 

Explanation

 The result of 50−15.5 is 34.5.

Explanation

Given:

Time taken by A and B to complete the work = 12 days

Time taken by B and C to complete the work = 8 days

Time taken by C and A to complete the work = 6  days

Formulae used:

Time = Total work / Efficiency

Calculation:

Let us assume the total work is 1 unit.

⇒ A and B complete 1 unit work in 12 days → (A and B)'s 1 day's work = 1/12​

⇒ B and C complete 1 unit work in 8 days → (B and C)'s 1 day's work = 1/8​

⇒ A and C complete 1 unit work in 6 days → (A and C)'s 1 day's work = 1/6​

Adding everyone's 1 day's work:

$\Rightarrow 2(A+B+C)=(1/12+(1/8)+(1/6)$

⇒A+B+C=9/48​

= A, B, and C's 1 day's work = 9/48

⇒ B's 1 day's work = $(A+B+C)-(A+C)$

⇒ B's 1 day's work =(9/48)−(1/6) = 9-8 x/48 = 1/ 48 ​

​

⇒ B completes 1/48​ of the work in 1 day.

Therefore, B alone will take 48 days to complete the work.

Explanation

Given:

A sphere of radius 3 cm

Formula Used:

Total surface area of sphere = $4\times 22/7\times r^2$; where r = radius of sphere

Calculation:

⇒ Total surface area of sphere = $4\times 22/7\times 3^2$

⇒ Total surface area of sphere = $\frac{792}{7}=113.4{\text{cm}}^2\approx 113{\text{cm}}^2$

∴ required Total surface area of sphere = 113cm2

Explanation

Cost of 15 toys = Rs. 234

Cost of 1 toy = Rs. 234 ÷ 15 = Rs. 15.60

Cost of 35 toys = Rs. 15.60 x 35 = Rs. 546

So, the correct answer is: Rs. 546

Explanation

48 → 45 (−3)

45 → 40 (−5)

40 → 33 (−7)

33 → 24 (−9)

Now continue the pattern: next difference should be −11

24 − 11 = 13

Explanation