Explanation

Given:

g : h = 8 : 9

h : i = 9 : 12

To find the combined ratio g : h : i, we need to make the ratio of h the same in both.

g : h = 8 : 9

h : i = 9 : 12

Since h has the same ratio in both (9), we can directly combine:

g : h : i = 8 : 9 : 12

Explanation

To factorize the quadratic expression x² - 12x + 35, we need to find two numbers whose product is 35 and whose sum is -12.

The numbers are -7 and -5, since (-7) * (-5) = 35 and (-7) + (-5) = -12.

So, the factorization is:

x² - 12x + 35 = (x - 7)(x - 5)

Explanation

Let's calculate the value of 3x – 4y – z using x = 2, y = -3, z = -5:

3(2) – 4(-3) – (-5)

= 6 + 12 + 5

= 23

Explanation

The greatest 3-digit number is 999, and the smallest 3-digit number is 100.

Their product: 999 × 100 = 99900.

Explanation

Pie chart represents data using sectors of a circle, where each sector shows a proportion of the whole.

It is commonly used for percentage or proportional comparisons in statistics.

Explanation

To find the area of the road, we need to find the area of the garden and subtract the area of the inner garden (without the road).

Garden area = Length * Width

= 75 cm * 82 cm

= 6150 cm²

Inner garden dimensions:

Length = 75 cm - 2 * 5 cm = 65 cm

Width = 82 cm - 2 * 5 cm = 72 cm

Inner garden area = 65 cm * 72 cm

= 4680 cm²

Road area = Garden area - Inner garden area

= 6150 cm² - 4680 cm²

= 1470 cm²

Explanation

Let's solve it step by step:

3(2x - 5) + 2

Distribute the 3:

3 × 2x = 6x

3 × (-5) = -15

Now add 2 to the result:

6x - 15 + 2 = 6x - 13

Explanation

Given x varies inversely to y:

x ∝ 1/y

x = k/y

When x = 3, y = 12:

3 = k/12

k = 36

So, the equation becomes:

x = 36/y

When x = 6:

6 = 36/y

y = 36/6

y = 6

Explanation

Given the equation:

log3 (4x + 3) = 3

We can rewrite this in exponential form:

3³ = 4x + 3

27 = 4x + 3

Subtracting 3 from both sides:

24 = 4x

Dividing both sides by 4:

x = 6

Explanation

Given:

Height of the hill = 240 m

Angle of depression to the top of the minaret = 30°

Angle of depression to the bottom of the minaret = 60°

Let's denote the distance from the base of the hill to the minaret as x.

For the bottom of the minaret (60° angle):

tan(60°) = 240 / x

√3 = 240 / x

x = 240 / √3

For the top of the minaret (30° angle):

tan(30°) = (240 - h) / x

1/√3 = (240 - h) / (240 / √3)

Simplifying:

240 - h = 240 / 3

240 - h = 80

h = 160