Explanation

Explanation

Given the points (x + 5, 8) and (9, y - 6) are equal, we can set up the equations:

x + 5 = 9 ... (1)

8 = y - 6 ... (2)

Solving (1):

x = 9 - 5

x = 4

Solving (2):

y = 8 + 6

y = 14

The values of x and y are x = 4 and y = 14.

Explanation

The given statement:

If a : b = c : d then a : c = b : d

This is known as the Alternendo theorem.

The Alternendo theorem states that if a/b = c/d, then a/c = b/d.

Explanation

The graph of x = a is a vertical line.

It is perpendicular to the y-axis, which is vertical.

Explanation

The orthocenter is the point where the three altitudes of a triangle intersect.

An altitude is a perpendicular line from a vertex to the opposite side (or its extension).

Explanation

In a triangle, if two angles are congruent, their opposite sides are also congruent (equal in length).

This is a property of isosceles triangles, where equal angles face equal sides.

Explanation

A bisector of an angle divides the angle into two equal parts.

It is a line or ray that starts from the angle's vertex and splits it evenly.

Explanation

A histogram visually shows the frequency distribution using bars representing intervals.

It helps to understand the distribution and spread of continuous data.

Explanation

Discount means a reduction in the marked or original price of an item.

It is commonly offered during sales, promotions, or special offers to attract buyers.

Explanation

Given the proportion:

40 : 60 = 50 : a

Let's solve for 'a' using the proportion:

40/60 = 50/a

40a = 50 × 60

40a = 3000

a = 3000 / 40

a = 75