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**tony123**- Replies: 2

where x

and y

denote real numbers.

**tony123**- Replies: 14

1.Positive integers m and n satisfy

Find

2.Find the positive integer n such that

3.A trapezoid has side lengths

and in some order. Find its area4.A rectangle with integer side lengths has the property that its area minus 5 times its perimeter equals

Find the minimum possible perimeter of this rectangle.5.For real numbers a, b, and c, the roots of the polynomial

arithmetic progression. Find

KerimF wrote:

It seems you forgot to add the initial speed of the bullet.

I guess this speed is also assumed constant (no friction).

Im sorry v=58.8m/s

**tony123**- Replies: 4

A bullet with a mass of 20 grams is horizontally fired at a body with a mass of 100 grams, suspended by a string with a length of 6 meters, . The bullet comes to rest in the body. Find the vertical distance that the combined system of the body and the bullet moves after the collision

very good phrontister

**tony123**- Replies: 2

Olivia cut a rectangle into exactly nine squares. On inspection, he observed that the area of one square was 64 cm²

, the areas of two other squares were 16 cm²

, and the rest of them were 4 cm²

each.

What was the perimeter of the original rectangl

**tony123**- Replies: 2

The isosceles right-angled triangle ABC

has its right angle at C. D is an interior point of side BC such that the angle CDA

is 75°. Given that triangle ADC has unit area, prove that BD=2.

**tony123**- Replies: 9

The opposite sides of a convex hexagon

are parallel, the distances separating the parallel pairs of sides are equal,

and the angles at vertices A and D are right angles. Prove that the diagonals BE

and CF enclose an angle of

Thanks Bob great job

**tony123**- Replies: 3

Find, without calculus, the largest possible value of

(sin 5x + cos 3x)/(sin 4x + cos 4x)

**tony123**- Replies: 1

if the two roots of the equation

are elements of the interval find the interval of

There is an important theorem in the external bisector of an angle in a triangle

This link can help

https://www.youtube.com/watch?v=ZKM6EYeYOhk

**tony123**- Replies: 3

In ∆ ABC, AB =7, AC=5.An external bisector of

∠BAC intersects the circumcircle of

∆ABC at E. Let F be the foot of

perpendicular from E to line AB.

find AF

Now we can say great job

Thanks bob

There are some mistakes in your solution dear Bob

nice work

thanks Bob

**tony123**- Replies: 8

Find the real solutions of the two equations

(1)

(2)

**tony123**- Replies: 4

Prove that if two right-angled triangles

have the same perimeter and the same area,

then they are congruent.

I'm glad you liked these problems

For the acute angles problem,

Someone sent this solution hope you like it

https://www.youtube.com/watch?v=TZi-x7ctxrU

**tony123**- Replies: 4

find x

**tony123**- Replies: 0

Let

and be acute angles such that . Prove that .**tony123**- Replies: 1

In an acute-angled triangle ABC, a tangent is drawn to the inscribed circle, parallel to side BC. The tangent intersects side AC at point D. F is the orthogonal projection of point D onto the side BC. Show that AB=AD+BF

**tony123**- Replies: 1

1.solve in

|x+2|≥|x+1|

2.if find the valuo of

**tony123**- Replies: 11

hard

**tony123**- Replies: 4

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