'calcula que signo tiene el producto de cien números enteros, sabiendo que 27 de ellos son positivos y que ninguno es cero''.

I need help to fill in the blanks.. please

Murljashka [212]

Answer:

Part a) alternate interior angles theorem

Part b) vertical angles theorem

Part c) AA Similarity theorem

Part d) triangle ABC is similar with triangle EDC

Part e) The length side b is 3 cm

Step-by-step explanation:

Part a) we know that

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.

In this problem

The transversal is the segment BD and the parallel lines are AB and DE

so

$m\angle 1=m\angle 4$ ----> by alternate interior angles theorem

Part b) we know that

Vertical Angles Theorem states that vertical angles are congruent. Vertical Angles are the angles opposite each other when two lines cross.

In this problem, the two lines that cross are BD and AE

so

$m\angle 5=m\angle 6$ ----> by vertical angles theorem

Part c) we know that

The AA Similarity Theorem states: If two angles of one triangle are congruent to two corresponding angles of another triangle, then the triangles are similar

In this problem

triangle ABC is similar with triangle EDC by AA Similarity Theorem

Because

$m\angle 1=m\angle 4$ ----> by alternate interior angles

$m\angle 5=m\angle 6$ ----> by vertical angles

Part d) triangle ABC is similar with triangle EDC by AA Similarity Theorem

see the explanation Part c)

Part e) Find the length of side b

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

we have that

triangle ABC is similar with triangle EDC

so

Applying proportion

$\frac{BC}{DC}=\frac{AC}{EC}$

substitute the given values

$\frac{2}{DC}=\frac{5}{7.5}$

solve for DC

$DC=2(7.5)/5=3\ cm$

therefore

The length side b is 3 cm

6 0

3 years ago

How many different rectangles can you make using 12 toothpicks, use all 12 each time

Savatey [412]

You can essentially make 3 rectangles out of the 12 toothpicks. Remember, squares are technically rectangles.

1. 1 by 5
2. 4 by 2
3. 3 by 3

8 0

3 years ago

Read 2 more answers

What is the solution to the inequality x + 4 + 2x ≤ 20 + 5x – 32

Illusion [34]

Answer:

x+4+2x = 20+5x-32

Step-by-step explanation:

x+4+2x

= 3x + 4

20+5x-32

= 20-32+5x

= 5x-12

Finding the value of X

3x+4 = 5x-12

= 4+12 = 5x-3x

= 16 = 2x

= 16/2 = X

= 8 = X

By putting the value of X in the equation

(3×8)+4

= 24 +4

= 28

(5×8)-12

= 40-12

28

28 = 28

so the X+4+2x < 20+5x-32 is wrong

5 0

3 years ago

You drive to Atlanta you travel for hours at a speed of 60 mph when you return home you drive slower how long will it take you t

adelina 88 [10]

Answer: if you drive 4 hours there then it would be 6 hours back.

Step-by-step explanation:

7 0

4 years ago

In the function, 9 (2-) = 9 - 5x, what is the value of g (3)?

vekshin1

Answer: 53

Step-by-step explanation:

3 0

3 years ago