Suppose A and B represent linear expressions.If A + B = 2x -2 and A

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

Jack is learning to save, spend, and give his money away. He has determined to give away 10% of his summer earnings. If he gives

Strike441 [17]

Answer:

$2,560

Step-by-step explanation:

Just multiply 256 by 10, and you get his money earned.

8 0

3 years ago

What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 ?

Natali5045456 [20]

Answer:

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -2 , 7)

To Find:

Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?

Solution:

$x-6y=42$ ..................Given

which can be written as

$y=mx+c$

Where m is the slope of the line

∴ $y=\dfrac{x}{6}-7$

On Comparing we get

$Slope = m = \dfrac{1}{6}$

The Required line is Perpendicular to the above line.

So,

Product of slopes = - 1

$m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6$

Slope of the required line is -6

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,

i.e equation in point - slope form

$(y-y_{1})=m(x-x_{1})$

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get

$(y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line$

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

3 0

3 years ago

What is 30% of 25.45?

Alekssandra [29.7K]

Answer:

7.635

Step-by-step explanation:

i hope it helps:)

3 0

3 years ago

Read 2 more answers

Can I please get some help!!!

Firlakuza [10]

Answer:

1-True

2-True

3-False

Step-by-step explanation:

1- All negative numbers are <0 and to the left on a number line. All positive numbers are >0 and are on the right of a number line.

2- When the number line moves to the right, the number gets larger.

3- You could have a negative number that is smaller than another number, but its distance from 0 could be greater. For example, -12 < 2. However, -12 is 12 places away from zero on the number line, but the number 2 is only two places away from zero on the number line.

3 0

3 years ago

Suppose A and B represent linear expressions.If A + B = 2x -2 and A - B = 4x- 8, find A and B.