All categories

3 years ago

Prove ABC~EDC ?

Mathematics

1 answer:

erastova [34]3 years ago

8 0

Answer:

AA similarity theorem

Step-by-step explanation:

we know that

<u>AA (Angle-Angle) Similarity</u> states that In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar

In this problem we have that

∠BCA=∠ECD ----> by vertical angles

∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)

therefore

Triangles ABC and EDC are similar by AA similarity theorem

You might be interested in

Use the formula for the area of a rectangle, A = lw, where A represents the area, l represents the length, and w represents the

IgorLugansk [536]

Answer:

Area = length × breadths

5 0

3 years ago

Bethany paid $408.75 for a pair of diamond stud earrings. The sale price was $375. What is the Percent of Sales Tax she paid for

9966 [12]

Answer:

She paid 9% of sales tax

Step-by-step explanation:

The sale price of diamond = $375

Let x be percent of sales tax

So, amount of tax = $x\% \times 375 = \frac{x}{100} \times 375 =3.75x$

So, Amount including tax = 375+3.75x

We are given that Bethany paid $408.75 for a pair of diamond stud earrings.

So, 375+3.75x=408.75

3.75x=408.75-375

$x=\frac{408.75-375}{3.75}$

x=9

Hence She paid 9% of sales tax

5 0

3 years ago

A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

6 0

3 years ago

Here are some photos of my math home work please show some work.

Reika [66]

Answer:

I can answer 2-19.

Step-by-step explanation:

The first equation is x=0.

the second equation has no solution.

4 0

3 years ago

Help please I really really need help

dem82 [27]

Answer:

In 22 minutes the remaining cell phone battery will be unknown.

In a of minutes the remaining cell phone battery will be 50%.

Step-by-step explanation:

7 0

3 years ago