Fill in the blank with the missing integer.

The lengths of the diagonals of rectangle ABCD intersect at E. If AE =x+4 and CE= 3x-12. What is the length of BD?

swat32

Answer:

DB = 24

Step-by-step explanation:

First, note that the diagonals of a rectangle are equal and bisect each other. In other words, DB = CA and CE = EA and DE = BE.

Also, AE + CE = CA

So, using this, we can write this equation:

AE = CE

x + 4 = 3x -12

Subtract 4 from both sides.

x = 3x -16

Subtract 3x from both sides.

-2x = -16

Divide both sides by -2

x = 8

Then, substitute this into AE + CE = CA

x + 4 + 3x - 12 =

8 + 4 + 24 - 12 = 24

Then, because CA = DB,

DB = 24

I hope this helps! Feel free to ask any questions! :)

5 0

2 years ago

Read 2 more answers

Graph F(x)=32x+2. Please

olga2289 [7]

Answer:

The required graph is shown below:

Step-by-step explanation:

Consider the provided graph $f(x)=32x+2$

The above function is a linear function.

We can draw the graph of the linear function with the help of two points.

Substitute x = 0 in $f(x)=32x+2$

$f(0)=32(0)+2$

$f(0)=2$

Hence, the coordinates are (0,2)

Substitute f(x) = 0 in $f(x)=32x+2$

$0=32x+2$

$32x=-2$

$x=-0.0625$

Hence, the coordinates are (-0.0625,0)

Now join the above points.

The required graph is shown below:

5 0

2 years ago

Read 2 more answers

To express a number in one unit as an equivalent value of another unit

ddd [48]

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equal 1 foot.

4 0

1 year ago

What number + (−56)=12 <br> How do I do this?

Mars2501 [29]

Answer:

Step-by-step explanation:

x+(-56)=12

exclude "x"

x=56+12

x=68

7 0

2 years ago

Read 2 more answers

Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.

nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

$\sin (x+y) = 3\sin (x-y)$

Using the identities

$\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\$

we get

$\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y$

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

$3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}$

7 0

3 years ago