See the picture attached with letters to better understand the problem

in the right triangle ABD
applying the Pythagoras theorem
8²=AD²+(x+4)²-----> AD²=64-(x+4)²------> equation 1

in the right triangle ADC
applying the Pythagoras theorem
12²=AD²+(2x+1)²-----> AD²=144-(2x+1)²------> equation 2

equate equation 1 and equation 2
64-(x+4)²=144-(2x+1)²-------> 64-[x²+8x+16]=144-[4x²+4x+1]
64-x²-8x-16=144-4x²-4x-1
4x²-x²-8x+4x=144-1-64+16
3x²-4x=95
3x²-4x-95=0

using a graph tool----> to resolve the second order equation
see the attached figure N 2
the solution is
x=6.33

the answer is
x=6.33 units

3 0

3 years ago

13. Given the volume, V, of the rectangular prism below, find h, the height of the prism. V = (x ^ 2 + 2x)/(x + 1) l= 2x + 4 w=

NikAS [45]

Given:

Volume of a rectangular prism is:

$V=\dfrac{x^2+2x}{x+1}$

Dimensions of the rectangular prism are:

$l=2x+4$

$w=\dfrac{x}{8}$

To find:

The height of the rectangular prism.

Solution:

The volume of a rectangular prism is:

$V=l\times w\times h$

After substituting the values, we get

$\dfrac{x^2+2x}{x+1}=(2x+4)\times \dfrac{x}{8}\times h$

$\dfrac{x(x+2)}{x+1}=\dfrac{2x(x+2)}{8}\times h$

$\dfrac{x(x+2)}{x+1}\times \dfrac{8}{2x(x+2)}=h$

$\dfrac{1}{x+1}\times \dfrac{8}{2}=h$

$\dfrac{4}{x+1}=h$

Therefore, the correct option is C.

8 0

3 years ago

HELP PLEASE

Helga [31]

7.
Discounted price X
————————— = ———
Original Price 100

45 x
—- = —-
72 100

Cross multiply

45 times 100= 4500
72 times x= 72x

72x=4500

Divide

4500/72= 62.5%

4 0

3 years ago

PLZ HELP QUICK

Anvisha [2.4K]

Answer:

Step-by-step explanation:

First you have to do everything in the brackets, or [ ]. -7+-3--8 is equivalent to 8-3-7, which equals -2. After that you have to do the braces, or {}. That is -5--2, which is the same thing as 2-5, which equals -3. Finally, you can finish it out. -4--2--3 is equivalent to 3+2-4, which equals 1. Hope this helps!

3 0

3 years ago

What expression is equivalent to ( X 3 ) 4 ?​

What expression is equivalent to ( X 3 ) 4 ?