In the image, as denoted by similar sides OP and MN, we can conclude that the 2 triangles are similar triangles. To look for the value of x (which we can substitute later to find the length of segment LP), we relate the relations of segments LO and LP to segments LM and LN. This relation is shown below:

LO/LP = LM/LN

22 / x+12 = 30 / x+12 + 5
22 / <span>x+12 = 30 / x+17
</span>
Cross-multiplying:
30x + 360 = 22x + 374

Isolating x to one side of the equation by subtracting 22x and 360 from both sides:

30x + 360 - 360 - 22x = 22x + 374 - 360 - 22x
8x = 14
x = 1.75

Since we now have the value of x, we substitute this to the equation of LP:
LP = x + 12
LP = 1.75 + 12
LP = 13.75

Therefore the value of LP is 13.75 in.

8 0

2 years ago

A written explanation solving the question how much fluid is needed using the Pythagorean method and finding the area of the tri

Alecsey [184]

Answer:

793 liters of washing fluid is needed

Step-by-step explanation:

step 1

Find the slant height of the triangular faces of pyramid

we know that

The lateral area of a square pyramid is equal to the area of its four triangular faces

$LA=4[\frac{1}{2}bl]$

where

b is the base of triangle (is the same that the length of the square base)

l is the slant height

To find out the slant height we need to apply the Pythagorean Theorem

$l^2=(b/2)^2+h^2$

we have

$b=35.42\ m$

$h=21.64\ m$

substitute

$l^2=(35.42/2)^2+21.64^2$

$l^2=781.9337$

$l=27.96\ m$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bl]$

we have

$l=27.96\ m$

$b=35.42\ m$

substitute

$LA=4[\frac{1}{2}(35.42)(27.96)]$

$LA=1,980.6864\ m^2$

step 3

Find out how much window washing fluid is needed

we know that

2 L of washing fluid cover 5 square meters

using proportion

$\frac{2}{5}\ \frac{L}{m^2}=\frac{x}{1,980.6864}\ \frac{L}{m^2}\\\\x=1,980.6864(2)/5\\\\x= 792.27\ L$

Round up

793 liters of washing fluid is needed

6 0

3 years ago

Can someone please help me with this

lana [24]

Answer:

its 55

Step-by-step explanation:

you minus 125 from 180 to get 55

4 0

2 years ago

Read 2 more answers

Need help with 15, 16, 17 and 18. Please provide an explanation. Also list in least to greatest. Thank you in advance!

EleoNora [17]

15. 99%, 0.95, 5/9, 9.5%
Make all decimals: .99, .95, .55, .095
List: Zero is less than 9 or 5 so it's first than 5 and than 9, you have two 9's so 5 is less than 9: .095, .55, .95, .99

16. 3/8, 50%, 0.35, 38%
Same steps: .375, .50, .35, .38
3 is less than 5 and 5 is less than 8 or 7 so: .35, .375, .38, .5

And do the same thing for the other two problems :)

8 0

3 years ago