Let ABC be a right triangle (∠C=90°). Let CH be the altitude of the triangle ABC.

LM=9, NR=16, SR=8. Find the perimeter of △SMP.

Amanda [17]

Answer:

<h2>perimeter of △SMP = 25</h2>

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM, NP = PR = <u>MS</u><u> = 8</u>

Also since LM = MN, MN = 9

From △SRP, SR = RP = <u>PS = 9</u>

Also SR =<u> MP = 8</u>

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

5 0

4 years ago

I NEED HELP ASAP

antoniya [11.8K]

a) The equation $V(m) = 8400 - 560\cdot m$ represents the discharge of the Grand Prismatic Spring.

b) The discharge of the Grand Prismatic Spring takes 15 minutes.

c) The remaining quantity after 7 minutes is 4480 gallons.

d) The hardness of cardboard is 2.

<h3>How to apply concepts of linear functions</h3>

a) In this case, the volume of water ( $V$ ), in gallons, decreases <em>linearly</em> in time ( $m$ ), in minutes. Then, we could model the situation by using the following expression:

$V(m) = V_{o} - \dot V \cdot m$ (1)

Where:

$V_{o}$ - Initial volume, in gallons.
$\dot V$ - Discharge rate, in gallons per minute.

If we know that $V_{o} = 8400\,gal$ and $\dot V = 560\,\frac{gal}{min}$ , then the volume of the Grand Prismatic Spring is represented by this expression:

$V(m) = 8400 - 560\cdot m$ (2)

The equation $V(m) = 8400 - 560\cdot m$ represents the discharge of the Grand Prismatic Spring. $\blacksquare$

b) By (1) and $V(m) = 0$ we find the time required for discharge:

$m = \frac{0 - 8400}{-560}$

$m = 15\,min$

The discharge of the Grand Prismatic Spring takes 15 minutes. $\blacksquare$

c) The quantity of gallons remaining is found by evaluating the function for $m = 7$ :

$V(7) = 8400 - 560\cdot (7)$

$V(7) = 4480\,gal$

The remaining quantity after 7 minutes is 4480 gallons. $\blacksquare$

d) According to Mohs scale, the hardness of feldspar is 6. The statement indicates the following relationship, as there is a constant relationship between both hardnesses:

$y = 3\cdot x$ (3)