All categories

2 years ago

If PN=14, NO=20, PO=16, QR=55, and SR=44, find the perimeter of ΔQRS. Round your answer to the nearest tenth if necessary

Mathematics

1 answer:

vfiekz [6]2 years ago

7 0

Answer:

The perimeter of QRS is 137.5

Step-by-step explanation:

From the given interval angles, we can see that the two triangles are congruent

so it is expected that the ratios of their corresponding sides are equal

this is because; 83 + 53 + 44 = 180

Now, let us work with the side facing the angle marked 53 in both triangles

For the smaller, we have the measure as 16

for the bigger, we have the measure as 44

So the scale factor here is 44/16 = 11/4 = 2.75

We have to multiply the measure of the sides of the smaller triangle by 2.75 to get that of the bigger triangle

in similar vein, we have to multiply the perimeter we have in the smaller triangle by 2.75 to get that of the bigger triangle

The perimeter of the smaller would be the sum of the side lengths

we have this as;

14 + 20 + 16 = 50

So the perimeter of the bigger triangle would be;

2.75 * 50 = 137.5

You might be interested in

L || m

Alona [7]

Answer:

c. m∠1 + m∠6 = m∠4 + m∠6

Step-by-step explanation:

Given: The lines l and m are parallel lines.

The parallel lines cut two transverse lines. Here we can use the properties of transverse and find the incorrect statements.

a. m∠1 + m∠2 = m∠3 + m∠4

Here m∠1 and m∠2 are supplementary angles add upto 180 degrees.

m∠3 and m∠4 are supplementary angles add upto 180 degrees.

Therefore, the statement is true.

b. m∠1 + m∠5 = m∠3 + m∠4

m∠1 + m∠5 = 180 same side of the adjacent angles.

m∠3 + m∠4 = 180, supplementary angles add upto 180 degrees.

Therefore, the statement is true.

Now let's check c.

m∠1 + m∠6 = m∠4 + m∠6

We can cancel out m∠6, we get

m∠1 = m∠4 which is not true

Now let's check d.

m∠3 + m∠4 = m∠7 + m∠4

We can cancel out m∠4, we get

m∠3 = m∠7, alternative interior angles are equal.

It is true.

Therefore, answer is c. m∠1 + m∠6 = m∠4 + m∠6

3 0

3 years ago

uranmaximum [27]

Answer:

x = 2515

Step-by-step explanation:

5000 = 2x - 30

2800 = x

<h2>have a great day! I hope this helps! </h2>

4 0

2 years ago

Both the La Plata river dolphin (Pontoporia blainvillei) and

Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$