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3 years ago

Why does the LL theorem hold for proving right triangles congruent?

Mathematics

2 answers:

Rufina [12.5K]3 years ago

5 0

B.) The right angle is included between the legs.

alina1380 [7]3 years ago

3 0

Answer:

(A) The legs in right triangles are equal.

Step-by-step explanation:

LL theorem or Leg-Leg theorem: The LL theorem is also known as the leg-leg theorem. It states that if the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent.

Thus, in order to prove that the two right triangles are congruent,w use the LL theorem which holds that The legs in right triangles are equal.

Hence, option A is correct.

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3 years ago

What is -1.2 times 1 1/5 divided by 3/10

djyliett [7]

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3 years ago

Please!!! Help!!! Brainliest of Right! it goes as 50 point in the end but i used 100 point if you help me i will help you!!

vekshin1

Answer:

2. 3.913 kg (3 dp)

3. light cream

4. 240 CoffeeStops

5. 7 CoffeeStops per square mile

6. 2,861 cups of coffee each day

Step-by-step explanation:

Given:

Skim milk density at 20 °C = 1.033 kg/l
Light cream density at 20 °C = 1.012 kg/l
1 liter = 0.264 gallons

Question 2

$\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}$

Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)

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Question 3

Given:

Volume of liquid = 9 liters
Mass of liquid = 9.108 kg

$\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}$

Therefore, the container holds light cream.

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Question 4

Given:

15 CoffeeStops per 100,000 people
Population of Manhattan ≈ 1,602,000 people

$\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}$

Therefore, there are 240 CoffeeStops.

---------------------------------------------------------------------------------------------

Question 5

Given

Manhattan ≈ 34 square miles

$\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}$

Therefore, the density of CoffeeStops is 7 per square mile.

---------------------------------------------------------------------------------------------

Question 6

Given:

Each person buys 3 cups of coffee per week

$\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}$

$\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}$