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2 years ago

If ΔABC ≅ ΔFDE, which of the following statements is true?

Mathematics

2 answers:

Fed [463]2 years ago

7 0

Answer:

Option D) ∠B ≅ ∠D

Step-by-step explanation:

we know that

If two triangles are congruent, then the corresponding sides and the corresponding angles are congruent

If ΔABC ≅ ΔFDE

the corresponding angles are

∠A and ∠F

∠B and ∠D

∠C and ∠E

∠A ≅ ∠F

∠B ≅ ∠D

∠C ≅ ∠E

therefore

The statement that is true is ∠B ≅ ∠D

salantis [7]2 years ago

6 0

Answer: ∠B ≅ ∠D

Explanation:

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El caño de una fuente está inclinado 60° sobre la horizontal. Si el agua sale del caño con una velocidad inicial de 10 m/s: a) ¿

jeka94

Answer:

A) Parabola; B) 3.83 m; C) 8.84 m; D) 10 m/s

Step-by-step explanation:

A) Shape of water jet

The water jet has the shape of a parabola.

B) Maximum height

Data:

θ = 60°

u = 10 m/s

a = 9.8 m·s⁻²

Calculations:

1. Calculate the horizontal and vertical components of the velocity

$u_{\text{h}} = u \cos \theta = \text{10 m/s} \times \cos 60 ^{\circ} = \text{10 m/s} \times 0.5 = \text{5 m/s}\\u_{\text{v}} = u \sin \theta = \text{10 m/s} \times \sin 60 ^{\circ} = \text{10 m/s} \times 0.866 = \text{8.66 m/s}$

2. Maximum height

$H = \dfrac{(u_{\text{v}})^{2}}{2a} = \dfrac{8.66^{2}}{2\times 9.8} =\textbf{3.83 m}$

C) Range

1. Calculate the time of flight

Use the vertical component of velocity to calculate the time to the maximum height of the stream.

$u_{\text{v}} = at\\t = \dfrac{ u_{\text{v}}}{a} = \dfrac{\text{8.66 m$\cdot$s}^{-1}}{\text{9.8 m$\cdot$s}^{-2}}= \text{0.884 s}$

It will take the same time to reach the ground.

Thus,

Time of flight = 2t = 2 × 0.884 s = 1.77 s

2. Calculate the horizontal distance

s = vt = 5 m·s⁻¹ × 1.77 s = 8.84 m

You should place the drain 8.84 m from the pipe.}

D) Modulus of velocity

The stream of water will hit the drain with the same velocity as when it left the pipe.

Thus, the modulus of the velocity is 10 m/s.

The graph below shows the trajectory of the water stream.

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2 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Scrat [10]

Formula is A=1/2bh so answer will be 27 divided by 2

3 0

2 years ago

. A system may become infected by some spyware through the internet or e-mail. Seventy percent of the time the spyware arrives v

dem82 [27]

Answer:

This spyware is detected 66% of the time.

Step-by-step explanation:

We have these following percentages:

70% of the time, the spyware arrives via the internet, and in this case, is detected 60% of the time.

30% of the time, the spyware arrives via e-mail, and in this case, is detected 80% of the time.

What percentage of times is this spyware detected

Sum of 60% of 70%(arrived via spyware, detecte) and 80% of 30%(arrive via e-mail, detected). So

$0.6*0.7 + 0.8*0.3 = 0.42 + 0.24 = 0.66$

This spyware is detected 66% of the time.

3 0

2 years ago

You are looking out your window in a skyscraper, and again your window is at a height of 450 feet above the ground. This time, h

jarptica [38.1K]

Answer:

The tomato fell from 1027.2ft

Step-by-step explanation:

Parameters given:

Height from window = 450ft

Time taken to get from window to ground = 2 secs

V0, initial speed of tomato from drop point = 0 ft/s

Acceleration due to gravity = 32.2 ft/s^2

When the tomato gets to the observer at the window, its initial speed is no longer 0ft/s but an unknown value, u.

We can apply one of the equations of linear motion to then find this initial velocity at the window using the other parameters given i.e.

s = ut + 1/2 at2^2

s = 450ft

t = 2 secs

a = g = 32.2ft/sec2^2

=> 450 = (u*2) + (1/2 * 32.2 * 2^2)

450 = 2u + 64.4

2u = 450 – 64.4

2u = 385.6

=> u = 192.8ft/s

Now that we know this initial velocity, we can use another equation of linear motion to find the height distance between the drop point and the window ,

v^2 - u^2 = 2gs

where s = distance between drop point and window

v = 192.8ft/s

u = 0ft/s;

=> 192.8^2 - 0^2 = 2*32.2*s

37171.84 = 64.4s

=> s = 37171.84/64.4

s = 577.20ft

Hence, distance from drop point to the ground, H, will be the addition of s and the height from the window to the ground:

=>H = 577.20 + 450

H = 1027.2ft

8 0

2 years ago

Read 2 more answers

An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per do

vaieri [72.5K]

Answer:

a) Binomial distribution B(n=12,p=0.01)

b) P=0.007

c) P=0.999924

d) P=0.366

Step-by-step explanation:

a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

$P(k=0)=\binom{12}{0}p^0(1-p)^{12}=1*1*0.99^{12}=1*0.886=0.886\\\\P(k=1)=\binom{12}{1}p^1(1-p)^{11}=12*0.01*0.99^{11}=12*0.01*0.895=0.107$

Then,

$P(k>1)=1-(P(k=0)+P(k=1))=1-(0.886+0.107)=1-0.993=0.007$

c) In this case, the distribution is B(1200,0.01)

$P(k=0)=\binom{1200}{0}p^0(1-p)^{12}=1*1*0.99^{1200}=1* 0.000006 = 0.000006 \\\\ P(k=1)=\binom{1200}{1}p^1(1-p)^{1199}=1200*0.01*0.99^{1199}=1200*0.01* 0.000006 \\\\P(k=1)= 0.00007\\\\\\P(k\leq1)=0.000006+0.000070=0.000076\\\\\\P(k>1)=1-P(k\leq 1)=1-0.000076=0.999924$

d) In this case, the distribution is B(100,0.01)

We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

$P(k=0)=\binom{100}{0}p^0(1-p)^{100}=0.99^{100}=0.366$

5 0

2 years ago