Triangle ABC is similar to triangle DEF. What is the value of x in centimeters?

A. 17 cm

B. 16.5 cm

C. 15.4 cm

D. 18 cm

Answer:

θ = [tex]\frac{\pi }{3}[/tex] (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ  ≤ 1

2cosθ - 1 = 0

cosθ = [tex]\frac{1}{2}[/tex] , so

θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )

Answer:

[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]

Step-by-step explanation:

[tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]

Answer:

6*6=36

Step-by-step explanation:

6*6. 6 with exponent of 2=36

Answer:

not sure but i think c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

∠2 = 80°

Step-by-step explanation:

∠1 and ∠2 are supplementary angles (their sum is 180°)

9514 1404 393

Answer:

  9, the sum of the numbers given in the ratio

Step-by-step explanation:

The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.

It is convenient to think of the line segment as being divided into 9 equal parts.

_____

Additional comments

It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.

It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.

Answer:

€4,378,000,000

Step-by-step explanation: just took the test :)

Answer:

A

Step-by-step explanation:

Took the test

Answer:  I dont know AZ

Answer:

9

Step-by-step explanation:

Answer:

12710 license plates

Step-by-step explanation:

Given that :

First character = one of 41 different hieroglyphs

Second character = one of 31 emojis

Third character = one of 10 polygons

A license plate consists of 3 characters

Number of 3-character license plates available :

Number of hieroglyphs * Number of emojis * number of polygons

41 * 31 * 10 = 12710 license plates.

Answer:

I'm sure it is 25 hope this helps!!!

Answer:

Should be 25

Step-by-step explanation:

Lol is that pearson realize? i hate that buddy good luck

Answer:

14.3 yd

Step-by-step explanation:

apply the pythagorean Theorem formula:

= sqrt(14^2 +3^2)

= sqrt(205)

roughly 14.3 yd

Answer: Carlos does not have enough wires by 0.1 meters

Step-by-step explanation:

To determine if Carlos has enough wires, you need to find out the total amount of wires needed and then compare this to the amount of wires that Carlos has already.

= 0.9 + 0.9 + 0.9

= 2.7 meters

Carlos has 2.6 meters of wire but needs 2.7 meters.  

Carlos therefore, does not have enough wires.

half of the triangle is a right angle triangle, so we use the phythagoras theorem and multipy our answer by 2

Answer:

i need more info

Step-by-step explanation:

Answer:

Step-by-step explanation:

The height of the building is 8 rad 3

Approximately 13.9 ft

Answer:

parallel

Step-by-step explanation:

Because a is pependicular to k

Answer:

y = 27

Step-by-step explanation:

The output is the value of y when x = 5

Substitute x = 5 into the function , that is

y = 12 + 3(5) = 12 + 15 = 27 ← output

Answer:

3. - 8n² -8n + 3

Step-by-step explanation:

(4n^4 - 8n +4) - (8n² + 4n^4 +1)

Firstly, open the brackets.

= 4n^4 - 8n +4 - 8n² -  4n^4 - 1

Now, group like terms.

= 4n^4 - 4n^4 - 8n² -8n - 1 + 4

4n^4 - 4n^4 cancel out with each other since one is negative and the other is positive. So we're left with - 8n² -8n - 1 + 4

= - 8n² -8n - 1 + 4

= - 8n² -8n + 3

Answer:

x = 5

Step-by-step explanation:

Angles DEB and AEC are vertical angles, so they are congruent, and their measures are equal.

8x - 3 = 5x + 12

3x = 15

Answer:

The tires are spinning at 660.49 revolutions per minute.

Step-by-step explanation:

The speed of the tires (v) is the same that the speed of the car, so to find the angular velocity of the tires we need to use the equation:

[tex] \omega = \frac{v}{r} [/tex]

Where:

r: is the radius of the tires = d/2 = 28 inches/2 = 14 inches

[tex]\omega = \frac{55 mph}{14 inches*\frac{1 mile}{63360 inches}} = 2.49 \cdot 10^{5} \frac{rad}{h}*\frac{1 h}{60 min}*\frac{1 rev}{2\pi rad} = 660.49 rpm[/tex]              

Therefore, the tires are spinning at 660.49 revolutions per minute.

I hope it helps you!          

Answer:

∠z = 55°

Step-by-step explanation:

90° - 35° = 55°

Answer:

p(e)=e-3

Step-by-step explanation:

De acuerdo a la información proporcionada, sabes que Paul tenía una determinada cantidad e y al comprar el libro recibió 3 de vuelto, lo que significa que el precio del libro sería igual a restar 3 de la cantidad que tenía al inicio, lo cual se puede expresar de la siguiente forma:

p(e)=e-3, donde

p es el precio del libro

e es la cantidad que Paul tenía al inicio

Answer:

23

Step-by-step explanation:

3c + 11

3(4) + 11

12 + 11

23

Answer:

A : 25

Step-by-step explanation:

In a neutral atom, the number of electrons is equal to the number of protons. The atomic number indicates the number of protons.

The mass number is the sum of the number of neutrons and the number of protons.

mass number=protons+neutrons

As we know from the atomic number, the number of neutrons is 14 and the number of electrons is 11.

mass number = 14 + 11