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3 years ago

A right triangle, DEF, is shown below. What is sin FDE?

Mathematics

1 answer:

RoseWind [281]3 years ago

3 0

Answer:

22.6°

Step-by-step explanation:

Reference angle = <FDE

Side opposite to <FDE = 5

Hypotenuse = 13

The trigonometric ratios to apply is:

$sin(\theta) = \frac{opp}{hyp}$

Plug in the values

$sin(\angle FDE) = \frac{5}{13}$

$sin(\angle FDE) = 0.3846$

$\angle FDE = sin^{-1}(0.3846)$

$\angle FDE = 22.6$ (nearest tenth)

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Which of the following would best be solved using factoring the difference of squares? 2² + 3x - 10 = 0 O 3r² + 12x = 8 2³ +52²

IgorC [24]

Given: Different equations

To Determine: Which would be best solved using difference of two squares

Solution

The factorization of a difference of two squares is given below

$a^2-b^2=(a-b)(a+b)$

Let us examine each of the given equation

$\begin{gathered} x^2+3x-10=0 \\ x^2-2x+5x-10=0 \\ x(x-2)+5(x-2)=0 \\ (x-2)(x+5)=0 \end{gathered}$ $\begin{gathered} 3x^2+12x=8 \\ 3x^2+12x-8=0 \end{gathered}$ $\begin{gathered} x^3+5x^2-9x-45=0 \\ x^2(x+5)-9(x+5)=0 \\ (x+5)(x^2-9)=0 \\ x^2-9=x^2-3^2=(x+3)(x-3) \\ Therefore \\ (x+5)(x+3)(x-3)=0 \end{gathered}$ $\begin{gathered} x^2-25=0 \\ x^2-5^2=0 \\ (x+5)(x-5)=0 \end{gathered}$

From the above,

$\begin{gathered} x^3+5x^2-9x-45=0 \\ AND \\ x^2-25=0 \end{gathered}$

The two equation above can be solved by difference of two square, but the equation below is the easiest solved using differnce of two square

x² - 25 = 0

3 0

1 year ago

An aquarium tank can hold 5400 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can

Nady [450]

Answer:

36 minutes when both pipes are working together

Step-by-step explanation:

capacity of tank = 5400 liters

Pipe A flow per mint. = 5400/90 = 60 liters per mint.

Pipe B flow per mint. = 5400/60 = 90 liters per mint.

Flow of A + B per mint. 60 + 90 = 150 liter per mint.

Therefore, 5400 / 150 = 36 minutes to fill the tank

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2 years ago

Help please i will give brainlist

Feliz [49]

Answer:

Angle 1 is 67 and Angle 2 is 46

Step-by-step explanation:

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3 years ago

What is the value of <br> 56÷37?<br> 56÷37?

Galina-37 [17]

Answer:

exact form is 56/37

decimal form is 1.513

mixed number form is 1 19/37

Step-by-step explanation:

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2 years ago

I just wanted to see if this was 8 or negative 8 :)

nirvana33 [79]

Answer:

It's a positive 8.

Step-by-step explanation:

You can't have a negative amount of money.

4 0

2 years ago