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3 years ago

NEED IT ASAP What is the value of x in the diagram below? A.18/ ROOT 3 B.18 ROOT 2/ROOT 3 C.18 ROOT 3/ ROOT 2 D. 18 ROOT 2

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

3 0

Answer:

x = B. 18 ROOT 2/ROOT 3

Step-by-step explanation:

There are two Triangles in the diagram above.

Step 1

We would solve for Triangle A First

Using Trigonometric function Cosine

cos θ = adjacent /hypotenuse

θ = 30°

Adjacent = 9 units

Hypotenuse = unknown

cos 30= 9/ Hypothenuse

Cross Multiply

cos 30 × Hypotenuse = 9

Hypotenuse = 9 / cos 30

cos 30 in surd form = √3/2

Hypotenuse = 9/√3/2

Hypotenuse = 9 × 2/√3

= 18/√3 units

Step 2

We would solve for the upper triangle = Triangle B

We are looking for x

θ = 45°

For Triangle B, the Hypotenuse we solved for in Triangle A is equivalent to the adjacent in Triangle B

Therefore ,

Hypotenuse for Triangle A = Adjacent side for Triangle B

θ = 45°

Adjacent = 18/√3 units

Hypotenuse = x = unknown

We would solve for this using Trigonometric function cosine

cos 45 = 18/√3 units / Hypothenuse

Cross Multiply

cos 45 × Hypotenuse = 18/√3 units

Hypotenuse = 18/√3 units / cos 45

cos 45 in surd form = 1/√2

Subtituting, we have

Hypotenuse (x) = 18/√3 units / 1/√2

Hypotenuse (x) = 18/√3 units ×√2/1

= 18× √2/ √3 units

= 18 √2/√3 units

Therefore x = Option B. 18 ROOT 2/ROOT 3

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3 years ago

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Tanya [424]

Answer:

(2)

Step-by-step explanation:

One property of a parallelogram is

• opposite angles are congruent, hence

∠L = ∠N and ∠M = ∠P

Using ∠L = ∠N, then

8x - 41 = 6x + 3 ( subtract 6x from both sides )

2x - 41 = 3 ( add 41 to both sides )

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3 years ago

Pedro has 3 boxes of 6 markers. Rafael has 5 boxes of 5 markers. One of the friends arranges all his markers into 2 equal groups

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Answer:

see below

Step-by-step explanation:

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3 years ago

The function f(t) = 3(1 + 0.5)^nt models the weight in pounds of an alligator each year from its birth. Based on the function, w

masha68 [24]

<h2>Hello!</h2>

The answer is: 50% (0.5)

Exponential growth equations are use to predict the growth (in function of time) using proportional information.

We can calculate the exponential growth using the following formula:

$y=S(1+r)^{t}$

Where,

S, is the starting value

r, is the growth rate

t, is the time

So, we are given the function:

$f(t) = 3(1 + 0.5)^{nt}$

Where,

f(t), is the function,

3, is the starting value (lb)

0.5 (50%) is the growth rate

nt, is the time elapsed.

Hence,

From the given function, we know that the growth rate is equal to 0.5, and it's equal to 50%.

We can turn the growth rate given in real numbers to percent value by multiplying by 100

$GrowthRate(Percentage)=0.5*100=50(Percent)$

So, the growth rate is 50%.

Have a nice day!

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3 years ago