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Mamont248 [21]
3 years ago
6

Find the length of side x in simplest radical form with a rational denominator.

Mathematics
1 answer:
mojhsa [17]3 years ago
6 0

Answer:

x = \frac{8\sqrt{3} }{3}

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin60° = \frac{\sqrt{3} }{2}

sin60° = \frac{opposite}{hypotenuse} = \frac{4}{x} = \frac{\sqrt{3} }{2} ( cross- multiply )

x × \sqrt{3} = 8 ( divide both sides by \sqrt{3} )

x = \frac{8}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } ( rationalising the denominator )

x = \frac{8\sqrt{3} }{3}

You might be interested in
Triangle ABC has side lengths:
Harlamova29_29 [7]

The length of HJ is 3.5 cm

<h3>What is Congruency?</h3>

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Given:

AB = 3.5 cm, BC = 2.4 cm, and AC = 4.2 cm

As, ΔABC ≅ ΔHJK

So,

AB = HJ

BC = JK

AC = HK

Thus, HJ= AB = 3.5 cm

Learn more about this concept here:

brainly.com/question/4229988

#SPJ1

8 0
1 year ago
The diagram shows a sector of a circle radius 10 cm. the angle is 135 degrees
Black_prince [1.1K]

Answer:

The perimeter is 43.6 cm

Step-by-step explanation:

In this question, we are tasked with calculating the perimeter of the sector.

Firstly, we define what a sector is. A sector is part of a circle which is is blinded by two radii and an arc. Hence we say a sector contains two radii.

Thus, to calculate the perimeter of the sector, we need the length of the arc added to 2 * length of the radius

Let’s calculate the length of the arc.

Mathematically, this is theta/360 * 2 * pi * r

where theta is the angle subtended at the middle of the circle which is 135 according to the question, and our radius is 10cm

Thus, we have

135/360 * 2 * 22/7 * 10 = 23.57 cm

Adding two radii to this, we have;

23.57 + 2(10)

= 23.57 + 20 = 43.57 = 43.6 cm to 1 decimal place

5 0
2 years ago
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (
Andrew [12]

Answer:

The function h (x) = StartFraction 11 Over x minus 4 EndFraction

has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the

domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

Step-by-step explanation:

m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3

As m (x) could be written as:

m(x) = \frac{x+5}{x-1}

n(x) = x – 3

(m ∘ n)(x) = m(n(x)) = m(x – 3)

              = \frac{(x-3) + 5}{(x-3) - 1}

              = \frac{x+2}{x-4}

In order to find the domain of (m ∘ n)(x) = \frac{x+2}{x-4}, we need to

make sure that denominator can not be zero,

So,

     x - 4 = 0

     x = 4    

So, our domain can be anything except for 4.

Hence, Domain = D = ( - ∞, 4) U (4, ∞ )

Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:

Option A: h (x) = x + 5 / 11

Option A has the Domain of h (x) = Set of all real numbers

So, Option A is false.

Option B: h (x) = 11 / x - 1

                        x - 1 = 0

                         x = 1

Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )

So, Option B is false.

Option C: h (x) = 11 / x - 4

                        x - 4 = 0

                         x = 4

Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )

So, Option C is true.

Option D: h (x) = 11 / x - 3

                        x - 3 = 0

                         x = 3

Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )

So, option D is also false.

Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

keywords: Domain, composite function

Learn more about the domain of function from brainly.com/question/13020740

#learnwithBrainly

4 0
3 years ago
Read 2 more answers
Please help with this question
stealth61 [152]

Answer:

hi Step-by-step explanation:April 12, 1861: Battle of Fort Sumter. ...

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6 0
3 years ago
What is the y-intercept of the line y+11= -2(x+5)?
poizon [28]

Answer:

<u>y-intercept</u><u> </u><u>is</u><u> </u><u>(</u><u>0</u><u>,</u><u> </u><u>-</u><u>2</u><u>1</u><u>)</u>

Step-by-step explanation:

For y-intercept, x = 0:

{ \sf{y + 11 =  - 2(0 + 5)}} \\ { \sf{y + 11 =  - 10}} \\ { \sf{y =  - 21}}

4 0
2 years ago
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