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In-s [12.5K]
3 years ago
12

Find x. 2√3 4√3 8√3 8

Mathematics
2 answers:
qwelly [4]3 years ago
7 0

Answer:

8

Step-by-step explanation:

sin theta = opposite side/ hypotenuse

sin 30 = 4/x

Multiply each side by x

x sin 30 = 4

Divide each side by sin 30

x sin 30 /sin 30 = 4 sin 30

x = 4 /sin 30

We know that sin 30 = 1/2

x = 4 / 1/2

x = 8

exis [7]3 years ago
5 0

For this case we have to, by trigonometric properties applied to rectangular triangles:

Sine (30) = \frac {Cathet \ opposite} {Hypotenuse}\\Sine (30) = \frac {4} {x}

Clearing x:

x = \frac {4} {Sine (30)}\\x = \frac {4} {\frac {1} {2}}\\x = 8

Thus, the value of the hypotenuse is 8.

Answer:

x = 8

Option D

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The quadrilateral shown is rotated 90° clockwise about the origin. In which quadrant is the image of the quadrilateral located?
Viktor [21]

Answer:

Option (2). 1

Step-by-step explanation:

Coordinates of point A, B, C and D are,

A(-4, 4), B(-2, 4), C(-2, 1) and D(-4, 3).

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Rule for the rotation of the vertices,

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Following the rule of rotation coordinates of the image points,

A(-4, 4) → A'(4, 4)

B(-2, 4) → B'(4, 2)

C(-2, 1) → C'(1, 2)

D(-4, 3) → D'(3, 4)

Since all image points have the positive coordinates (x and y coordinates), image quadrilateral A'B'C'D' will be located in 1st quadrant.

Option (2) is the correct option.

4 0
2 years ago
To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before ad
vovikov84 [41]

Answer:

use -9 to multiply the first equation

use -4 to multiply the second equation.

Step-by-step explanation:

5x-4y=28.....eqn (1)×-9

3x-9y=30....eqn(2)×-4

-45x+36y=-252

-(-12x+36y=-120)

therefore, -33x÷33 =-132÷-33

x=4.

substitute (x=4) in any of the equation. I'm just going to use eqn 1.

5x-4y=28

5(4)-4y=28

20-4y=28

-4y =28-20

-4y÷-4 = 8÷-4

y=-2

so, x=4, y=-2

Note: for proof of answers substitute the answers for x and y and see if you have the same result...e.g

5(4)-4(-2)=28.

6 0
2 years ago
Read 2 more answers
Verify the identity. cot x / 1 + csc x = csc x - 1 / cot x
svetlana [45]

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

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Distribute the denominator:

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Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

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5 0
3 years ago
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