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3 years ago

5

In the right triangle, angle B equals 60° and AB equals 18How long is AC? I'm stuck!

1 answer:

svlad2 [7]3 years ago

3 0

Answer:

AC = 15.588

Step-by-step explanation:

(all rounded to nearest thousandth)

sin(60) = x/18

first solve: sin(60) = 0.866

0.866 = x/18

multiply 18 on both sides

x = 15.588

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In which of the options below will the number 3 correctly fill in the blank. Select all that apply. A) ___ : 4 = 12 : 16 B) 1 :

aniked [119]

Answer:

A and B

Step-by-step explanation:

Given

List of given options

Required

Which will correctly take 3 to fill the blank

Represent the blanks with x

Option A:

$x : 4 = 12 : 16$

Convert to fractions

$\frac{x}{4} = \frac{12}{16}$

Multiply through by 4

$4 * \frac{x}{4} = 4 * \frac{12}{16}$

$x = \frac{48}{16}$

$x = 3$

Option B:

$1 : 5= x : 15$

Convert to fraction;

$\frac{1}{5} = \frac{x}{15}$

Multiply through by 15

$15 * \frac{1}{5} = \frac{x}{15} * 15$

$15 * \frac{1}{5} = x$

$3 = x$

$x = 3$

Option C:

$x : 1 = 12 : 3$

Convert to fraction

$\frac{x}{1} = \frac{12}{3}$

$x = 4$

Option D

$15:x = 3:1$

Convert to fraction

$\frac{15}{x} = \frac{3}{1}$

Cross Multiply

$3 * x = 15 * 1$

$3 * x = 15$

Divide through by 3

$x = 5$

From the above calculations.

<em>Option A and B can be filled with 3</em>

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3 years ago

What property is being used in the equation 3a+0=3a

Georgia [21]

The identity of zero

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3 years ago

For the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?

slava [35]

<span>Opposite angles of a parallelogram are equal, so:

5x - 28 = 3x - 10

2x = 18

x = 9

Plug x = 9 into the equations

m angle 2 = 5x - 28 = 5 * 9 - 28 = 17

m angle 4 = 3x - 10 = 3 * 9 - 10 = 17

The sum of all angles in a parallelogram is 360,

and we know: m angle 1 = m angle 3, so:

m angle 1 + m angle 2 + m angle 3 + m angle 4 = 360

m angle 3 + 17 + m angle 3 + 17 = 360

2 * (m angle 3) = 360 - 17 - 17 = 326

m angle 3 = 163</span>

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3 years ago

Graph this line using the slope and y-intercept:<br> y = x + 9

prohojiy [21]

Answer:

Step-by-step explanation:

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4 years ago

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

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Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

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3 years ago