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saul85 [17]
3 years ago
15

What is the value of x?

Mathematics
1 answer:
allsm [11]3 years ago
6 0
First need to find the length of line LJ

Line LJ = 8sqrt2 * sin(30) = 5.6569

 now use that to find x

x = 5.6569 * sin(45) = 4

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Please help i beg i never get these right
Anuta_ua [19.1K]

Answer:

\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}

Step-by-step explanation:

Given

\sin(105^o)

Required

Solve

Using sine rule, we have:

\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)

This gives:

\sin(105^o) = \sin(60 + 45)

So, we have:

\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)

In radical forms, we have:

\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}

\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}

Take LCM

\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}

Rewrite as:

\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}

Hence:

\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}

3 0
2 years ago
find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.
solniwko [45]
Check the picture below, so, that'd be the square inscribed in the circle.

so... hmm the diagonals for the square are the diameter of the circle, and keep in mind that the radius of a circle is half the diameter, so let's find the diameter.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
\stackrel{diameter}{d}=\sqrt{[-8-(-2)]^2+[-3-5]^2}
\\\\\\
d=\sqrt{(-8+2)^2+(-3-5)^2}\implies d=\sqrt{(-6)^2+(-8)^2}
\\\\\\
d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10

that means the radius r = 5.

now, what's the center?  well, the Midpoint of the diagonals, is really the center of the circle, let's check,

\bf \textit{middle point of 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{-8-2}{2}~,~\cfrac{-3+5}{2} \right)\implies (-5~,~1)

so, now we know the center coordinates and the radius, let's plug them in,

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}\\
&-5&1&5
\end{array}
\\\\\\\
[x-(-5)]^2-[y-1]^2=5^2\implies (x+5)^2-(y-1)^2=25

8 0
3 years ago
SHOW WORK! IF YOUR RIGHT ILL GIVE YOU 100,000 COOKIES
k0ka [10]

Answer: 144 ft^3 is the volume of the prism

Step-by-step explanation: Volume=Length*Height*Width. So first I decided to multiply 12*6=72. The I multiplied 72*2=144.

4 0
2 years ago
What is the square root of 67
Inessa [10]

Every positive number has two square roots.

The square roots of  67  are  8.185... (rounded) and  -8.185... (rounded) .

Both are irrational numbers, so they can't be completely written down
with digits.  No matter how many decimal places I write, it can never be
enough, because these decimals go on forever and never end.

3 0
3 years ago
Read 2 more answers
James and Amy play 3 more games.They have played the same number of games as last week .Fill in the blanks to make the equation
Fiesta28 [93]

Question is Incomplete; Complete question is given below;

James and Amy played 12 games of checkers last week. This week they played 7 games on Monday and 2 games on Wednesday.James and Amy play 3 more games. They have played the same number of games as last week. Fill in the blanks to make the equation true. Use +,-, or =. 12_7_2_3 Explain how you chose the symbols.

Answer:

12<u> = </u>7<u> + </u>2<u> + </u>3

Step-by-step explanation:

Given:

Number of games played last week = 12

Number of games played on Monday this week = 7

Number of games played on Wednesday this week = 2

Also given:

James and Amy play 3 more games.

So Number of games played more = 3

We need to fill in the blanks 12 __ 7__2__3 with signs '+', '-','='.

Solution:

It is given that they have played the same number of games as last week.

So we can say that;

Number of games played last week is equal to Number of games played on Monday this week plus Number of games played on Wednesday this week plus Number of games played more.

framing in equation form we get;

12 = 7 + 2+3

Hence we have fill the blanks as 12<u> = </u>7<u> + </u>2<u> + </u>3.

8 0
3 years ago
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