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max2010maxim [7]
3 years ago
11

Use the diagram below to find the value of each variable.

Mathematics
1 answer:
s2008m [1.1K]3 years ago
8 0
Z=95° as opposite angles are equal
The angle next to 120° is 60° as angles on a straight line sum to 180°
This means that y=25° because angles in a triangle sum to 180°
Therefore x=155° as angles on a straight line sum to 180°
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Gemiola [76]

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4 0
3 years ago
Kate sold 12 of her paintings and purchased 7 more. if kate has 21 paintings now, how many paintings did she have to begin with?
kicyunya [14]
First, let x or any variable represent the number of paintings Kate initially has. After selling 12 of it, her paintings now becomes only x - 12. Then, she purchased 7 more making the number of her paintings become x - 12 + 7 = x - 5. This number tantamount to 21. 

                                           x - 5 = 21      ; x = 26

Thus, Kate initially had 26 paintings. 
7 0
3 years ago
Use Cramer’s Rule to solve system of equation.
alisha [4.7K]

\left\{\begin{array}{ccc}5x+2y=4\\3x+4y+2z=6\\7x+3y+4z=29\end{array}\right\\\\A=\left[\begin{array}{ccc}5&2&0\\3&4&2\\7&3&4\end{array}\right]\\\\\det A=5\cdot4\cdot4+3\cdot3\cdot0+2\cdot2\cdot7-7\cdot4\cdot0-3\cdot2\cdot5-3\cdot2\cdot4=54\\W_x=\left[\begin{array}{ccc}4&2&0\\6&4&2\\29&3&4\end{array}\right]\\\det W_x=4\cdot4\cdot4+2\cdot2\cdot29+6\cdot3\cdot0-29\cdot4\cdot0-3\cdot2\cdot4-6\cdot2\cdot4=108

W_y=\left[\begin{array}{ccc}5&4&0\\3&6&2\\7&29&4\end{array}\right]\\\det W_y=5\cdot6\cdot4+3\cdot29\cdot0+4\cdot2\cdot7-7\cdot6\cdot0-29\cdot2\cdot5-3\cdot4\cdot4=-162\\W_z=\left[\begin{array}{ccc}5&2&4\\3&4&6\\7&3&29\end{array}\right]\\\det W_z=5\cdot4\cdot29+3\cdot3\cdot4+6\cdot2\cdot7-7\cdot4\cdot4-3\cdot6\cdot5-3\cdot2\cdot29=324\\\\x=\dfrac{\det W_x}{\det A}=\dfrac{108}{54}=2\\\\y=\dfrac{\det W_y}{\det A}=\dfrac{-62}{54}=-3\\\\z=\dfrac{\det W_z}{\det A}=\dfrac{324}{54}=6

5 0
3 years ago
Be sure to show your work and solve for g:<br> g<br> +<br> 6<br> −<br> 3<br> =<br> 31
Iteru [2.4K]

28 + 6 = 34 and 34 - 3 = 31!!!!!!!

4 0
3 years ago
A stone is dropped of a 1296-ft-cliff. The height of the stone above the ground is given by the equation h= - 16t^2+1296, where
stich3 [128]

When stone hits the ground, it's height will be zero, and since we're finding the time that's required for the stone to hit the ground, we can set h = 0 and solve for t.

3 0
2 years ago
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