Answer:
Step-by-step explanation:
Answer:
B=23.19
Step-by-step explanation:
First, find the last side of the triangle using the Pythagorean theorem.
![a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2Bb%5E%7B2%7D%20%3Dc%5E%7B2%7D%20%5C%5C21%5E%7B2%7D%20%2B9%5E%7B2%7D%20%3Dc%5E%7B2%7D%20%5C%5C441%2B81%3Dc%5E%7B2%7D%20%5C%5C%5Csqrt%5B3%5D%7B58%7D%3Dc)
Then, find the missing angle, lets name it B.
The angle B can be found using the inverse sine function.
B=arcsin(opp/hyp)
![B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19](https://tex.z-dn.net/?f=B%3Darcsin%28%5Cfrac%7B9%7D%7B%5Csqrt%5B3%5D%7B58%7D%20%7D%20%29%5C%5CB%3D23.19)
Vertex is -b/2a. The variable b=2 and a=2. That finds the x coordinate of the vertex. Then to find the y coordinate you just plug the number you got for x (-1/2) into the equation. Like so:
y = 2x+2
y = 2(-1/2)+2
y = -1+2
y = 1
So your vertex is ( -1/2, 1 )
To graph your vertex you take your x coordinate (-1/2) and find it on the x axis of the graph (horizontal line). Then do the same for y (1) (on the vertical axis.
Now that you have your vertex graphed you can find out if it is minimum or maximum by looking at the direction in which the slope is going. If it goes in the positive direction (up) then it is a minimum since that is the lowest point that the line touches. If it is maximum it is opposite. The line faces down and the highest point the line touches is that point.
Answer:
Matt used 65 carpet tiles.
Step-by-step explanation:
4(x - 2) + 6 = 2(5x - 6) <em>use distributive property</em>
(4)(x) + (4)(-2) + 6 = (2)(5x) + (2)(-6)
4x - 8 + 6 = 10x - 12
4x - 2 = 10x - 12 <em>add 2 to both sides</em>
4x = 10x - 10 <em>subtract 10 from both sides</em>
-6x = -10 <em>divide both sides by (-6)</em>
x = 10/6
<h3>x = 5/3</h3>
