Answer:
25. a = 60
26. a = 17
Step-by-step explanation:
In these two problems we are going to use a property of parallelograms that says: opposite angles have equal measure
so we have
25.
![6a+10=130\\\\6a=130-10\\\\6a=120\\\\a=60](https://tex.z-dn.net/?f=6a%2B10%3D130%5C%5C%5C%5C6a%3D130-10%5C%5C%5C%5C6a%3D120%5C%5C%5C%5Ca%3D60)
and for 26 we have
![4a-4=2a+30\\\\4a=2a+30+4\\\\4a=2a+34\\\\4a-2a=34\\\\2a=34\\\\a=17](https://tex.z-dn.net/?f=4a-4%3D2a%2B30%5C%5C%5C%5C4a%3D2a%2B30%2B4%5C%5C%5C%5C4a%3D2a%2B34%5C%5C%5C%5C4a-2a%3D34%5C%5C%5C%5C2a%3D34%5C%5C%5C%5Ca%3D17)
Answer:
8 ft
Step-by-step explanation:
t = a + b/2 times 2
2 + 6 = 8
8/2 = 4
4 x 2 = 8
Answer:
10.5 in
Step-by-step explanation:
Given
![tan(55) = \frac{15}{b}](https://tex.z-dn.net/?f=tan%2855%29%20%3D%20%5Cfrac%7B15%7D%7Bb%7D)
Required
Find length AC
The question is not detailed enough; so, I'll assume that b represents line AC.
Having said that;
We start by multiplying both sides by b
![tan(55) = \frac{15}{b}](https://tex.z-dn.net/?f=tan%2855%29%20%3D%20%5Cfrac%7B15%7D%7Bb%7D)
![b * tan(55) = \frac{15}{b} * b](https://tex.z-dn.net/?f=b%20%2A%20tan%2855%29%20%3D%20%5Cfrac%7B15%7D%7Bb%7D%20%2A%20b)
![b * tan(55) =15](https://tex.z-dn.net/?f=b%20%2A%20tan%2855%29%20%3D15)
Divide both sides by tan(55)
![\frac{b * tan(55)}{tan(55)} = \frac{15}{tan(55)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%20%2A%20tan%2855%29%7D%7Btan%2855%29%7D%20%3D%20%5Cfrac%7B15%7D%7Btan%2855%29%7D)
![b = \frac{15}{tan(55)}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B15%7D%7Btan%2855%29%7D)
Find tan(55)
![b = \frac{15}{1.42814800674}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B15%7D%7B1.42814800674%7D)
![b = 10.5031130731](https://tex.z-dn.net/?f=b%20%3D%2010.5031130731)
<em>(Approximated)</em>
<em />
Length AC is 10.5
Answer:
![A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)](https://tex.z-dn.net/?f=A%28x%2Cy%29%2CB%28x%2B10%2Cy%29%2CC%28x%2B10%2Cy-10%29%20%5C%3Aand%5C%3A%20D%28x%2Cy-10%29)
Step-by-step explanation:
If a Rectangle has a perimeter of 40 units, then we can write that formula and find the a formula for the coordinates:
![\left\{\begin{matrix}w+l=20 & \\ w*l=100 & \end{matrix}\right.\Rightarrow w=20-l\Rightarrow (20-l)l=100\Rightarrow -l^2+20l-100=0\Rightarrow l^2-20l+100\Rightarrow (l-10)(l-10)\Rightarrow l=10\therefore l=10\: and\: w=10](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dw%2Bl%3D20%20%26%20%5C%5C%20w%2Al%3D100%20%26%20%5Cend%7Bmatrix%7D%5Cright.%5CRightarrow%20w%3D20-l%5CRightarrow%20%2820-l%29l%3D100%5CRightarrow%20-l%5E2%2B20l-100%3D0%5CRightarrow%20l%5E2-20l%2B100%5CRightarrow%20%28l-10%29%28l-10%29%5CRightarrow%20l%3D10%5Ctherefore%20l%3D10%5C%3A%20and%5C%3A%20w%3D10)
Therefore we can say:
![A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)](https://tex.z-dn.net/?f=A%28x%2Cy%29%2CB%28x%2B10%2Cy%29%2CC%28x%2B10%2Cy-10%29%20%5C%3Aand%5C%3A%20D%28x%2Cy-10%29)
Technically when
in this rectangle is a square, a degenerate square.