3:7 =
3/7
3/7 = x/35
7x = 105
x = 15
answer : clara borrowed 15 books
Answer
Find out the Area of a triangle .
To proof
Formula
Area of Triangle
![= \frac{1}{2}\times( {x_1(y_{2}-y_{3}) +x_{2}(y_{3} - y_{1})+x_{3}(y_{1}-y_{2})})](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%28%20%7Bx_1%28y_%7B2%7D-y_%7B3%7D%29%20%2Bx_%7B2%7D%28y_%7B3%7D%20-%20y_%7B1%7D%29%2Bx_%7B3%7D%28y_%7B1%7D-y_%7B2%7D%29%7D%29)
Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .
![= \frac{1}{2} (3\times(-1 +5) + 3\times(-5-3)-2\times(3+1))](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%20%283%5Ctimes%28-1%20%2B5%29%20%2B%203%5Ctimes%28-5-3%29-2%5Ctimes%283%2B1%29%29)
Solving the above
![= \frac{1}{2}(3\times4+3\times-8 -2\times4)](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%283%5Ctimes4%2B3%5Ctimes-8%20-2%5Ctimes4%29)
![=\frac{1}{2} (12-24-8)\\ =\frac{1}{2} (-32+12)\\=\frac{1}{2} (-20)](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%20%2812-24-8%29%5C%5C%20%3D%5Cfrac%7B1%7D%7B2%7D%20%28-32%2B12%29%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%20%28-20%29)
= -10 units²
(Neglected the negative sign as area cannot be negative.)
= 10 units ²
Area of a triangle is 10 units ²
Hence proved
-d would equal 3. just flip its around right?
3^x = 729
log(3^x) = log(729)
xlog(3) = log(729)
x = log(729)/log(3)
x = 6