Step-by-step explanation:
the volume of a box (or prism) is always
length × width × height
so, box A
13 × 12 × 16 = 2,496 in³
box B
18 × 25 × 16 = 7,200 in³
box C
12 × 14 × 22 = 3,696 in³
box D
20 × 22 × 17 = 7,480 in³
so, she can use B or D.
Using the Sine rule,
![\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BLet%20A%20%3D%2014m%2C%7D%20%5C%5C%20Substituting%20the%20variables%20into%20the%20formula%2C%3Cp%3EWhere%20the%20length%20of%20the%20wires%20are%2C%20AP%20%3D%20xm%20and%20BP%20%3D%20ym%3C%2Fp%3E%5Btex%5D%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%5Csin80%5E0%7D%7B14%7D%3D%5Cfrac%7B%5Csin40%5E0%7D%7Bx%7D%20%5C%5C%20%5Ctext%7BCrossmultiply%2C%7D%20%5C%5C%20x%5Ctimes%5Csin%2080%5E0%3D14%5Ctimes%5Csin%2040%5E0%20%5C%5C%20Divide%5Ctext%7B%20both%20sides%20by%20%7D%5Csin%2080%5E0%20%5C%5C%20x%3D%5Cfrac%7B14%5Csin40%5E0%7D%7B%5Csin80%5E0%7D%20%5C%5C%20x%3D9.14m%20%5Cend%7Bgathered%7D)
Hence, the length of wire AP (x) is 9.14m.
For wire BP (y)m,
Sum of angles in a triangle is 180 degrees,
Using the side rule to find the length of wire BP,
Hence, the length of wire BP (y) is 12.31m
Therefore, the length of the wires are (9.14m and 12.31m).
<span>Simplifying
8x + -6y = -20
</span><span>Solving
8x + -6y = -20
</span><span>Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right
</span><span>Add '6y' to each side of the equation.
8x + -6y + 6y = -20 + 6y
</span><span>Combine like terms: -6y + 6y = 0
8x + 0 = -20 + 6y
8x = -20 + 6y
</span>
Divide each side by '8'.
x = -2.5 + 0.75y
<span>Simplifying
x = -2.5 + 0.75y</span>
Composite, it can be divided
