Answer:
Check pdf
Step-by-step explanation:
Answer:
it is SAS
Step-by-step explanation:
because BC is common side in both triangles
so
now two triangles have 2 sides equal and 1 angle equal so
it is congruent by SAS rule
Answer:
If two angles are acute angles, then they are complementary. Incorrect. The converse is “If two angles are complementary, then they are acute angles” which is true and the original statement was false because two acute angles are not always complementary.
Step-by-step explanation:
Answer:
in
Step-by-step explanation:
Let x be the side of square.
Length of box=8-2x
Width of box=15-2x
Height of box=x
Volume of box=![L\times B\times H](https://tex.z-dn.net/?f=L%5Ctimes%20B%5Ctimes%20H)
Substitute the values then we get
Volume of box=V(x)=![(8-2x)(15-2x)x=(15x-2x^2)(8-2x)](https://tex.z-dn.net/?f=%288-2x%29%2815-2x%29x%3D%2815x-2x%5E2%29%288-2x%29)
![V(x)=120x-30x^2-16x^2+4x^3](https://tex.z-dn.net/?f=V%28x%29%3D120x-30x%5E2-16x%5E2%2B4x%5E3)
![V(x)=4x^3-46x^2+120x](https://tex.z-dn.net/?f=V%28x%29%3D4x%5E3-46x%5E2%2B120x)
Differentiate w.r.t x
![V'(x)=12x^2-92x+120](https://tex.z-dn.net/?f=V%27%28x%29%3D12x%5E2-92x%2B120)
![V'(x)=0](https://tex.z-dn.net/?f=V%27%28x%29%3D0)
![12x^2-92x+120=0](https://tex.z-dn.net/?f=12x%5E2-92x%2B120%3D0)
![3x^2-23x+30=0](https://tex.z-dn.net/?f=3x%5E2-23x%2B30%3D0)
![3x^2-18x-5x+30=0](https://tex.z-dn.net/?f=3x%5E2-18x-5x%2B30%3D0)
![3x(x-6)-5(x-6)=0](https://tex.z-dn.net/?f=3x%28x-6%29-5%28x-6%29%3D0)
![(x-6)(3x-5)=0](https://tex.z-dn.net/?f=%28x-6%29%283x-5%29%3D0)
![x-6=0\implies x=6](https://tex.z-dn.net/?f=x-6%3D0%5Cimplies%20x%3D6)
![3x-5=0\implies x=\frac{5}{3}](https://tex.z-dn.net/?f=3x-5%3D0%5Cimplies%20x%3D%5Cfrac%7B5%7D%7B3%7D)
Again differentiate w.r.t x
![V''(x)=24x-92](https://tex.z-dn.net/?f=V%27%27%28x%29%3D24x-92)
Substitute x=6
![V''(6)=24(6)-92=52>0](https://tex.z-dn.net/?f=V%27%27%286%29%3D24%286%29-92%3D52%3E0)
Substitute x=5/3
![V''(5/3)=24(5/3)-92=-52](https://tex.z-dn.net/?f=V%27%27%285%2F3%29%3D24%285%2F3%29-92%3D-52%3C0)
Hence, the volume is maximum at x=![\frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D)
Therefore, the side of the square ,
in cutout that gives the box the largest possible volume.
Answer:
1 3/4
Step-by-step explanation:
For every cup of flour the recipe uses, it uses 3/4 cups of sugar. So, 1 cup of flour plus 3/4 of sugar is 1 3/4.