Answer:
![27y^{3} +125z^{3} =(3y)^{3} +(5z)^{3}](https://tex.z-dn.net/?f=27y%5E%7B3%7D%20%2B125z%5E%7B3%7D%20%3D%283y%29%5E%7B3%7D%20%2B%285z%29%5E%7B3%7D)
Apply the formula for sum of cubes: ![a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})](https://tex.z-dn.net/?f=a%5E%7B3%7D%2Bb%5E%7B3%7D%3D%28a%2Bb%29%28a%5E%7B2%7D-ab%2Bb%5E%7B2%7D%29)
Therefore:
![\left(3y\right)^3+\left(5z\right)^3=\left(3y+5z\right)\left(3^2y^2-3\cdot \:5yz+5^2z^2\right)](https://tex.z-dn.net/?f=%5Cleft%283y%5Cright%29%5E3%2B%5Cleft%285z%5Cright%29%5E3%3D%5Cleft%283y%2B5z%5Cright%29%5Cleft%283%5E2y%5E2-3%5Ccdot%20%5C%3A5yz%2B5%5E2z%5E2%5Cright%29)
![=\left(3y+5z\right)\left(9y^2-15yz+25z^2\right)](https://tex.z-dn.net/?f=%3D%5Cleft%283y%2B5z%5Cright%29%5Cleft%289y%5E2-15yz%2B25z%5E2%5Cright%29)
Surface area of larger box is 69% more so as a scale factor that is 1.69
Square root 1.69 = 1.3
Height of smaller box x 1.3 is height of larger box.
18 x 1.3 = 23.4 cm
Height = 23.4 cm
I’m not completely sure but i don’t think so. triangle ABC should be equal to 180°. this is equal to 190 °.
For the first one Y = -6
3x + 2Y = -16
-2y -2y
3x = -18y
— —
3x 3x
Then divide -18y divided by 3X
To get Y= -6
Hope that helped!
Answer:
cups of sugar.
Step-by-step explanation:
We have been given that Sabrina is baking cookies the recipe calls for 3/4 of a cup of sugar. Sabrina needs to double the recipe because she has a large cookie loving family.
To find the amount of sugar needed for recipe, we need to multiply 3/4 by 2 as:
![\text{Sugar needed for double recipe}=2\times \frac{3}{4}](https://tex.z-dn.net/?f=%5Ctext%7BSugar%20needed%20for%20double%20recipe%7D%3D2%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D)
![\text{Sugar needed for double recipe}=1\times \frac{3}{2}](https://tex.z-dn.net/?f=%5Ctext%7BSugar%20needed%20for%20double%20recipe%7D%3D1%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D)
![\text{Sugar needed for double recipe}=\frac{3}{2}](https://tex.z-dn.net/?f=%5Ctext%7BSugar%20needed%20for%20double%20recipe%7D%3D%5Cfrac%7B3%7D%7B2%7D)
![\text{Sugar needed for double recipe}=1\frac{1}{2}](https://tex.z-dn.net/?f=%5Ctext%7BSugar%20needed%20for%20double%20recipe%7D%3D1%5Cfrac%7B1%7D%7B2%7D)
Therefore, Sabrina needs
cups of sugar.