Answer:
The answer to your question is 32 rose and 8 tulip
Step-by-step explanation:
Data
rose/ 4 = tulip
total number of arrangements = 40
Rose arrangement = R = ?
Tulip arrangement = T = ?
Process
1.- Write equations to solve this problem
R/4 = T
R + T = 40
2.- Solve the system by substitution
R + R/4 = 40
(4R + R) / 4 = 40
4R + R = 4(40)
5R = 160
R = 160 / 5
R = 32
- Find T
32 + T = 40
T = 40 - 32
T = 8
3.- Conclusion
She made 32 rose arrangement and 8 tulip arrangements.
Answer:
![\huge\boxed{x^o=67^o,\ y^o=113^o,\ z^o=52^o}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%5Eo%3D67%5Eo%2C%5C%20y%5Eo%3D113%5Eo%2C%5C%20z%5Eo%3D52%5Eo%7D)
Step-by-step explanation:
![\text{We know:}\\\text{The angles in each triangles add up to 180}^o.](https://tex.z-dn.net/?f=%5Ctext%7BWe%20know%3A%7D%5C%5C%5Ctext%7BThe%20angles%20in%20each%20triangles%20add%20up%20to%20180%7D%5Eo.)
![\text{In the triangle ABC:}\\\\85+28+15+z=180\\128+z=180\qquad\text{subtract 128 from both sides}\\128-128+z=180-128\\\boxed{z=52}](https://tex.z-dn.net/?f=%5Ctext%7BIn%20the%20triangle%20ABC%3A%7D%5C%5C%5C%5C85%2B28%2B15%2Bz%3D180%5C%5C128%2Bz%3D180%5Cqquad%5Ctext%7Bsubtract%20128%20from%20both%20sides%7D%5C%5C128-128%2Bz%3D180-128%5C%5C%5Cboxed%7Bz%3D52%7D)
![\\\\\text{In the triangle ADC}:\\\\85+28+x=180\\113+x=180\qquad\text{subtract 113 from both sides}\\113-113+x=180-113\\\boxed{x=67}](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5Ctext%7BIn%20the%20triangle%20ADC%7D%3A%5C%5C%5C%5C85%2B28%2Bx%3D180%5C%5C113%2Bx%3D180%5Cqquad%5Ctext%7Bsubtract%20113%20from%20both%20sides%7D%5C%5C113-113%2Bx%3D180-113%5C%5C%5Cboxed%7Bx%3D67%7D)
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Answer
i believe the answer would be 3^9
hope this helps and have a wonderful day :)
Answer:
a. 45 π
b. 12 π
c. 16 π
Step-by-step explanation:
a.
If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:
Radius: 3
Height: 5
Then the volume of the cylinder is:
V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π
b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:
Radius: 3
Height: 4
Then the volume of the cone is:
V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π
c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):
Then we will have:
Radius: 4
Height: 3
Then the volume of the cone is:
V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π