-(-z + 3) equals z - 3
5 = z - 3
z = 8
Answer: figures C and D.
Explanation:
The question is which two figures have the same volume. Hence, you have to calculate the volumes of each figure until you find the two with the same volume.
1) Figure A. It is a slant cone.
Dimensions:
- slant height, l = 6 cm
- height, h: 5 cm
- base area, b: 20 cm²
The volume of a slant cone is the same as the volume of a regular cone if the height and radius of both cones are the same.
Formula: V = (1/3)(base area)(height) = (1/3)b·h
Calculations:
- V = (1/3)×20cm²×5cm = 100/3 cm³
2. Figure B. It is a right cylinder
Dimensions:
- base area, b: 20 cm²
- height, h: 6 cm
Formula: V = (base area)(height) = b·h
Calculations:
- V = 20 cm²· 6cm = 120 cm³
3. Figure C. It is a slant cylinder.
Dimensions:
- base area, b: 20 cm²
- slant height, l: 6 cm
- height, h: 5 cm
The volume of a slant cylinder is the same as the volume of a regular cylinder if the height and radius of both cylinders are the same.
Formula: V = (base area)(height) = b·h
Calculations:
- V = 20cm² · 5cm = 100 cm³
4. Fiigure D. It is a rectangular pyramid.
Dimensions:
- length, l: 6cm
- base area, b: 20 cm²
- height, h: 5 cm
Formula: V = (base area) (height) = b·h
Calculations:
- V = 20 cm² · 5 cm = 100 cm³
→ Now, you have found the two figures with the same volume: figure C and figure D. ←
Y intercept is 24. ( y intercept is when x=0 )
Answer:
2
Step-by-step explanation:
Option A: 
is the value of 
Explanation:
It is given that the first term is 
The common difference is 
We need to determine the sum of 25 terms.
The sum of terms of an arithmetic series can be determined using the formula, ![S_n=\frac{n[2a_1+(n-1)d]}{2}](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%5B2a_1%2B%28n-1%29d%5D%7D%7B2%7D)
Substituting 
, and
Thus, we have,
![S_{25}=\frac{25[2(20)+(25-1)(-10)]}{2}](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%5B2%2820%29%2B%2825-1%29%28-10%29%5D%7D%7B2%7D)
Simplifying the values, we get,
![S_{25}=\frac{25[40+(24)(-10)]}{2}](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%5B40%2B%2824%29%28-10%29%5D%7D%7B2%7D)
![S_{25}=\frac{25[40-240]}{2}](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%5B40-240%5D%7D%7B2%7D)
Subtracting the terms within the bracket, we get,
![S_{25}=\frac{25[-200]}{2}](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%5B-200%5D%7D%7B2%7D)
Multiplying the terms in the numerator, we have,
Dividing, we get,
Thus, the sum of the 25 terms is
Therefore, Option A is the correct answer.
