Answer:
3000 cm³
Step-by-step explanation:
Volume = Difference of Volumes of the two pyramids
Volume, V1, of the larger pyramid with tip at L:
Base area = area of EFGH = 10²
Height = ML = 15
V2 = ⅓×(10²)×15 = 4000
Volume, V2, of the smaller pyramid with tip at L:
Base area = area of = 10²
Height = OL = OM+ML = 15+15 = 30
V1 = ⅓×(10²)×30 = 1000
Volume = V1 - V2
= 4000-1000 = 3000 cm³
The side opposite the right angle.
Answer:
C. $538,021.66
Step-by-step explanation:
It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,
Amount withdrawn every quarter, P = $4567
Rate of interest, r = 
= 0.002525
Time period, n = 35 × 4 = 140
Now, as we know the formula for annuity as,
where P = installments, PV = present value, r = rate of interest and n = time period.
This gives, ![PV=\frac{P \times [1-(1+r)^{-n}]}{r}](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7BP%20%5Ctimes%20%5B1-%281%2Br%29%5E%7B-n%7D%5D%7D%7Br%7D)
i.e. ![PV=\frac{4567 \times [1-(1+0.002525)^{-140}]}{0.002525}](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7B4567%20%5Ctimes%20%5B1-%281%2B0.002525%29%5E%7B-140%7D%5D%7D%7B0.002525%7D)
i.e. ![PV=\frac{4567 \times [1-(1.002525)^{-140}]}{0.002525}](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7B4567%20%5Ctimes%20%5B1-%281.002525%29%5E%7B-140%7D%5D%7D%7B0.002525%7D)
i.e. ![PV=\frac{4567 \times [1-0.7021]}{0.002525}](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7B4567%20%5Ctimes%20%5B1-0.7021%5D%7D%7B0.002525%7D)
i.e. 
i.e. 
i.e. 
So, the closest answer to initial value of the account is $538,021.66
Hence, option C is correct.
Answer:
Step-by-step explanation:
(f + g)x translates into a more readable f(x) + g(x) so all you do is
f(x) + g(x) = 4x^2 + 1 + x^2 - 5
f(x) + g(x) = 5x^2 - 4
Answer:
3(4x - 1)(2x + 3)
Step-by-step explanation:
Rearrange the equation into standard form
Subtract 9 - 30x from both sides
24x² + 30x - 9 = 0 ← in standard form
Take out 3 as a common factor
3(8x² + 10x - 3) = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term
product = 8 × - 3 = - 24, sum = 10
The factors are - 2 and + 12
Use these factors to replace the x- term, that is
8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )
2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)
(4x - 1)(2x + 3)
24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form
