Answer:
The missing dimension of the prism is (x-4)
Step-by-step explanation:
Here, we want to find the missing dimensions of the prism
To get the volume, we are to multiply three dimensions since we are talking about volume
Mathematically, to find the third dimension, we need to divide the original polynomial by the product of the two other dimensions
The product of the two other dimensions is;
(x-1)(x-9) = x^2-9x-x + 9
= x^2-10x+ 9
So we divide;
(x^3-14x^2+49x-36)/(x^2-10x+ 9)
We can use long division to get this
using long division, the answer here is x-4
in sale normal prices are reduced by 10% nathaile bought a pair of shoes in the sale for $54 10% of 54 is 59.4
Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Answer:
25.
Step-by-step explanation:
I am assuming you only mean the small triangles, not the composite ones.
The second triangle set has 3 triangles on bottom row and 1 on the top - total 4.
The 3rd triangle set has 5 triangles on the bottom , 3 on the next up and 1 on the top - total 9
Following the pattern 4th set will have the number of triaNGLES
7 + 5 + 3 + 1 = 16.
So the 5th will have 9 + 7 + 5 + 3 +1 = 25 triangles.
