Answer: BX = 7
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Explanation:
For any rectangle, the diagonals are the same length and they cut each other in half (aka bisect each other).
This means diagonal BD = AC = 14 and BX = BD/2 = 14/2 = 7. The value of AB is never used.
The formula for compound interest is:
![\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20%5C%5C%20%5Ctext%7Bwhere%2C%7D%20%5C%5C%20A%3D%5Ctext%7B%20Final%20amount%7D%20%5C%5C%20r%3D%5Ctext%7B%20Interest%20rate%7D%20%5C%5C%20n%3D%5Ctext%7B%20Number%20of%20times%20interest%20applied%20per%20period%7D%20%5C%5C%20t%3D%5Ctext%7B%20Number%20of%20time%20period%20elapsed%7D%20%5C%5C%20P%3D%5Ctext%7B%20Intial%20principal%20balance%7D%20%5Cend%7Bgathered%7D)
Given data:
![\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%3D%5Ctext%7B%20%5C%241500%7D%20%5C%5C%20r%3D6%5Ctext%7B%20%5C%25%7D%3D0.06%20%5C%5C%20n%3D4%5Ctext%7B%20times%20%28compounded%20quarterly%29%7D%20%5Cend%7Bgathered%7D)
a. After ten years, that is t = 10 years, the amount in the account will be
![\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D1500%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B4%5Ctimes10%7D%20%5C%5C%20A%3D%5Ctext%7B%20%7D1500%281%2B0.015%29%5E%7B40%7D%20%5C%5C%20A%3D%5Ctext%7B%20%7D1500%281.015%29%5E%7B40%7D%20%5C%5C%20A%3D%5Ctext%7B%20%5C%242721.03%7D%20%5Cend%7Bgathered%7D)
b. After twenty years, that is t = 20 years, the amount in the account will be:
![\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D1500%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B4%5Ctimes20%7D%20%5C%5C%20A%3D1500%281.015%29%5E%7B4%5Ctimes20%7D%20%5C%5C%20A%3D1500%281.015%29%5E%7B80%7D%20%5C%5C%20A%3D%5Ctext%7B%20%5C%24%7D4935.99%20%5Cend%7Bgathered%7D)
c. The time it takes for Harry's initial account value to double will be:
![\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D2%5Ctext%7B%20x%20initial%20value%20%3D%202%20%7D%5Ctimes%5Ctext%7B%20%5C%241500%20%3D%20%5C%243000%7D%20%5C%5C%203000%3D1500%281.015%29%5E%7B4t%7D%20%5C%5C%20%281.015%29%5E%7B4t%7D%3D%5Cfrac%7B3000%7D%7B1500%7D%20%5C%5C%20%281.015%29%5E%7B4t%7D%3D2%20%5C%5C%20%5Ctext%7B%20Find%20the%20logarithm%20of%20both%20sides%7D%20%5C%5C%20%5Cln%20%281.015%29%5E%7B4t%7D%3D%5Cln%202%20%5C%5C%204t%3D%5Cfrac%7B%5Cln%202%7D%7B%5Cln%201.015%7D%20%5C%5C%204t%3D46.56%20%5C%5C%20t%3D%5Cfrac%7B46.56%7D%7B4%7D%3D11.64%20%5Cend%7Bgathered%7D)
Therefore, the time it takes Harry's initial account to double is approximately 11 years
9.4/10 is the simplest form
The number of days it will take to consume the given power = 4.5 days
<h3>Calculation of energy consumption</h3>
The amount of power consumed per day = 1440watt-hours
Therefore X days = 6480 watt-hours?
Make X the subject formula;
X = 1 × 6480/1440
X = 4.5 days
Therefore, The number of days it will take to consume the given power = 4.5 days.
Learn more about energy consumption here:
brainly.com/question/2900615
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Answer:
the slope is -2/5
Step-by-step explanation:
you do y2-y1 on top of the division sign and x2-x1 on the bottom.