Answer:
B.) 162 miles
Step-by-step explanation:
It really helps to draw a model when you are working with these. After having drawn a model, you can see that a right triangle was made, with the distance from Sameer's house to his cousin's being the hypotenuse. So, you can use the Pythagorean theorem:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Solve for c. Fill in values:
![135^2+90^2=c^2](https://tex.z-dn.net/?f=135%5E2%2B90%5E2%3Dc%5E2)
Evaluate exponents:
![18,225+8,100=c^2](https://tex.z-dn.net/?f=18%2C225%2B8%2C100%3Dc%5E2)
Simplify addition:
![26,355=c^2](https://tex.z-dn.net/?f=26%2C355%3Dc%5E2)
Find the square of both sides:
![\sqrt{26,355} =\sqrt{c^2}\\\\162.34=c](https://tex.z-dn.net/?f=%5Csqrt%7B26%2C355%7D%20%3D%5Csqrt%7Bc%5E2%7D%5C%5C%5C%5C162.34%3Dc)
Flip
![c=162.34](https://tex.z-dn.net/?f=c%3D162.34)
Round to the nearest mile
![c=162](https://tex.z-dn.net/?f=c%3D162)
Done.
Answer:
Total copies sold= 486,585
Step-by-step explanation:
Giving the following information:
Number of copies sold in the first month= 39,900
% of copies sold in the first month= 8.2%
<u>To calculate the total number of copies sold, we need to use the following formula:</u>
<u></u>
Total copies sold= Number of copies sold in the first month/% of copies sold in the first month
Total copies sold= 39,900 / 0.082
Total copies sold= 486,585
2/3 + n = 2n + 3 <== ur equation
2/3 - 3 = 2n - n
2/3 - 9/3 = n
-7/3 = n <== ur solution
or
2/3 + n = 2n + 3...multiply everything by common denominator of 3
2 + 3n = 6n + 9
2 - 9 = 6n - 3n
-7 = 3n
-7/3 = n
Answer:
Lamar wrapped 7 gifts
Step-by-step explanation:
Lamar wrapped = g
then Nicole wrapped = 4g
then 4 g = 28
g =
= 7
∵Therefore, Lamar wrapped 7 gifts
Answer:
![l = 28](https://tex.z-dn.net/?f=l%20%3D%2028)
Step-by-step explanation:
Given
![S = \sum (2k - 3); k = 4\ to\ l](https://tex.z-dn.net/?f=S%20%3D%20%5Csum%20%282k%20-%203%29%3B%20k%20%3D%204%5C%20to%5C%20l)
Required
What is l when S = 725
This can be solved using Sum of n terms of an AP;
![S_n = \frac{n}{2}(T_1 + T_n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28T_1%20%2B%20T_n%29)
Where
![S_n = 725](https://tex.z-dn.net/?f=S_n%20%3D%20725)
![T_1 = first\ term](https://tex.z-dn.net/?f=T_1%20%3D%20first%5C%20term)
To get T1; we substitute 4 for k in 2k - 3
![T_1 = 2 * 4 - 3](https://tex.z-dn.net/?f=T_1%20%3D%202%20%2A%204%20-%203)
![T_1 = 8 - 3](https://tex.z-dn.net/?f=T_1%20%3D%208%20-%203)
![T_1 = 5](https://tex.z-dn.net/?f=T_1%20%3D%205)
![T_n = last\ term](https://tex.z-dn.net/?f=T_n%20%3D%20last%5C%20term)
To get Tn; we substitute l for k in 2k - 3
![T_n = 2 * l - 3](https://tex.z-dn.net/?f=T_n%20%3D%202%20%2A%20l%20-%203)
![T_n = 2l - 3](https://tex.z-dn.net/?f=T_n%20%3D%202l%20-%203)
n = the number of terms;
Since k = 4 to l, then
![n = l - 4 +1](https://tex.z-dn.net/?f=n%20%3D%20l%20-%204%20%2B1)
![n = l - 3](https://tex.z-dn.net/?f=n%20%3D%20l%20-%203)
Substitute these values in ![S_n = \frac{n}{2}(T_1 + T_n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28T_1%20%2B%20T_n%29)
![725 = \frac{l-3}{2}(5 + 2l - 3)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%285%20%2B%202l%20-%203%29)
Collect Like Terms
![725 = \frac{l-3}{2}(2l + 5- 3)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%282l%20%2B%205-%203%29)
![725 = \frac{l-3}{2}(2l + 2)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%282l%20%2B%202%29)
Open the bracket
![725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%20%2A%202l%20%2B%20%5Cfrac%7Bl-3%7D%7B2%7D%20%2A%202)
![725 = (l-3) * l + (l-3)](https://tex.z-dn.net/?f=725%20%3D%20%28l-3%29%20%2A%20l%20%2B%20%28l-3%29)
![725 = l^2-3l + l-3](https://tex.z-dn.net/?f=725%20%3D%20l%5E2-3l%20%2B%20l-3)
![725 = l^2-2l -3](https://tex.z-dn.net/?f=725%20%3D%20l%5E2-2l%20-3)
Subtract 725 from both sides
![725 - 725 = l^2-2l -3 - 725](https://tex.z-dn.net/?f=725%20-%20725%20%3D%20l%5E2-2l%20-3%20-%20725)
![l^2-2l -3 - 725 = 0](https://tex.z-dn.net/?f=l%5E2-2l%20-3%20-%20725%20%3D%200)
![l^2-2l - 728 = 0](https://tex.z-dn.net/?f=l%5E2-2l%20-%20728%20%3D%200)
![l^2 + 26l - 28l - 728 = 0](https://tex.z-dn.net/?f=l%5E2%20%2B%2026l%20-%2028l%20-%20728%20%3D%200)
![l(l + 26) - 28(l + 26) = 0](https://tex.z-dn.net/?f=l%28l%20%2B%2026%29%20-%2028%28l%20%2B%2026%29%20%3D%200)
![(l - 28)(l + 26) = 0](https://tex.z-dn.net/?f=%28l%20-%2028%29%28l%20%2B%2026%29%20%3D%200)
or ![l + 26 = 0](https://tex.z-dn.net/?f=l%20%2B%2026%20%3D%200)
or ![l = -26](https://tex.z-dn.net/?f=l%20%3D%20-26)
But l must be positive;
Hence, ![l = 28](https://tex.z-dn.net/?f=l%20%3D%2028)