Answer:
5 units
Step-by-step explanation:
Distance between 2 points
![= \sqrt{(y1 - y2)^{2} + (x1 - x2)^{2} } \\ = \sqrt{(5 - 1)^{2} + ( - 6 + 3)^{2} } \\ = \sqrt{ {4}^{2} + ( - 3)^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} \\ = 5 \: units](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B%28y1%20-%20y2%29%5E%7B2%7D%20%20%2B%20%28x1%20-%20x2%29%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%20%5Csqrt%7B%285%20-%201%29%5E%7B2%7D%20%2B%20%28%20-%206%20%2B%203%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%7B4%7D%5E%7B2%7D%20%2B%20%28%20-%203%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B16%20%2B%209%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B25%7D%20%20%5C%5C%20%20%3D%205%20%5C%3A%20units)
Answer:
n+3 = 15 ; n = 12
3n -6 = 12; n=6
Step-by-step explanation:
more than means it comes after
a number
n
3 more than
n+3
is 15
n+3 = 15
Subtract 3 from each side
n+3-3 = 15-3
n = 12
Subtract from comes after
three times a number
3n
six subtracted from
3n -6
is 12 means equal to
3n -6 = 12
To solve add 6 to each side
3n -6+6 =12+6
3n = 18
Divide by 3
3n/3 =18/3
n =6
Answer:
12
Step-by-step explanation:
I think you have to use the product rule for counting- which is where you multiply the two numbers. I'm not sure if this is right but I hope I helped
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
![a_n = ar^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20ar%5E%7Bn-1%7D)
1) ![a_n = 50000(1.05)^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%2050000%281.05%29%5E%7Bn-1%7D)
2) In order to find salary in 5 years we need to plug n=5, we get
![a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4](https://tex.z-dn.net/?f=a_5%20%3D%2050000%281.05%29%5E%7B5-1%7D%3D%2050000%281.05%29%5E4)
= 50000(1.21550625)
<h3>=$60775.3125.</h3>
3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
![S_n = \frac{a(1-r^n}{1-r}](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Ba%281-r%5En%7D%7B1-r%7D)
Plugging n=10, a = 50000 and r= 1.05.
![S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}](https://tex.z-dn.net/?f=S_10%20%3D%20%5Cfrac%7B50000%281-%281.05%29%5E%7B10%7D%7D%7B1-1.05%7D)
![S_10 = \frac{50000(0.050)^{10}}{0.05}](https://tex.z-dn.net/?f=S_10%20%3D%20%5Cfrac%7B50000%280.050%29%5E%7B10%7D%7D%7B0.05%7D)
= 628894.62678.
<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>