Answer: See below
Step-by-step explanation:
a) 6(3x+4y-8)
Use the distributive property:
6*3x + 6*4y - 6*8
18x + 24y - 48
<u>So D is the correct answer</u>
b) Factor out 4 because it can fit into 12 - 3 times - and 4 - one time.
12+4x
= 4(3+x)
<u>So D is the correct answer</u>
c) When you expand both <u>C and D</u> and simplify, you get 16x+36 as solution
d) 14x+2y+10z
Factor out 2 because it can fit into 14, 7 times. 2, one time. And 10, 5 times
14x+2y+10z
= 2(7x+y+5z)
<u>So D is the correct answer again ;)</u>
96/100, Is .96 in fraction form.
I hope this helps
Answer:
sometimes
Step-by-step explanation:
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>