Answer:
The missing terms are 768, 192, 48.
Step-by-step explanation:
From the given geometric sequence
First term= a_1=3072
Fifth Term= a_5=12
The general form of a geometric sequence is:
a_n=ar^(n-1)
here a_nis the nth term, a is the first term and r is the common ratio.
We will use the general form for term 5 to calculate the value of r.
So the general form for term 5 will be
a_5=3072* r^(5-1)
Putting the value of a_5
12=3072* r^4
r^4= 12/3072
r^4= 1/256
r^4= 1/[(4)^4]
Solving for r
r= 1/4
Now
a_2= ar^(2-1)
a_2=3072*r
a_2=3072* 1/4
a_2=768
a_3= ar^(3-1)
a_3=3072*r^2
a_3=3072*(1/4)^2
a_3=3072* 1/16
a_3=192
a_4= ar^(4-1)
a_4=3072*r^3
a_4=3072*(1/4)^3
a_4=3072* 1/64
a_4=48
Answer:
- Sequon has more money after 4 weeks.
- It would take 5 weeks for their savings accounts to be equal.
Step-by-step explanation:
Daniel
Daniel starts with $50 and each week he adds $8. To find out the amount he has in any given week, the following formula would work:
= 50 + 8x
The x is the number of weeks and is multiplied by 8 because the amount of money he has increase by 8 every week.
After 4 weeks he would have:
= 50 + (8 * 4)
= 50 + 32
= $82
Saquon
Applying the same formula:
= 65 + 5x
After 4 weeks:
= 65 + (5 * 4)
= 65 + 20
= $85
Saquon has more money after 4 weeks.
<u>Number of weeks it would take for both of them to have the same amount.</u>
To find this out, equate both formulas and solve for x.
50 + 8x = 65 + 5x
8x - 5x = 65 - 50
3x = 15
x = 15/3
x = 5 weeks
<em>At 5 weeks they will both have:</em>
<em>50 + 8 * 5 = $90</em>
<em>65 + 5 * 5 = $90</em>
Answer: Each blueberry pie costs $14 and each blackberry pie costs $18.
Step-by-step explanation:
If X is the price of a blueberry pie and Y is the price of a blackberry pie we have that:
3*X + 12*Y = $258
4*X + 3*Y = $110
We have a system of equations, to solve it first we can isolate one of the variables in one of the equations, let's isolate X in the first equation.
3*X = $258 - 12*Y
X = $258/3 - (12*Y)/3 = 86 - 4*Y
now we can replace it in the second equation and get:
4*(86 - 4*Y) + 3*Y = 110
344 - 16Y + 3Y = 110
344 - 13Y = 110
13Y = 344 - 110 = 234
Y = 234/13 = 18
So each blackberry pie costs $18.
And we can replace it in the equation for X and get the value of X.
X = 86 - 4*Y = 86 - 4*18 = 14
So the price of a blueberry pie is $14.
Step-by-step explanation:
Please refer to the attachment
Answer:
c=2
Step-by-step explanation:
hope it helps :)
Simplifying
3 + -1(2c + -8) = 7
Reorder the terms:
3 + -1(-8 + 2c) = 7
3 + (-8 * -1 + 2c * -1) = 7
3 + (8 + -2c) = 7
Combine like terms: 3 + 8 = 11
11 + -2c = 7
Solving
11 + -2c = 7
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + -2c = 7 + -11
Combine like terms: 11 + -11 = 0
0 + -2c = 7 + -11
-2c = 7 + -11
Combine like terms: 7 + -11 = -4
-2c = -4
Divide each side by '-2'.
c = 2
Simplifying
c = 2