Answer:
2
Step-by-step explanation:
We can find the slope between two points by using
m= (y2-y1)/(x2-x1)
= (3 - -3)/(0 - -3)
= (3+3)/(0+3)
= 6/3
=2
You can use 27 $10 bills which gets your at a total of $270 then you can use 1 $5 bill so now you're at $275 then you can use 4 $1 bills that gets you at your total of $279. The least number of bills you can use is 32.
The first term (a) is - 18
You add 5 to get to the next term. Or you can solve it by taking any 2 consecutive terms and find their difference.
Formula
d = t4- t3
Givens
t4 = - 3
t3 = - 8
Solution 1
d = t4 - t3 Substitute
d = -3 - ( - 8) Remove the brackets
d = -3 + 8 Combine
d = 5 Difference
Remark
Find the general formula
tn = - a + (n - 1)d Substitute
So term 20 = Example
t20 = -18 + (20 - 1)*5 Combine the inside of the brackets. Remove the brackets
t20 = - 18 + 19*5 Combine 19 and 5
t20 = -18 + 95 "Subtract"
t20 = 77 Answer
Answer:
The common ratio of a geometric series is \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170
The first term is 128
Step-by-step explanation:
The common ratio of the geometric series is given as:
![r = \frac{1}{4}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D)
The sum of the first 4 term is 170.
The sum of first n terms of a geometric sequence is given b;
![s_n=\frac{a_1(1-r^n)}{1-r}](https://tex.z-dn.net/?f=s_n%3D%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D)
common ratio, n=4 and equate to 170.
![\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170](https://tex.z-dn.net/?f=%5Cfrac%7Ba_1%281-%28%20%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%29%7D%7B1-%20%5Cfrac%7B1%7D%7B4%7D%20%7D%20%3D%20170)
![\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128](https://tex.z-dn.net/?f=%5Cfrac%7Ba_1%281-%20%5Cfrac%7B1%7D%7B256%7D%20%29%7D%7B%20%5Cfrac%7B3%7D%7B4%7D%20%7D%20%3D%20170%5C%5C%5C%5C%20%5Cfrac%7B255%7D%7B256%7D%20a_1%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20%20%5Ctimes%20170%5C%5C%5C%5C%5Cfrac%7B255%7D%7B256%7D%20a_1%20%3D%20%5Cfrac%7B255%7D%7B2%7D%20%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B256%7D%20a_1%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%5C%5C%5C%5C%20a_1%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%20%5Ctimes%20256%5C%5C%5C%5Ca_1%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%20%5Ctimes%20256%20%5C%5C%5C%5C%3D%20128)
You will multiply 2 1/4 x 1 1/4 to determine how many pounds of apples Alex buys.
2 1/4 x 1 1/4
9/4 x 5/4 = 45/4 or 11 1/4